Merge pull request #45 from 0xisk/main

refactor: minor enhancements on the lib package

.cargo/config

@@ -1,5 +1,5 @@
 [target.wasm32-unknown-unknown]
-rustflags = ["-C", "target-feature=+atomics,+bulk-memory,+mutable-globals", "-C", "link-arg=--max-memory=4294967296"]
+rustflags = ["-C", "link-arg=--max-memory=4294967296"]
 
 [unstable]
 build-std = ["panic_abort", "std"]

.github/workflows/publish.yaml

@@ -0,0 +1,42 @@
+name: Publish Package to npmjs
+on:
+  release:
+    types: [published]
+  workflow_dispatch:
+
+jobs:
+  publish:
+    runs-on: macos-latest
+    steps:
+      - uses: actions/checkout@v3
+        with:
+          ref: ${{ github.ref_name }}
+      # Setup Node.js
+      - uses: actions/setup-node@v3
+        with:
+          node-version: 18
+          registry-url: "https://registry.npmjs.org"
+      # Setup Rust
+      - uses: actions-rs/toolchain@v1
+        with:
+          toolchain: nightly-2022-10-31
+      - run: rustup component add rust-src
+      - run: rustup target add x86_64-apple-darwin
+      # Install circom-secq
+      - uses: GuillaumeFalourd/clone-github-repo-action@v2
+        with:
+          owner: "DanTehrani"
+          repository: "circom-secq"
+      - run: cd circom-secq && cargo build --release && cargo install --path circom
+      # Install wasm-pack
+      - uses: jetli/wasm-pack-action@v0.4.0
+        with:
+          version: "v0.10.3"
+      - run: cargo test --release
+      - run: yarn
+      - run: yarn build
+      - run: yarn test
+      - run: npm publish
+        working-directory: ./packages/lib
+        env:
+          NODE_AUTH_TOKEN: ${{ secrets.NPM_TOKEN }}

.gitignore

@@ -2,9 +2,6 @@
 # will have compiled files and executables
 /target/
 
-# Remove Cargo.lock from gitignore if creating an executable, leave it for libraries
-# More information here https://doc.rust-lang.org/cargo/guide/cargo-toml-vs-cargo-lock.html
-Cargo.lock
 
 # These are backup files generated by rustfmt
 **/*.rs.bk
@@ -26,6 +23,7 @@ circom_witness.wtns
 *.ptau
 
 build/
+dist/
 
 *.r1cs
 *.sym
@@ -36,7 +34,7 @@ packages/prover/test_circuit/test_circuit_js/
 packages/prover/test_circuit/*.json 
 
 
-wasm_bytes.ts
+wasmBytes.ts
 **/sage/*.sage.py
 packages/lib/src/circuits/
 

Cargo.toml

@@ -3,4 +3,6 @@ members = [
     "packages/spartan_wasm",
     "packages/secq256k1",
     "packages/poseidon",
+    "packages/Spartan-secq",
+    "packages/circuit_reader",
 ]

README.md

@@ -1,6 +1,24 @@
 # Spartan-ecdsa
 
-Spartan-ecdsa (which to our knowledge) is the fastest open-source method to verify ECDSA (secp256k1) signatures in zero-knowledge. It can prove ECDSA group membership 10 times faster than [efficient-zk-ecdsa](https://github.com/personaelabs/efficient-zk-ecdsa), our previous implementation of fast ECDSA signature proving. Please refer to our blog post for further information.
+Spartan-ecdsa (which to our knowledge) is the fastest open-source method to verify ECDSA (secp256k1) signatures in zero-knowledge. It can prove ECDSA group membership 10 times faster than [efficient-zk-ecdsa](https://github.com/personaelabs/efficient-zk-ecdsa), our previous implementation of fast ECDSA signature proving. Please refer to [this blog post](https://personaelabs.org/posts/spartan-ecdsa/) for further information.
+
+## Constraint breakdown
+
+spartan-ecdsa achieves the phenomenal result of **hashing becoming the bottleneck instead of ECC operations** for the `pubkey_membership.circom` circuit. In particular, there are **3,039** constraints for efficient ECDSA signature verification, and **5,037** constraints for a depth 20 merkle tree membership check + 1 Poseidon hash of the ECDSA public key. The drop from the original 1.5 million constraints of [circom-ecdsa](https://github.com/0xPARC/circom-ecdsa) comes primarily from doing right-field arithmetic with secq and avoiding SNARK-unfriendly range checks and big integer math.
+
+We also use [efficient ECDSA signatures](https://personaelabs.org/posts/efficient-ecdsa-1/) instead of standard ECDSA siagnatures to save an additional **14,505** constraints. To review, the standard ECDSA signature consists of $(r, s)$ for a public key $Q_a$ and message $m$, where $r$ is the x-coordinate of a random elliptic curve point $R$. Standard ECDSA signature verification checks if
+
+```math
+R == m s ^{-1} * G + r s ^{-1} * Q_a
+```
+
+where $G$ is the generator point of the curve. The efficient ECDSA signature consists of $s$ as well as $T = r^{-1} * R$ and $U = -r^{-1} * m * G$, which can both be computed outside of the SNARK without breaking correctness. Efficient ECDSA signature verification checks if
+
+```math
+s * T + U == Q_a
+```
+
+Thus, verifying a standard ECDSA signature instead of the efficient ECDSA signature requires (1) computing $s^{-1}$, $r \* s^{-1}$, $m \* s^{-1}$, and (2) an extra ECC scalar multiply to compute $m s ^{-1} * G$. The former computations happen in the scalar field of secp, which is unequal to the scalar field of secq, and so we incur 11,494 additional constraints for the wrong-field math. The latter can use the `Secp256k1Mul` subroutine and incurs 3,011 additional constraints.
 
 ## Benchmarks
 
@@ -35,7 +53,17 @@ yarn add @personaelabs/spartan-ecdsa
 
 v18 or later
 
-### Install dependencies & Build all packages
+### Build
+1. Install Circom with secq256k1 support
+
+```
+git clone https://github.com/DanTehrani/circom-secq
+cd circom-secq && cargo build --release && cargo install --path circom
+```
+
+2. Install [wasm-pack](https://rustwasm.github.io/wasm-pack/installer/)
+
+4. Install dependencies & Build all packages
 
 ```jsx
 yarn && yarn build

package.json

@@ -6,7 +6,8 @@
   "repository": "https://github.com/DanTehrani/spartan-wasm.git",
   "author": "Daniel Tehrani <contact@dantehrani.com>",
   "scripts": {
-    "build": "sh ./scripts/build.sh && lerna run build"
+    "build": "sh ./scripts/build.sh && lerna run build",
+    "test": "sh ./scripts/test.sh"
   },
   "devDependencies": {
     "@types/jest": "^29.2.4",
@@ -15,8 +16,7 @@
     "eslint-plugin-react": "7.32.1",
     "eslint-plugin-react-hooks": "4.6.0",
     "eslint-plugin-security": "1.7.0",
-    "lerna": "^6.4.0",
-    "snarkjs": "^0.5.0"
+    "lerna": "^6.4.0"
   },
   "workspaces": [
     "packages/lib",

packages/Spartan-secq/CODE_OF_CONDUCT.md

@@ -0,0 +1,9 @@
+# Microsoft Open Source Code of Conduct
+
+This project has adopted the [Microsoft Open Source Code of Conduct](https://opensource.microsoft.com/codeofconduct/).
+
+Resources:
+
+- [Microsoft Open Source Code of Conduct](https://opensource.microsoft.com/codeofconduct/)
+- [Microsoft Code of Conduct FAQ](https://opensource.microsoft.com/codeofconduct/faq/)
+- Contact [opencode@microsoft.com](mailto:opencode@microsoft.com) with questions or concerns

packages/Spartan-secq/CONTRIBUTING.md

@@ -0,0 +1,12 @@
+This project welcomes contributions and suggestions. Most contributions require you to
+agree to a Contributor License Agreement (CLA) declaring that you have the right to,
+and actually do, grant us the rights to use your contribution. For details, visit
+https://cla.microsoft.com.
+
+When you submit a pull request, a CLA-bot will automatically determine whether you need
+to provide a CLA and decorate the PR appropriately (e.g., label, comment). Simply follow the
+instructions provided by the bot. You will only need to do this once across all repositories using our CLA.
+
+This project has adopted the [Microsoft Open Source Code of Conduct](https://opensource.microsoft.com/codeofconduct/).
+For more information see the [Code of Conduct FAQ](https://opensource.microsoft.com/codeofconduct/faq/)
+or contact [opencode@microsoft.com](mailto:opencode@microsoft.com) with any additional questions or comments.

packages/Spartan-secq/Cargo.toml

@@ -0,0 +1,57 @@
+[package]
+name = "spartan"
+version = "0.7.1"
+authors = ["Srinath Setty <srinath@microsoft.com>"]
+edition = "2021"
+description = "High-speed zkSNARKs without trusted setup"
+documentation = "https://docs.rs/spartan/"
+readme = "README.md"
+repository = "https://github.com/microsoft/Spartan"
+license-file = "LICENSE"
+keywords = ["zkSNARKs", "cryptography", "proofs"]
+
+[dependencies]
+num-bigint-dig = "^0.7"
+secq256k1 = { path = "../secq256k1" }
+merlin = "3.0.0"
+rand = "0.7.3"
+digest = "0.8.1"
+sha3 = "0.8.2"
+byteorder = "1.3.4"
+rayon = { version = "1.3.0", optional = true }
+serde = { version = "1.0.106", features = ["derive"] }
+bincode = "1.2.1"
+subtle = { version = "2.4", default-features = false }
+rand_core = { version = "0.6", default-features = false }
+zeroize = { version = "1", default-features = false }
+itertools = "0.10.0"
+colored = "2.0.0"
+flate2 = "1.0.14"
+thiserror = "1.0"
+num-traits = "0.2.15"
+hex-literal = { version = "0.3" }
+multiexp = "0.2.2"
+
+[dev-dependencies]
+criterion = "0.3.1"
+
+[lib]
+name = "libspartan"
+path = "src/lib.rs"
+crate-type = ["cdylib", "rlib"]
+
+[[bin]]
+name = "snark"
+path = "profiler/snark.rs"
+
+[[bin]]
+name = "nizk"
+path = "profiler/nizk.rs"
+
+[[bench]]
+name = "snark"
+harness = false
+
+[[bench]]
+name = "nizk"
+harness = false

packages/Spartan-secq/LICENSE

@@ -0,0 +1,21 @@
+    MIT License
+
+    Copyright (c) Microsoft Corporation.
+
+    Permission is hereby granted, free of charge, to any person obtaining a copy
+    of this software and associated documentation files (the "Software"), to deal
+    in the Software without restriction, including without limitation the rights
+    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+    copies of the Software, and to permit persons to whom the Software is
+    furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included in all
+    copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+    SOFTWARE

packages/Spartan-secq/README.md

@@ -0,0 +1,10 @@
+## Fork of [Spartan](https://github.com/microsoft/Spartan)
+_This fork is still under development._
+
+Modify Spartan to operate over the **base field** of secp256k1.
+
+### Changes from the original Spartan
+- Use the secq256k1 crate instead of curve25519-dalek
+- Modify values in scalar.rs (originally ristretto255.rs) 
+
+Please refer to [spartan-ecdsa](https://github.com/personaelabs/spartan-ecdsa) for development status.

packages/Spartan-secq/SECURITY.md

@@ -0,0 +1,41 @@
+<!-- BEGIN MICROSOFT SECURITY.MD V0.0.3 BLOCK -->
+
+## Security
+
+Microsoft takes the security of our software products and services seriously, which includes all source code repositories managed through our GitHub organizations, which include [Microsoft](https://github.com/Microsoft), [Azure](https://github.com/Azure), [DotNet](https://github.com/dotnet), [AspNet](https://github.com/aspnet), [Xamarin](https://github.com/xamarin), and [our GitHub organizations](https://opensource.microsoft.com/).
+
+If you believe you have found a security vulnerability in any Microsoft-owned repository that meets Microsoft's [Microsoft's definition of a security vulnerability](https://docs.microsoft.com/en-us/previous-versions/tn-archive/cc751383(v=technet.10)) of a security vulnerability, please report it to us as described below.
+
+## Reporting Security Issues
+
+**Please do not report security vulnerabilities through public GitHub issues.**
+
+Instead, please report them to the Microsoft Security Response Center (MSRC) at [https://msrc.microsoft.com/create-report](https://msrc.microsoft.com/create-report).
+
+If you prefer to submit without logging in, send email to [secure@microsoft.com](mailto:secure@microsoft.com).  If possible, encrypt your message with our PGP key; please download it from the the [Microsoft Security Response Center PGP Key page](https://www.microsoft.com/en-us/msrc/pgp-key-msrc).
+
+You should receive a response within 24 hours. If for some reason you do not, please follow up via email to ensure we received your original message. Additional information can be found at [microsoft.com/msrc](https://www.microsoft.com/msrc).
+
+Please include the requested information listed below (as much as you can provide) to help us better understand the nature and scope of the possible issue:
+
+  * Type of issue (e.g. buffer overflow, SQL injection, cross-site scripting, etc.)
+  * Full paths of source file(s) related to the manifestation of the issue
+  * The location of the affected source code (tag/branch/commit or direct URL)
+  * Any special configuration required to reproduce the issue
+  * Step-by-step instructions to reproduce the issue
+  * Proof-of-concept or exploit code (if possible)
+  * Impact of the issue, including how an attacker might exploit the issue
+
+This information will help us triage your report more quickly.
+
+If you are reporting for a bug bounty, more complete reports can contribute to a higher bounty award. Please visit our [Microsoft Bug Bounty Program](https://microsoft.com/msrc/bounty) page for more details about our active programs.
+
+## Preferred Languages
+
+We prefer all communications to be in English.
+
+## Policy
+
+Microsoft follows the principle of [Coordinated Vulnerability Disclosure](https://www.microsoft.com/en-us/msrc/cvd).
+
+<!-- END MICROSOFT SECURITY.MD BLOCK -->

packages/Spartan-secq/benches/nizk.rs

@@ -0,0 +1,92 @@
+#![allow(clippy::assertions_on_result_states)]
+extern crate byteorder;
+extern crate core;
+extern crate criterion;
+extern crate digest;
+extern crate libspartan;
+extern crate merlin;
+extern crate rand;
+extern crate sha3;
+
+use libspartan::{Instance, NIZKGens, NIZK};
+use merlin::Transcript;
+
+use criterion::*;
+
+fn nizk_prove_benchmark(c: &mut Criterion) {
+  for &s in [10, 12, 16].iter() {
+    let plot_config = PlotConfiguration::default().summary_scale(AxisScale::Logarithmic);
+    let mut group = c.benchmark_group("NIZK_prove_benchmark");
+    group.plot_config(plot_config);
+
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
+
+    let name = format!("NIZK_prove_{}", num_vars);
+    group.bench_function(&name, move |b| {
+      b.iter(|| {
+        let mut prover_transcript = Transcript::new(b"example");
+        NIZK::prove(
+          black_box(&inst),
+          black_box(vars.clone()),
+          black_box(&inputs),
+          black_box(&gens),
+          black_box(&mut prover_transcript),
+        );
+      });
+    });
+    group.finish();
+  }
+}
+
+fn nizk_verify_benchmark(c: &mut Criterion) {
+  for &s in [10, 12, 16].iter() {
+    let plot_config = PlotConfiguration::default().summary_scale(AxisScale::Logarithmic);
+    let mut group = c.benchmark_group("NIZK_verify_benchmark");
+    group.plot_config(plot_config);
+
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
+
+    // produce a proof of satisfiability
+    let mut prover_transcript = Transcript::new(b"example");
+    let proof = NIZK::prove(&inst, vars, &inputs, &gens, &mut prover_transcript);
+
+    let name = format!("NIZK_verify_{}", num_cons);
+    group.bench_function(&name, move |b| {
+      b.iter(|| {
+        let mut verifier_transcript = Transcript::new(b"example");
+        assert!(proof
+          .verify(
+            black_box(&inst),
+            black_box(&inputs),
+            black_box(&mut verifier_transcript),
+            black_box(&gens)
+          )
+          .is_ok());
+      });
+    });
+    group.finish();
+  }
+}
+
+fn set_duration() -> Criterion {
+  Criterion::default().sample_size(10)
+}
+
+criterion_group! {
+name = benches_nizk;
+config = set_duration();
+targets = nizk_prove_benchmark, nizk_verify_benchmark
+}
+
+criterion_main!(benches_nizk);

packages/Spartan-secq/benches/snark.rs

@@ -0,0 +1,131 @@
+#![allow(clippy::assertions_on_result_states)]
+extern crate libspartan;
+extern crate merlin;
+
+use libspartan::{Instance, SNARKGens, SNARK};
+use merlin::Transcript;
+
+use criterion::*;
+
+fn snark_encode_benchmark(c: &mut Criterion) {
+  for &s in [10, 12, 16].iter() {
+    let plot_config = PlotConfiguration::default().summary_scale(AxisScale::Logarithmic);
+    let mut group = c.benchmark_group("SNARK_encode_benchmark");
+    group.plot_config(plot_config);
+
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+    let (inst, _vars, _inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // produce public parameters
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_cons);
+
+    // produce a commitment to R1CS instance
+    let name = format!("SNARK_encode_{}", num_cons);
+    group.bench_function(&name, move |b| {
+      b.iter(|| {
+        SNARK::encode(black_box(&inst), black_box(&gens));
+      });
+    });
+    group.finish();
+  }
+}
+
+fn snark_prove_benchmark(c: &mut Criterion) {
+  for &s in [10, 12, 16].iter() {
+    let plot_config = PlotConfiguration::default().summary_scale(AxisScale::Logarithmic);
+    let mut group = c.benchmark_group("SNARK_prove_benchmark");
+    group.plot_config(plot_config);
+
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // produce public parameters
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_cons);
+
+    // produce a commitment to R1CS instance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a proof
+    let name = format!("SNARK_prove_{}", num_cons);
+    group.bench_function(&name, move |b| {
+      b.iter(|| {
+        let mut prover_transcript = Transcript::new(b"example");
+        SNARK::prove(
+          black_box(&inst),
+          black_box(&comm),
+          black_box(&decomm),
+          black_box(vars.clone()),
+          black_box(&inputs),
+          black_box(&gens),
+          black_box(&mut prover_transcript),
+        );
+      });
+    });
+    group.finish();
+  }
+}
+
+fn snark_verify_benchmark(c: &mut Criterion) {
+  for &s in [10, 12, 16].iter() {
+    let plot_config = PlotConfiguration::default().summary_scale(AxisScale::Logarithmic);
+    let mut group = c.benchmark_group("SNARK_verify_benchmark");
+    group.plot_config(plot_config);
+
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // produce public parameters
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_cons);
+
+    // produce a commitment to R1CS instance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a proof of satisfiability
+    let mut prover_transcript = Transcript::new(b"example");
+    let proof = SNARK::prove(
+      &inst,
+      &comm,
+      &decomm,
+      vars,
+      &inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the proof
+    let name = format!("SNARK_verify_{}", num_cons);
+    group.bench_function(&name, move |b| {
+      b.iter(|| {
+        let mut verifier_transcript = Transcript::new(b"example");
+        assert!(proof
+          .verify(
+            black_box(&comm),
+            black_box(&inputs),
+            black_box(&mut verifier_transcript),
+            black_box(&gens)
+          )
+          .is_ok());
+      });
+    });
+    group.finish();
+  }
+}
+
+fn set_duration() -> Criterion {
+  Criterion::default().sample_size(10)
+}
+
+criterion_group! {
+name = benches_snark;
+config = set_duration();
+targets = snark_encode_benchmark, snark_prove_benchmark, snark_verify_benchmark
+}
+
+criterion_main!(benches_snark);

packages/Spartan-secq/examples/cubic.rs

@@ -0,0 +1,147 @@
+//! Demonstrates how to produces a proof for canonical cubic equation: `x^3 + x + 5 = y`.
+//! The example is described in detail [here].
+//!
+//! The R1CS for this problem consists of the following 4 constraints:
+//! `Z0 * Z0 - Z1 = 0`
+//! `Z1 * Z0 - Z2 = 0`
+//! `(Z2 + Z0) * 1 - Z3 = 0`
+//! `(Z3 + 5) * 1 - I0 = 0`
+//!
+//! [here]: https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649
+#![allow(clippy::assertions_on_result_states)]
+use libspartan::{InputsAssignment, Instance, SNARKGens, VarsAssignment, SNARK};
+use merlin::Transcript;
+use rand_core::OsRng;
+use secq256k1::elliptic_curve::Field;
+use secq256k1::Scalar;
+
+#[allow(non_snake_case)]
+fn produce_r1cs() -> (
+  usize,
+  usize,
+  usize,
+  usize,
+  Instance,
+  VarsAssignment,
+  InputsAssignment,
+) {
+  // parameters of the R1CS instance
+  let num_cons = 4;
+  let num_vars = 4;
+  let num_inputs = 1;
+  let num_non_zero_entries = 8;
+
+  // We will encode the above constraints into three matrices, where
+  // the coefficients in the matrix are in the little-endian byte order
+  let mut A: Vec<(usize, usize, [u8; 32])> = Vec::new();
+  let mut B: Vec<(usize, usize, [u8; 32])> = Vec::new();
+  let mut C: Vec<(usize, usize, [u8; 32])> = Vec::new();
+
+  let one: [u8; 32] = Scalar::ONE.to_bytes().into();
+
+  // R1CS is a set of three sparse matrices A B C, where is a row for every
+  // constraint and a column for every entry in z = (vars, 1, inputs)
+  // An R1CS instance is satisfiable iff:
+  // Az \circ Bz = Cz, where z = (vars, 1, inputs)
+
+  // constraint 0 entries in (A,B,C)
+  // constraint 0 is Z0 * Z0 - Z1 = 0.
+  A.push((0, 0, one));
+  B.push((0, 0, one));
+  C.push((0, 1, one));
+
+  // constraint 1 entries in (A,B,C)
+  // constraint 1 is Z1 * Z0 - Z2 = 0.
+  A.push((1, 1, one));
+  B.push((1, 0, one));
+  C.push((1, 2, one));
+
+  // constraint 2 entries in (A,B,C)
+  // constraint 2 is (Z2 + Z0) * 1 - Z3 = 0.
+  A.push((2, 2, one));
+  A.push((2, 0, one));
+  B.push((2, num_vars, one));
+  C.push((2, 3, one));
+
+  // constraint 3 entries in (A,B,C)
+  // constraint 3 is (Z3 + 5) * 1 - I0 = 0.
+  A.push((3, 3, one));
+  A.push((3, num_vars, Scalar::from(5u32).to_bytes().into()));
+  B.push((3, num_vars, one));
+  C.push((3, num_vars + 1, one));
+
+  let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
+
+  // compute a satisfying assignment
+  let mut csprng: OsRng = OsRng;
+  let z0 = Scalar::random(&mut csprng);
+  let z1 = z0 * z0; // constraint 0
+  let z2 = z1 * z0; // constraint 1
+  let z3 = z2 + z0; // constraint 2
+  let i0 = z3 + Scalar::from(5u32); // constraint 3
+
+  // create a VarsAssignment
+  let mut vars: Vec<[u8; 32]> = vec![Scalar::ZERO.to_bytes().into(); num_vars];
+  vars[0] = z0.to_bytes().into();
+  vars[1] = z1.to_bytes().into();
+  vars[2] = z2.to_bytes().into();
+  vars[3] = z3.to_bytes().into();
+  let assignment_vars = VarsAssignment::new(&vars).unwrap();
+
+  // create an InputsAssignment
+  let mut inputs: Vec<[u8; 32]> = vec![Scalar::ZERO.to_bytes().into(); num_inputs];
+  inputs[0] = i0.to_bytes().into();
+  let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
+
+  // check if the instance we created is satisfiable
+  let res = inst.is_sat(&assignment_vars, &assignment_inputs);
+  assert!(res.unwrap(), "should be satisfied");
+
+  (
+    num_cons,
+    num_vars,
+    num_inputs,
+    num_non_zero_entries,
+    inst,
+    assignment_vars,
+    assignment_inputs,
+  )
+}
+
+fn main() {
+  // produce an R1CS instance
+  let (
+    num_cons,
+    num_vars,
+    num_inputs,
+    num_non_zero_entries,
+    inst,
+    assignment_vars,
+    assignment_inputs,
+  ) = produce_r1cs();
+
+  // produce public parameters
+  let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
+
+  // create a commitment to the R1CS instance
+  let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+  // produce a proof of satisfiability
+  let mut prover_transcript = Transcript::new(b"snark_example");
+  let proof = SNARK::prove(
+    &inst,
+    &comm,
+    &decomm,
+    assignment_vars,
+    &assignment_inputs,
+    &gens,
+    &mut prover_transcript,
+  );
+
+  // verify the proof of satisfiability
+  let mut verifier_transcript = Transcript::new(b"snark_example");
+  assert!(proof
+    .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
+    .is_ok());
+  println!("proof verification successful!");
+}

packages/Spartan-secq/profiler/nizk.rs

@@ -0,0 +1,52 @@
+#![allow(non_snake_case)]
+#![allow(clippy::assertions_on_result_states)]
+
+extern crate flate2;
+extern crate libspartan;
+extern crate merlin;
+extern crate rand;
+
+use flate2::{write::ZlibEncoder, Compression};
+use libspartan::{Instance, NIZKGens, NIZK};
+use merlin::Transcript;
+
+fn print(msg: &str) {
+  let star = "* ";
+  println!("{:indent$}{}{}", "", star, msg, indent = 2);
+}
+
+pub fn main() {
+  // the list of number of variables (and constraints) in an R1CS instance
+  let inst_sizes = vec![10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20];
+
+  println!("Profiler:: NIZK");
+  for &s in inst_sizes.iter() {
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+
+    // produce a synthetic R1CSInstance
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // produce public generators
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
+
+    // produce a proof of satisfiability
+    let mut prover_transcript = Transcript::new(b"nizk_example");
+    let proof = NIZK::prove(&inst, vars, &inputs, &gens, &mut prover_transcript);
+
+    let mut encoder = ZlibEncoder::new(Vec::new(), Compression::default());
+    bincode::serialize_into(&mut encoder, &proof).unwrap();
+    let proof_encoded = encoder.finish().unwrap();
+    let msg_proof_len = format!("NIZK::proof_compressed_len {:?}", proof_encoded.len());
+    print(&msg_proof_len);
+
+    // verify the proof of satisfiability
+    let mut verifier_transcript = Transcript::new(b"nizk_example");
+    assert!(proof
+      .verify(&inst, &inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+
+    println!();
+  }
+}

packages/Spartan-secq/profiler/snark.rs

@@ -0,0 +1,62 @@
+#![allow(non_snake_case)]
+#![allow(clippy::assertions_on_result_states)]
+
+extern crate flate2;
+extern crate libspartan;
+extern crate merlin;
+
+use flate2::{write::ZlibEncoder, Compression};
+use libspartan::{Instance, SNARKGens, SNARK};
+use merlin::Transcript;
+
+fn print(msg: &str) {
+  let star = "* ";
+  println!("{:indent$}{}{}", "", star, msg, indent = 2);
+}
+
+pub fn main() {
+  // the list of number of variables (and constraints) in an R1CS instance
+  let inst_sizes = vec![10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20];
+
+  println!("Profiler:: SNARK");
+  for &s in inst_sizes.iter() {
+    let num_vars = (2_usize).pow(s as u32);
+    let num_cons = num_vars;
+    let num_inputs = 10;
+
+    // produce a synthetic R1CSInstance
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // produce public generators
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_cons);
+
+    // create a commitment to R1CSInstance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a proof of satisfiability
+    let mut prover_transcript = Transcript::new(b"snark_example");
+    let proof = SNARK::prove(
+      &inst,
+      &comm,
+      &decomm,
+      vars,
+      &inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    let mut encoder = ZlibEncoder::new(Vec::new(), Compression::default());
+    bincode::serialize_into(&mut encoder, &proof).unwrap();
+    let proof_encoded = encoder.finish().unwrap();
+    let msg_proof_len = format!("SNARK::proof_compressed_len {:?}", proof_encoded.len());
+    print(&msg_proof_len);
+
+    // verify the proof of satisfiability
+    let mut verifier_transcript = Transcript::new(b"snark_example");
+    assert!(proof
+      .verify(&comm, &inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+
+    println!();
+  }
+}

packages/Spartan-secq/rustfmt.toml

@@ -0,0 +1,4 @@
+edition = "2018"
+tab_spaces = 2
+newline_style = "Unix"
+use_try_shorthand = true

packages/Spartan-secq/src/bin/mont_params.rs

@@ -0,0 +1,54 @@
+use hex_literal::hex;
+use num_bigint_dig::{BigInt, BigUint, ModInverse, ToBigInt};
+use num_traits::{FromPrimitive, ToPrimitive};
+use std::ops::Neg;
+
+fn get_words(n: &BigUint) -> [u64; 4] {
+  let mut words = [0u64; 4];
+  for i in 0..4 {
+    let word = n.clone() >> (64 * i) & BigUint::from(0xffffffffffffffffu64);
+    words[i] = word.to_u64().unwrap();
+  }
+  words
+}
+
+fn render_hex(label: String, words: &[u64; 4]) {
+  println!("// {}", label);
+  for word in words {
+    println!("0x{:016x},", word);
+  }
+}
+
+fn main() {
+  let modulus = BigUint::from_bytes_be(&hex!(
+    "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f"
+  ));
+
+  let r = BigUint::from_u8(2)
+    .unwrap()
+    .modpow(&BigUint::from_u64(256).unwrap(), &modulus);
+
+  let r2 = BigUint::from_u8(2)
+    .unwrap()
+    .modpow(&BigUint::from_u64(512).unwrap(), &modulus);
+
+  let r3 = BigUint::from_u8(2)
+    .unwrap()
+    .modpow(&BigUint::from_u64(768).unwrap(), &modulus);
+
+  let two_pow_64 = BigUint::from_u128(18446744073709551616u128).unwrap();
+  let one = BigInt::from_u8(1).unwrap();
+
+  let inv = modulus
+    .clone()
+    .mod_inverse(&two_pow_64)
+    .unwrap()
+    .neg()
+    .modpow(&one, &two_pow_64.to_bigint().unwrap());
+
+  render_hex("Modulus".to_string(), &get_words(&modulus));
+  render_hex("R".to_string(), &get_words(&r));
+  render_hex("R2".to_string(), &get_words(&r2));
+  render_hex("R3".to_string(), &get_words(&r3));
+  render_hex("INV".to_string(), &get_words(&inv.to_biguint().unwrap()));
+}

packages/Spartan-secq/src/commitments.rs

@@ -0,0 +1,96 @@
+use super::group::{GroupElement, VartimeMultiscalarMul};
+use super::scalar::Scalar;
+use digest::{ExtendableOutput, Input};
+use secq256k1::AffinePoint;
+use sha3::Shake256;
+use std::io::Read;
+
+#[derive(Debug)]
+pub struct MultiCommitGens {
+  pub n: usize,
+  pub G: Vec<GroupElement>,
+  pub h: GroupElement,
+}
+
+impl MultiCommitGens {
+  pub fn new(n: usize, label: &[u8]) -> Self {
+    let mut shake = Shake256::default();
+    shake.input(label);
+    shake.input(AffinePoint::generator().compress().as_bytes());
+
+    let mut reader = shake.xof_result();
+    let mut gens: Vec<GroupElement> = Vec::new();
+    let mut uniform_bytes = [0u8; 128];
+    for _ in 0..n + 1 {
+      reader.read_exact(&mut uniform_bytes).unwrap();
+      gens.push(AffinePoint::from_uniform_bytes(&uniform_bytes));
+    }
+
+    MultiCommitGens {
+      n,
+      G: gens[..n].to_vec(),
+      h: gens[n],
+    }
+  }
+
+  pub fn clone(&self) -> MultiCommitGens {
+    MultiCommitGens {
+      n: self.n,
+      h: self.h,
+      G: self.G.clone(),
+    }
+  }
+
+  pub fn scale(&self, s: &Scalar) -> MultiCommitGens {
+    MultiCommitGens {
+      n: self.n,
+      h: self.h,
+      G: (0..self.n).map(|i| s * self.G[i]).collect(),
+    }
+  }
+
+  pub fn split_at(&self, mid: usize) -> (MultiCommitGens, MultiCommitGens) {
+    let (G1, G2) = self.G.split_at(mid);
+
+    (
+      MultiCommitGens {
+        n: G1.len(),
+        G: G1.to_vec(),
+        h: self.h,
+      },
+      MultiCommitGens {
+        n: G2.len(),
+        G: G2.to_vec(),
+        h: self.h,
+      },
+    )
+  }
+}
+
+pub trait Commitments {
+  fn commit(&self, blind: &Scalar, gens_n: &MultiCommitGens) -> GroupElement;
+}
+
+impl Commitments for Scalar {
+  fn commit(&self, blind: &Scalar, gens_n: &MultiCommitGens) -> GroupElement {
+    assert_eq!(gens_n.n, 1);
+    GroupElement::vartime_multiscalar_mul(
+      [*self, *blind].to_vec(),
+      [gens_n.G[0], gens_n.h].to_vec(),
+    )
+  }
+}
+
+impl Commitments for Vec<Scalar> {
+  fn commit(&self, blind: &Scalar, gens_n: &MultiCommitGens) -> GroupElement {
+    assert_eq!(gens_n.n, self.len());
+    GroupElement::vartime_multiscalar_mul((*self).clone(), gens_n.G.clone()) + blind * gens_n.h
+  }
+}
+
+impl Commitments for [Scalar] {
+  fn commit(&self, blind: &Scalar, gens_n: &MultiCommitGens) -> GroupElement {
+    assert_eq!(gens_n.n, self.len());
+    GroupElement::vartime_multiscalar_mul(self.to_vec(), gens_n.G.clone()) + blind * gens_n.h
+  }
+}

packages/Spartan-secq/src/dense_mlpoly.rs

@@ -0,0 +1,602 @@
+#![allow(clippy::too_many_arguments)]
+use super::commitments::{Commitments, MultiCommitGens};
+use super::errors::ProofVerifyError;
+use super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
+use super::math::Math;
+use super::nizk::{DotProductProofGens, DotProductProofLog};
+use super::random::RandomTape;
+use super::scalar::Scalar;
+use super::transcript::{AppendToTranscript, ProofTranscript};
+use crate::group::DecompressEncodedPoint;
+use core::ops::Index;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+#[cfg(feature = "multicore")]
+use rayon::prelude::*;
+
+#[derive(Debug)]
+pub struct DensePolynomial {
+  num_vars: usize, // the number of variables in the multilinear polynomial
+  len: usize,
+  Z: Vec<Scalar>, // evaluations of the polynomial in all the 2^num_vars Boolean inputs
+}
+
+pub struct PolyCommitmentGens {
+  pub gens: DotProductProofGens,
+}
+
+impl PolyCommitmentGens {
+  // the number of variables in the multilinear polynomial
+  pub fn new(num_vars: usize, label: &'static [u8]) -> PolyCommitmentGens {
+    let (_left, right) = EqPolynomial::compute_factored_lens(num_vars);
+    let gens = DotProductProofGens::new(right.pow2(), label);
+    PolyCommitmentGens { gens }
+  }
+}
+
+pub struct PolyCommitmentBlinds {
+  blinds: Vec<Scalar>,
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct PolyCommitment {
+  C: Vec<CompressedGroup>,
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct ConstPolyCommitment {
+  C: CompressedGroup,
+}
+
+pub struct EqPolynomial {
+  r: Vec<Scalar>,
+}
+
+impl EqPolynomial {
+  pub fn new(r: Vec<Scalar>) -> Self {
+    EqPolynomial { r }
+  }
+
+  pub fn evaluate(&self, rx: &[Scalar]) -> Scalar {
+    assert_eq!(self.r.len(), rx.len());
+    (0..rx.len())
+      .map(|i| self.r[i] * rx[i] + (Scalar::one() - self.r[i]) * (Scalar::one() - rx[i]))
+      .product()
+  }
+
+  pub fn evals(&self) -> Vec<Scalar> {
+    let ell = self.r.len();
+
+    let mut evals: Vec<Scalar> = vec![Scalar::one(); ell.pow2()];
+    let mut size = 1;
+    for j in 0..ell {
+      // in each iteration, we double the size of chis
+      size *= 2;
+      for i in (0..size).rev().step_by(2) {
+        // copy each element from the prior iteration twice
+        let scalar = evals[i / 2];
+        evals[i] = scalar * self.r[j];
+        evals[i - 1] = scalar - evals[i];
+      }
+    }
+    evals
+  }
+
+  pub fn compute_factored_lens(ell: usize) -> (usize, usize) {
+    (ell / 2, ell - ell / 2)
+  }
+
+  pub fn compute_factored_evals(&self) -> (Vec<Scalar>, Vec<Scalar>) {
+    let ell = self.r.len();
+    let (left_num_vars, _right_num_vars) = EqPolynomial::compute_factored_lens(ell);
+
+    let L = EqPolynomial::new(self.r[..left_num_vars].to_vec()).evals();
+    let R = EqPolynomial::new(self.r[left_num_vars..ell].to_vec()).evals();
+
+    (L, R)
+  }
+}
+
+pub struct IdentityPolynomial {
+  size_point: usize,
+}
+
+impl IdentityPolynomial {
+  pub fn new(size_point: usize) -> Self {
+    IdentityPolynomial { size_point }
+  }
+
+  pub fn evaluate(&self, r: &[Scalar]) -> Scalar {
+    let len = r.len();
+    assert_eq!(len, self.size_point);
+    (0..len)
+      .map(|i| Scalar::from((len - i - 1).pow2() as u64) * r[i])
+      .sum()
+  }
+}
+
+impl DensePolynomial {
+  pub fn new(Z: Vec<Scalar>) -> Self {
+    DensePolynomial {
+      num_vars: Z.len().log_2(),
+      len: Z.len(),
+      Z,
+    }
+  }
+
+  pub fn get_num_vars(&self) -> usize {
+    self.num_vars
+  }
+
+  pub fn len(&self) -> usize {
+    self.len
+  }
+
+  pub fn clone(&self) -> DensePolynomial {
+    DensePolynomial::new(self.Z[0..self.len].to_vec())
+  }
+
+  pub fn split(&self, idx: usize) -> (DensePolynomial, DensePolynomial) {
+    assert!(idx < self.len());
+    (
+      DensePolynomial::new(self.Z[..idx].to_vec()),
+      DensePolynomial::new(self.Z[idx..2 * idx].to_vec()),
+    )
+  }
+
+  #[cfg(feature = "multicore")]
+  fn commit_inner(&self, blinds: &[Scalar], gens: &MultiCommitGens) -> PolyCommitment {
+    let L_size = blinds.len();
+    let R_size = self.Z.len() / L_size;
+    assert_eq!(L_size * R_size, self.Z.len());
+    let C = (0..L_size)
+      .into_par_iter()
+      .map(|i| {
+        self.Z[R_size * i..R_size * (i + 1)]
+          .commit(&blinds[i], gens)
+          .compress()
+      })
+      .collect();
+    PolyCommitment { C }
+  }
+
+  #[cfg(not(feature = "multicore"))]
+  fn commit_inner(&self, blinds: &[Scalar], gens: &MultiCommitGens) -> PolyCommitment {
+    let L_size = blinds.len();
+    let R_size = self.Z.len() / L_size;
+    assert_eq!(L_size * R_size, self.Z.len());
+    let C = (0..L_size)
+      .map(|i| {
+        self.Z[R_size * i..R_size * (i + 1)]
+          .commit(&blinds[i], gens)
+          .compress()
+      })
+      .collect();
+    PolyCommitment { C }
+  }
+
+  pub fn commit(
+    &self,
+    gens: &PolyCommitmentGens,
+    random_tape: Option<&mut RandomTape>,
+  ) -> (PolyCommitment, PolyCommitmentBlinds) {
+    let n = self.Z.len();
+    let ell = self.get_num_vars();
+    assert_eq!(n, ell.pow2());
+
+    let (left_num_vars, right_num_vars) = EqPolynomial::compute_factored_lens(ell);
+    let L_size = left_num_vars.pow2();
+    let R_size = right_num_vars.pow2();
+    assert_eq!(L_size * R_size, n);
+
+    let blinds = if let Some(t) = random_tape {
+      PolyCommitmentBlinds {
+        blinds: t.random_vector(b"poly_blinds", L_size),
+      }
+    } else {
+      PolyCommitmentBlinds {
+        blinds: vec![Scalar::zero(); L_size],
+      }
+    };
+
+    (self.commit_inner(&blinds.blinds, &gens.gens.gens_n), blinds)
+  }
+
+  pub fn bound(&self, L: &[Scalar]) -> Vec<Scalar> {
+    let (left_num_vars, right_num_vars) = EqPolynomial::compute_factored_lens(self.get_num_vars());
+    let L_size = left_num_vars.pow2();
+    let R_size = right_num_vars.pow2();
+    (0..R_size)
+      .map(|i| (0..L_size).map(|j| L[j] * self.Z[j * R_size + i]).sum())
+      .collect()
+  }
+
+  pub fn bound_poly_var_top(&mut self, r: &Scalar) {
+    let n = self.len() / 2;
+    for i in 0..n {
+      self.Z[i] = self.Z[i] + r * (self.Z[i + n] - self.Z[i]);
+    }
+    self.num_vars -= 1;
+    self.len = n;
+  }
+
+  pub fn bound_poly_var_bot(&mut self, r: &Scalar) {
+    let n = self.len() / 2;
+    for i in 0..n {
+      self.Z[i] = self.Z[2 * i] + r * (self.Z[2 * i + 1] - self.Z[2 * i]);
+    }
+    self.num_vars -= 1;
+    self.len = n;
+  }
+
+  // returns Z(r) in O(n) time
+  pub fn evaluate(&self, r: &[Scalar]) -> Scalar {
+    // r must have a value for each variable
+    assert_eq!(r.len(), self.get_num_vars());
+    let chis = EqPolynomial::new(r.to_vec()).evals();
+    assert_eq!(chis.len(), self.Z.len());
+    DotProductProofLog::compute_dotproduct(&self.Z, &chis)
+  }
+
+  fn vec(&self) -> &Vec<Scalar> {
+    &self.Z
+  }
+
+  pub fn extend(&mut self, other: &DensePolynomial) {
+    // TODO: allow extension even when some vars are bound
+    assert_eq!(self.Z.len(), self.len);
+    let other_vec = other.vec();
+    assert_eq!(other_vec.len(), self.len);
+    self.Z.extend(other_vec);
+    self.num_vars += 1;
+    self.len *= 2;
+    assert_eq!(self.Z.len(), self.len);
+  }
+
+  pub fn merge<'a, I>(polys: I) -> DensePolynomial
+  where
+    I: IntoIterator<Item = &'a DensePolynomial>,
+  {
+    let mut Z: Vec<Scalar> = Vec::new();
+    for poly in polys.into_iter() {
+      Z.extend(poly.vec());
+    }
+
+    // pad the polynomial with zero polynomial at the end
+    Z.resize(Z.len().next_power_of_two(), Scalar::zero());
+
+    DensePolynomial::new(Z)
+  }
+
+  pub fn from_usize(Z: &[usize]) -> Self {
+    DensePolynomial::new(
+      (0..Z.len())
+        .map(|i| Scalar::from(Z[i] as u64))
+        .collect::<Vec<Scalar>>(),
+    )
+  }
+}
+
+impl Index<usize> for DensePolynomial {
+  type Output = Scalar;
+
+  #[inline(always)]
+  fn index(&self, _index: usize) -> &Scalar {
+    &(self.Z[_index])
+  }
+}
+
+impl AppendToTranscript for PolyCommitment {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_message(label, b"poly_commitment_begin");
+    for i in 0..self.C.len() {
+      transcript.append_point(b"poly_commitment_share", &self.C[i]);
+    }
+    transcript.append_message(label, b"poly_commitment_end");
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct PolyEvalProof {
+  proof: DotProductProofLog,
+}
+
+impl PolyEvalProof {
+  fn protocol_name() -> &'static [u8] {
+    b"polynomial evaluation proof"
+  }
+
+  pub fn prove(
+    poly: &DensePolynomial,
+    blinds_opt: Option<&PolyCommitmentBlinds>,
+    r: &[Scalar],                  // point at which the polynomial is evaluated
+    Zr: &Scalar,                   // evaluation of \widetilde{Z}(r)
+    blind_Zr_opt: Option<&Scalar>, // specifies a blind for Zr
+    gens: &PolyCommitmentGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (PolyEvalProof, CompressedGroup) {
+    transcript.append_protocol_name(PolyEvalProof::protocol_name());
+
+    // assert vectors are of the right size
+    assert_eq!(poly.get_num_vars(), r.len());
+
+    let (left_num_vars, right_num_vars) = EqPolynomial::compute_factored_lens(r.len());
+    let L_size = left_num_vars.pow2();
+    let R_size = right_num_vars.pow2();
+
+    let default_blinds = PolyCommitmentBlinds {
+      blinds: vec![Scalar::zero(); L_size],
+    };
+    let blinds = blinds_opt.map_or(&default_blinds, |p| p);
+
+    assert_eq!(blinds.blinds.len(), L_size);
+
+    let zero = Scalar::zero();
+    let blind_Zr = blind_Zr_opt.map_or(&zero, |p| p);
+
+    // compute the L and R vectors
+    let eq = EqPolynomial::new(r.to_vec());
+    let (L, R) = eq.compute_factored_evals();
+    assert_eq!(L.len(), L_size);
+    assert_eq!(R.len(), R_size);
+
+    // compute the vector underneath L*Z and the L*blinds
+    // compute vector-matrix product between L and Z viewed as a matrix
+    let LZ = poly.bound(&L);
+    let LZ_blind: Scalar = (0..L.len()).map(|i| blinds.blinds[i] * L[i]).sum();
+
+    // a dot product proof of size R_size
+    let (proof, _C_LR, C_Zr_prime) = DotProductProofLog::prove(
+      &gens.gens,
+      transcript,
+      random_tape,
+      &LZ,
+      &LZ_blind,
+      &R,
+      Zr,
+      blind_Zr,
+    );
+
+    (PolyEvalProof { proof }, C_Zr_prime)
+  }
+
+  pub fn verify(
+    &self,
+    gens: &PolyCommitmentGens,
+    transcript: &mut Transcript,
+    r: &[Scalar],           // point at which the polynomial is evaluated
+    C_Zr: &CompressedGroup, // commitment to \widetilde{Z}(r)
+    comm: &PolyCommitment,
+  ) -> Result<(), ProofVerifyError> {
+    transcript.append_protocol_name(PolyEvalProof::protocol_name());
+
+    // compute L and R
+    let eq = EqPolynomial::new(r.to_vec());
+    let (L, R) = eq.compute_factored_evals();
+
+    // compute a weighted sum of commitments and L
+    let C_decompressed = comm.C.iter().map(|pt| pt.decompress().unwrap());
+
+    let C_LZ = GroupElement::vartime_multiscalar_mul(L, C_decompressed.collect()).compress();
+
+    self
+      .proof
+      .verify(R.len(), &gens.gens, transcript, &R, &C_LZ, C_Zr)
+  }
+
+  pub fn verify_plain(
+    &self,
+    gens: &PolyCommitmentGens,
+    transcript: &mut Transcript,
+    r: &[Scalar], // point at which the polynomial is evaluated
+    Zr: &Scalar,  // evaluation \widetilde{Z}(r)
+    comm: &PolyCommitment,
+  ) -> Result<(), ProofVerifyError> {
+    // compute a commitment to Zr with a blind of zero
+    let C_Zr = Zr.commit(&Scalar::zero(), &gens.gens.gens_1).compress();
+
+    self.verify(gens, transcript, r, &C_Zr, comm)
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::super::scalar::ScalarFromPrimitives;
+  use super::*;
+  use rand_core::OsRng;
+
+  fn evaluate_with_LR(Z: &[Scalar], r: &[Scalar]) -> Scalar {
+    let eq = EqPolynomial::new(r.to_vec());
+    let (L, R) = eq.compute_factored_evals();
+
+    let ell = r.len();
+    // ensure ell is even
+    assert!(ell % 2 == 0);
+    // compute n = 2^\ell
+    let n = ell.pow2();
+    // compute m = sqrt(n) = 2^{\ell/2}
+    let m = n.square_root();
+
+    // compute vector-matrix product between L and Z viewed as a matrix
+    let LZ = (0..m)
+      .map(|i| (0..m).map(|j| L[j] * Z[j * m + i]).sum())
+      .collect::<Vec<Scalar>>();
+
+    // compute dot product between LZ and R
+    DotProductProofLog::compute_dotproduct(&LZ, &R)
+  }
+
+  #[test]
+  fn check_polynomial_evaluation() {
+    // Z = [1, 2, 1, 4]
+    let Z = vec![
+      Scalar::one(),
+      (2_usize).to_scalar(),
+      (1_usize).to_scalar(),
+      (4_usize).to_scalar(),
+    ];
+
+    // r = [4,3]
+    let r = vec![(4_usize).to_scalar(), (3_usize).to_scalar()];
+
+    let eval_with_LR = evaluate_with_LR(&Z, &r);
+    let poly = DensePolynomial::new(Z);
+
+    let eval = poly.evaluate(&r);
+    assert_eq!(eval, (28_usize).to_scalar());
+    assert_eq!(eval_with_LR, eval);
+  }
+
+  pub fn compute_factored_chis_at_r(r: &[Scalar]) -> (Vec<Scalar>, Vec<Scalar>) {
+    let mut L: Vec<Scalar> = Vec::new();
+    let mut R: Vec<Scalar> = Vec::new();
+
+    let ell = r.len();
+    assert!(ell % 2 == 0); // ensure ell is even
+    let n = ell.pow2();
+    let m = n.square_root();
+
+    // compute row vector L
+    for i in 0..m {
+      let mut chi_i = Scalar::one();
+      for j in 0..ell / 2 {
+        let bit_j = ((m * i) & (1 << (r.len() - j - 1))) > 0;
+        if bit_j {
+          chi_i *= r[j];
+        } else {
+          chi_i *= Scalar::one() - r[j];
+        }
+      }
+      L.push(chi_i);
+    }
+
+    // compute column vector R
+    for i in 0..m {
+      let mut chi_i = Scalar::one();
+      for j in ell / 2..ell {
+        let bit_j = (i & (1 << (r.len() - j - 1))) > 0;
+        if bit_j {
+          chi_i *= r[j];
+        } else {
+          chi_i *= Scalar::one() - r[j];
+        }
+      }
+      R.push(chi_i);
+    }
+    (L, R)
+  }
+
+  pub fn compute_chis_at_r(r: &[Scalar]) -> Vec<Scalar> {
+    let ell = r.len();
+    let n = ell.pow2();
+    let mut chis: Vec<Scalar> = Vec::new();
+    for i in 0..n {
+      let mut chi_i = Scalar::one();
+      for j in 0..r.len() {
+        let bit_j = (i & (1 << (r.len() - j - 1))) > 0;
+        if bit_j {
+          chi_i *= r[j];
+        } else {
+          chi_i *= Scalar::one() - r[j];
+        }
+      }
+      chis.push(chi_i);
+    }
+    chis
+  }
+
+  pub fn compute_outerproduct(L: Vec<Scalar>, R: Vec<Scalar>) -> Vec<Scalar> {
+    assert_eq!(L.len(), R.len());
+    (0..L.len())
+      .map(|i| (0..R.len()).map(|j| L[i] * R[j]).collect::<Vec<Scalar>>())
+      .collect::<Vec<Vec<Scalar>>>()
+      .into_iter()
+      .flatten()
+      .collect::<Vec<Scalar>>()
+  }
+
+  #[test]
+  fn check_memoized_chis() {
+    let mut csprng: OsRng = OsRng;
+
+    let s = 10;
+    let mut r: Vec<Scalar> = Vec::new();
+    for _i in 0..s {
+      r.push(Scalar::random(&mut csprng));
+    }
+    let chis = tests::compute_chis_at_r(&r);
+    let chis_m = EqPolynomial::new(r).evals();
+    assert_eq!(chis, chis_m);
+  }
+
+  #[test]
+  fn check_factored_chis() {
+    let mut csprng: OsRng = OsRng;
+
+    let s = 10;
+    let mut r: Vec<Scalar> = Vec::new();
+    for _i in 0..s {
+      r.push(Scalar::random(&mut csprng));
+    }
+    let chis = EqPolynomial::new(r.clone()).evals();
+    let (L, R) = EqPolynomial::new(r).compute_factored_evals();
+    let O = compute_outerproduct(L, R);
+    assert_eq!(chis, O);
+  }
+
+  #[test]
+  fn check_memoized_factored_chis() {
+    let mut csprng: OsRng = OsRng;
+
+    let s = 10;
+    let mut r: Vec<Scalar> = Vec::new();
+    for _i in 0..s {
+      r.push(Scalar::random(&mut csprng));
+    }
+    let (L, R) = tests::compute_factored_chis_at_r(&r);
+    let eq = EqPolynomial::new(r);
+    let (L2, R2) = eq.compute_factored_evals();
+    assert_eq!(L, L2);
+    assert_eq!(R, R2);
+  }
+
+  #[test]
+  fn check_polynomial_commit() {
+    let Z = vec![
+      (1_usize).to_scalar(),
+      (2_usize).to_scalar(),
+      (1_usize).to_scalar(),
+      (4_usize).to_scalar(),
+    ];
+    let poly = DensePolynomial::new(Z);
+
+    // r = [4,3]
+    let r = vec![(4_usize).to_scalar(), (3_usize).to_scalar()];
+    let eval = poly.evaluate(&r);
+    assert_eq!(eval, (28_usize).to_scalar());
+
+    let gens = PolyCommitmentGens::new(poly.get_num_vars(), b"test-two");
+    let (poly_commitment, blinds) = poly.commit(&gens, None);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, C_Zr) = PolyEvalProof::prove(
+      &poly,
+      Some(&blinds),
+      &r,
+      &eval,
+      None,
+      &gens,
+      &mut prover_transcript,
+      &mut random_tape,
+    );
+
+    let mut verifier_transcript = Transcript::new(b"example");
+
+    assert!(proof
+      .verify(&gens, &mut verifier_transcript, &r, &C_Zr, &poly_commitment)
+      .is_ok());
+  }
+}

packages/Spartan-secq/src/errors.rs

@@ -0,0 +1,32 @@
+use core::fmt::Debug;
+use thiserror::Error;
+
+#[derive(Error, Debug)]
+pub enum ProofVerifyError {
+  #[error("Proof verification failed")]
+  InternalError,
+  #[error("Compressed group element failed to decompress: {0:?}")]
+  DecompressionError([u8; 32]),
+}
+
+impl Default for ProofVerifyError {
+  fn default() -> Self {
+    ProofVerifyError::InternalError
+  }
+}
+
+#[derive(Clone, Debug, Eq, PartialEq)]
+pub enum R1CSError {
+  /// returned if the number of constraints is not a power of 2
+  NonPowerOfTwoCons,
+  /// returned if the number of variables is not a power of 2
+  NonPowerOfTwoVars,
+  /// returned if a wrong number of inputs in an assignment are supplied
+  InvalidNumberOfInputs,
+  /// returned if a wrong number of variables in an assignment are supplied
+  InvalidNumberOfVars,
+  /// returned if a [u8;32] does not parse into a valid Scalar in the field of secq256k1
+  InvalidScalar,
+  /// returned if the supplied row or col in (row,col,val) tuple is out of range
+  InvalidIndex,
+}

packages/Spartan-secq/src/group.rs

@@ -0,0 +1,138 @@
+use secq256k1::{AffinePoint, ProjectivePoint};
+
+use super::errors::ProofVerifyError;
+use super::scalar::{Scalar, ScalarBytes, ScalarBytesFromScalar};
+use core::ops::{Mul, MulAssign};
+use multiexp::multiexp;
+
+pub type GroupElement = secq256k1::AffinePoint;
+pub type CompressedGroup = secq256k1::EncodedPoint;
+pub trait CompressedGroupExt {
+  type Group;
+  fn unpack(&self) -> Result<Self::Group, ProofVerifyError>;
+}
+
+impl CompressedGroupExt for CompressedGroup {
+  type Group = secq256k1::AffinePoint;
+  fn unpack(&self) -> Result<Self::Group, ProofVerifyError> {
+    let result = AffinePoint::decompress(*self);
+    if result.is_some().into() {
+      return Ok(result.unwrap());
+    } else {
+      Err(ProofVerifyError::DecompressionError(
+        (*self.to_bytes()).try_into().unwrap(),
+      ))
+    }
+  }
+}
+
+pub trait DecompressEncodedPoint {
+  fn decompress(&self) -> Option<GroupElement>;
+}
+
+impl DecompressEncodedPoint for CompressedGroup {
+  fn decompress(&self) -> Option<GroupElement> {
+    Some(self.unpack().unwrap())
+  }
+}
+
+impl<'b> MulAssign<&'b Scalar> for GroupElement {
+  fn mul_assign(&mut self, scalar: &'b Scalar) {
+    let result = (self as &GroupElement) * Scalar::decompress_scalar(scalar);
+    *self = result;
+  }
+}
+
+impl<'a, 'b> Mul<&'b Scalar> for &'a GroupElement {
+  type Output = GroupElement;
+  fn mul(self, scalar: &'b Scalar) -> GroupElement {
+    *self * Scalar::decompress_scalar(scalar)
+  }
+}
+
+impl<'a, 'b> Mul<&'b GroupElement> for &'a Scalar {
+  type Output = GroupElement;
+
+  fn mul(self, point: &'b GroupElement) -> GroupElement {
+    (*point * Scalar::decompress_scalar(self)).into()
+  }
+}
+
+macro_rules! define_mul_variants {
+  (LHS = $lhs:ty, RHS = $rhs:ty, Output = $out:ty) => {
+    impl<'b> Mul<&'b $rhs> for $lhs {
+      type Output = $out;
+      fn mul(self, rhs: &'b $rhs) -> $out {
+        &self * rhs
+      }
+    }
+
+    impl<'a> Mul<$rhs> for &'a $lhs {
+      type Output = $out;
+      fn mul(self, rhs: $rhs) -> $out {
+        self * &rhs
+      }
+    }
+
+    impl Mul<$rhs> for $lhs {
+      type Output = $out;
+      fn mul(self, rhs: $rhs) -> $out {
+        &self * &rhs
+      }
+    }
+  };
+}
+
+macro_rules! define_mul_assign_variants {
+  (LHS = $lhs:ty, RHS = $rhs:ty) => {
+    impl MulAssign<$rhs> for $lhs {
+      fn mul_assign(&mut self, rhs: $rhs) {
+        *self *= &rhs;
+      }
+    }
+  };
+}
+
+define_mul_assign_variants!(LHS = GroupElement, RHS = Scalar);
+define_mul_variants!(LHS = GroupElement, RHS = Scalar, Output = GroupElement);
+define_mul_variants!(LHS = Scalar, RHS = GroupElement, Output = GroupElement);
+
+pub trait VartimeMultiscalarMul {
+  type Scalar;
+  fn vartime_multiscalar_mul(scalars: Vec<Scalar>, points: Vec<GroupElement>) -> Self;
+}
+
+impl VartimeMultiscalarMul for GroupElement {
+  type Scalar = super::scalar::Scalar;
+  // TODO Borrow the arguments so we don't have to clone them, as it was in the original implementation
+  fn vartime_multiscalar_mul(scalars: Vec<Scalar>, points: Vec<GroupElement>) -> Self {
+    let points: Vec<ProjectivePoint> = points.iter().map(|p| ProjectivePoint::from(p.0)).collect();
+
+    let pairs: Vec<(ScalarBytes, ProjectivePoint)> = scalars
+      .into_iter()
+      .enumerate()
+      .map(|(i, s)| (Scalar::decompress_scalar(&s), points[i]))
+      .collect();
+
+    let result = multiexp::<ProjectivePoint>(pairs.as_slice());
+
+    AffinePoint(result.to_affine())
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::*;
+  #[test]
+  fn msm() {
+    let scalars = vec![Scalar::from(1), Scalar::from(2), Scalar::from(3)];
+    let points = vec![
+      GroupElement::generator(),
+      GroupElement::generator(),
+      GroupElement::generator(),
+    ];
+    let result = GroupElement::vartime_multiscalar_mul(scalars, points);
+
+    assert_eq!(result, GroupElement::generator() * Scalar::from(6));
+  }
+}

packages/Spartan-secq/src/lib.rs

@@ -0,0 +1,751 @@
+#![allow(non_snake_case)]
+#![doc = include_str!("../README.md")]
+#![deny(missing_docs)]
+#![allow(clippy::assertions_on_result_states)]
+
+extern crate byteorder;
+extern crate core;
+extern crate digest;
+extern crate merlin;
+extern crate rand;
+extern crate sha3;
+
+#[cfg(feature = "multicore")]
+extern crate rayon;
+
+mod commitments;
+mod dense_mlpoly;
+mod errors;
+mod group;
+mod math;
+mod nizk;
+mod product_tree;
+mod r1csinstance;
+mod r1csproof;
+mod random;
+mod scalar;
+mod sparse_mlpoly;
+mod sumcheck;
+mod timer;
+mod transcript;
+mod unipoly;
+
+use core::cmp::max;
+use errors::{ProofVerifyError, R1CSError};
+use merlin::Transcript;
+use r1csinstance::{
+  R1CSCommitment, R1CSCommitmentGens, R1CSDecommitment, R1CSEvalProof, R1CSInstance,
+};
+use r1csproof::{R1CSGens, R1CSProof};
+use random::RandomTape;
+use scalar::Scalar;
+use serde::{Deserialize, Serialize};
+use timer::Timer;
+use transcript::{AppendToTranscript, ProofTranscript};
+
+/// `ComputationCommitment` holds a public preprocessed NP statement (e.g., R1CS)
+pub struct ComputationCommitment {
+  comm: R1CSCommitment,
+}
+
+/// `ComputationDecommitment` holds information to decommit `ComputationCommitment`
+pub struct ComputationDecommitment {
+  decomm: R1CSDecommitment,
+}
+
+/// `Assignment` holds an assignment of values to either the inputs or variables in an `Instance`
+#[derive(Serialize, Deserialize, Clone)]
+pub struct Assignment {
+  assignment: Vec<Scalar>,
+}
+
+impl Assignment {
+  /// Constructs a new `Assignment` from a vector
+  pub fn new(assignment: &[[u8; 32]]) -> Result<Assignment, R1CSError> {
+    let bytes_to_scalar = |vec: &[[u8; 32]]| -> Result<Vec<Scalar>, R1CSError> {
+      let mut vec_scalar: Vec<Scalar> = Vec::new();
+      for v in vec {
+        let val = Scalar::from_bytes(v);
+        if val.is_some().unwrap_u8() == 1 {
+          vec_scalar.push(val.unwrap());
+        } else {
+          return Err(R1CSError::InvalidScalar);
+        }
+      }
+      Ok(vec_scalar)
+    };
+
+    let assignment_scalar = bytes_to_scalar(assignment);
+
+    // check for any parsing errors
+    if assignment_scalar.is_err() {
+      return Err(R1CSError::InvalidScalar);
+    }
+
+    Ok(Assignment {
+      assignment: assignment_scalar.unwrap(),
+    })
+  }
+
+  /// pads Assignment to the specified length
+  fn pad(&self, len: usize) -> VarsAssignment {
+    // check that the new length is higher than current length
+    assert!(len > self.assignment.len());
+
+    let padded_assignment = {
+      let mut padded_assignment = self.assignment.clone();
+      padded_assignment.extend(vec![Scalar::zero(); len - self.assignment.len()]);
+      padded_assignment
+    };
+
+    VarsAssignment {
+      assignment: padded_assignment,
+    }
+  }
+}
+
+/// `VarsAssignment` holds an assignment of values to variables in an `Instance`
+pub type VarsAssignment = Assignment;
+
+/// `InputsAssignment` holds an assignment of values to variables in an `Instance`
+pub type InputsAssignment = Assignment;
+
+/// `Instance` holds the description of R1CS matrices and a hash of the matrices
+#[derive(Serialize, Deserialize)]
+pub struct Instance {
+  /// R1CS instance
+  pub inst: R1CSInstance,
+  digest: Vec<u8>,
+}
+
+impl Instance {
+  /// Constructs a new `Instance` and an associated satisfying assignment
+  pub fn new(
+    num_cons: usize,
+    num_vars: usize,
+    num_inputs: usize,
+    A: &[(usize, usize, [u8; 32])],
+    B: &[(usize, usize, [u8; 32])],
+    C: &[(usize, usize, [u8; 32])],
+  ) -> Result<Instance, R1CSError> {
+    let (num_vars_padded, num_cons_padded) = {
+      let num_vars_padded = {
+        let mut num_vars_padded = num_vars;
+
+        // ensure that num_inputs + 1 <= num_vars
+        num_vars_padded = max(num_vars_padded, num_inputs + 1);
+
+        // ensure that num_vars_padded a power of two
+        if num_vars_padded.next_power_of_two() != num_vars_padded {
+          num_vars_padded = num_vars_padded.next_power_of_two();
+        }
+        num_vars_padded
+      };
+
+      let num_cons_padded = {
+        let mut num_cons_padded = num_cons;
+
+        // ensure that num_cons_padded is at least 2
+        if num_cons_padded == 0 || num_cons_padded == 1 {
+          num_cons_padded = 2;
+        }
+
+        // ensure that num_cons_padded is power of 2
+        if num_cons.next_power_of_two() != num_cons {
+          num_cons_padded = num_cons.next_power_of_two();
+        }
+        num_cons_padded
+      };
+
+      (num_vars_padded, num_cons_padded)
+    };
+
+    let bytes_to_scalar =
+      |tups: &[(usize, usize, [u8; 32])]| -> Result<Vec<(usize, usize, Scalar)>, R1CSError> {
+        let mut mat: Vec<(usize, usize, Scalar)> = Vec::new();
+        for &(row, col, val_bytes) in tups {
+          // row must be smaller than num_cons
+          if row >= num_cons {
+            return Err(R1CSError::InvalidIndex);
+          }
+
+          // col must be smaller than num_vars + 1 + num_inputs
+          if col >= num_vars + 1 + num_inputs {
+            return Err(R1CSError::InvalidIndex);
+          }
+
+          let val = Scalar::from_bytes(&val_bytes);
+          if val.is_some().unwrap_u8() == 1 {
+            // if col >= num_vars, it means that it is referencing a 1 or input in the satisfying
+            // assignment
+            if col >= num_vars {
+              mat.push((row, col + num_vars_padded - num_vars, val.unwrap()));
+            } else {
+              mat.push((row, col, val.unwrap()));
+            }
+          } else {
+            return Err(R1CSError::InvalidScalar);
+          }
+        }
+
+        // pad with additional constraints up until num_cons_padded if the original constraints were 0 or 1
+        // we do not need to pad otherwise because the dummy constraints are implicit in the sum-check protocol
+        if num_cons == 0 || num_cons == 1 {
+          for i in tups.len()..num_cons_padded {
+            mat.push((i, num_vars, Scalar::zero()));
+          }
+        }
+
+        Ok(mat)
+      };
+
+    let A_scalar = bytes_to_scalar(A);
+    if A_scalar.is_err() {
+      return Err(A_scalar.err().unwrap());
+    }
+
+    let B_scalar = bytes_to_scalar(B);
+    if B_scalar.is_err() {
+      return Err(B_scalar.err().unwrap());
+    }
+
+    let C_scalar = bytes_to_scalar(C);
+    if C_scalar.is_err() {
+      return Err(C_scalar.err().unwrap());
+    }
+
+    let inst = R1CSInstance::new(
+      num_cons_padded,
+      num_vars_padded,
+      num_inputs,
+      &A_scalar.unwrap(),
+      &B_scalar.unwrap(),
+      &C_scalar.unwrap(),
+    );
+
+    let digest = inst.get_digest();
+
+    Ok(Instance { inst, digest })
+  }
+
+  /// Checks if a given R1CSInstance is satisfiable with a given variables and inputs assignments
+  pub fn is_sat(
+    &self,
+    vars: &VarsAssignment,
+    inputs: &InputsAssignment,
+  ) -> Result<bool, R1CSError> {
+    if vars.assignment.len() > self.inst.get_num_vars() {
+      return Err(R1CSError::InvalidNumberOfInputs);
+    }
+
+    if inputs.assignment.len() != self.inst.get_num_inputs() {
+      return Err(R1CSError::InvalidNumberOfInputs);
+    }
+
+    // we might need to pad variables
+    let padded_vars = {
+      let num_padded_vars = self.inst.get_num_vars();
+      let num_vars = vars.assignment.len();
+      if num_padded_vars > num_vars {
+        vars.pad(num_padded_vars)
+      } else {
+        vars.clone()
+      }
+    };
+
+    Ok(
+      self
+        .inst
+        .is_sat(&padded_vars.assignment, &inputs.assignment),
+    )
+  }
+
+  /// Constructs a new synthetic R1CS `Instance` and an associated satisfying assignment
+  pub fn produce_synthetic_r1cs(
+    num_cons: usize,
+    num_vars: usize,
+    num_inputs: usize,
+  ) -> (Instance, VarsAssignment, InputsAssignment) {
+    let (inst, vars, inputs) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+    let digest = inst.get_digest();
+    (
+      Instance { inst, digest },
+      VarsAssignment { assignment: vars },
+      InputsAssignment { assignment: inputs },
+    )
+  }
+}
+
+/// `SNARKGens` holds public parameters for producing and verifying proofs with the Spartan SNARK
+pub struct SNARKGens {
+  gens_r1cs_sat: R1CSGens,
+  gens_r1cs_eval: R1CSCommitmentGens,
+}
+
+impl SNARKGens {
+  /// Constructs a new `SNARKGens` given the size of the R1CS statement
+  /// `num_nz_entries` specifies the maximum number of non-zero entries in any of the three R1CS matrices
+  pub fn new(num_cons: usize, num_vars: usize, num_inputs: usize, num_nz_entries: usize) -> Self {
+    let num_vars_padded = {
+      let mut num_vars_padded = max(num_vars, num_inputs + 1);
+      if num_vars_padded != num_vars_padded.next_power_of_two() {
+        num_vars_padded = num_vars_padded.next_power_of_two();
+      }
+      num_vars_padded
+    };
+
+    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars_padded);
+    let gens_r1cs_eval = R1CSCommitmentGens::new(
+      b"gens_r1cs_eval",
+      num_cons,
+      num_vars_padded,
+      num_inputs,
+      num_nz_entries,
+    );
+    SNARKGens {
+      gens_r1cs_sat,
+      gens_r1cs_eval,
+    }
+  }
+}
+
+/// `SNARK` holds a proof produced by Spartan SNARK
+#[derive(Serialize, Deserialize, Debug)]
+pub struct SNARK {
+  r1cs_sat_proof: R1CSProof,
+  inst_evals: (Scalar, Scalar, Scalar),
+  r1cs_eval_proof: R1CSEvalProof,
+}
+
+impl SNARK {
+  fn protocol_name() -> &'static [u8] {
+    b"Spartan SNARK proof"
+  }
+
+  /// A public computation to create a commitment to an R1CS instance
+  pub fn encode(
+    inst: &Instance,
+    gens: &SNARKGens,
+  ) -> (ComputationCommitment, ComputationDecommitment) {
+    let timer_encode = Timer::new("SNARK::encode");
+    let (comm, decomm) = inst.inst.commit(&gens.gens_r1cs_eval);
+    timer_encode.stop();
+    (
+      ComputationCommitment { comm },
+      ComputationDecommitment { decomm },
+    )
+  }
+
+  /// A method to produce a SNARK proof of the satisfiability of an R1CS instance
+  pub fn prove(
+    inst: &Instance,
+    comm: &ComputationCommitment,
+    decomm: &ComputationDecommitment,
+    vars: VarsAssignment,
+    inputs: &InputsAssignment,
+    gens: &SNARKGens,
+    transcript: &mut Transcript,
+  ) -> Self {
+    let timer_prove = Timer::new("SNARK::prove");
+
+    // we create a Transcript object seeded with a random Scalar
+    // to aid the prover produce its randomness
+    let mut random_tape = RandomTape::new(b"proof");
+
+    transcript.append_protocol_name(SNARK::protocol_name());
+    comm.comm.append_to_transcript(b"comm", transcript);
+
+    let (r1cs_sat_proof, rx, ry) = {
+      let (proof, rx, ry) = {
+        // we might need to pad variables
+        let padded_vars = {
+          let num_padded_vars = inst.inst.get_num_vars();
+          let num_vars = vars.assignment.len();
+          if num_padded_vars > num_vars {
+            vars.pad(num_padded_vars)
+          } else {
+            vars
+          }
+        };
+
+        R1CSProof::prove(
+          &inst.inst,
+          padded_vars.assignment,
+          &inputs.assignment,
+          &gens.gens_r1cs_sat,
+          transcript,
+          &mut random_tape,
+        )
+      };
+
+      let proof_encoded: Vec<u8> = bincode::serialize(&proof).unwrap();
+      Timer::print(&format!("len_r1cs_sat_proof {:?}", proof_encoded.len()));
+
+      (proof, rx, ry)
+    };
+
+    // We send evaluations of A, B, C at r = (rx, ry) as claims
+    // to enable the verifier complete the first sum-check
+    let timer_eval = Timer::new("eval_sparse_polys");
+    let inst_evals = {
+      let (Ar, Br, Cr) = inst.inst.evaluate(&rx, &ry);
+      Ar.append_to_transcript(b"Ar_claim", transcript);
+      Br.append_to_transcript(b"Br_claim", transcript);
+      Cr.append_to_transcript(b"Cr_claim", transcript);
+      (Ar, Br, Cr)
+    };
+    timer_eval.stop();
+
+    let r1cs_eval_proof = {
+      let proof = R1CSEvalProof::prove(
+        &decomm.decomm,
+        &rx,
+        &ry,
+        &inst_evals,
+        &gens.gens_r1cs_eval,
+        transcript,
+        &mut random_tape,
+      );
+
+      let proof_encoded: Vec<u8> = bincode::serialize(&proof).unwrap();
+      Timer::print(&format!("len_r1cs_eval_proof {:?}", proof_encoded.len()));
+      proof
+    };
+
+    timer_prove.stop();
+    SNARK {
+      r1cs_sat_proof,
+      inst_evals,
+      r1cs_eval_proof,
+    }
+  }
+
+  /// A method to verify the SNARK proof of the satisfiability of an R1CS instance
+  pub fn verify(
+    &self,
+    comm: &ComputationCommitment,
+    input: &InputsAssignment,
+    transcript: &mut Transcript,
+    gens: &SNARKGens,
+  ) -> Result<(), ProofVerifyError> {
+    let timer_verify = Timer::new("SNARK::verify");
+    transcript.append_protocol_name(SNARK::protocol_name());
+
+    // append a commitment to the computation to the transcript
+    comm.comm.append_to_transcript(b"comm", transcript);
+
+    let timer_sat_proof = Timer::new("verify_sat_proof");
+    assert_eq!(input.assignment.len(), comm.comm.get_num_inputs());
+    let (rx, ry) = self.r1cs_sat_proof.verify(
+      comm.comm.get_num_vars(),
+      comm.comm.get_num_cons(),
+      &input.assignment,
+      &self.inst_evals,
+      transcript,
+      &gens.gens_r1cs_sat,
+    )?;
+    timer_sat_proof.stop();
+
+    let timer_eval_proof = Timer::new("verify_eval_proof");
+    let (Ar, Br, Cr) = &self.inst_evals;
+    Ar.append_to_transcript(b"Ar_claim", transcript);
+    Br.append_to_transcript(b"Br_claim", transcript);
+    Cr.append_to_transcript(b"Cr_claim", transcript);
+    self.r1cs_eval_proof.verify(
+      &comm.comm,
+      &rx,
+      &ry,
+      &self.inst_evals,
+      &gens.gens_r1cs_eval,
+      transcript,
+    )?;
+    timer_eval_proof.stop();
+    timer_verify.stop();
+    Ok(())
+  }
+}
+
+/// `NIZKGens` holds public parameters for producing and verifying proofs with the Spartan NIZK
+pub struct NIZKGens {
+  gens_r1cs_sat: R1CSGens,
+}
+
+impl NIZKGens {
+  /// Constructs a new `NIZKGens` given the size of the R1CS statement
+  pub fn new(num_cons: usize, num_vars: usize, num_inputs: usize) -> Self {
+    let num_vars_padded = {
+      let mut num_vars_padded = max(num_vars, num_inputs + 1);
+      if num_vars_padded != num_vars_padded.next_power_of_two() {
+        num_vars_padded = num_vars_padded.next_power_of_two();
+      }
+      num_vars_padded
+    };
+
+    let gens_r1cs_sat = R1CSGens::new(b"gens_r1cs_sat", num_cons, num_vars_padded);
+    NIZKGens { gens_r1cs_sat }
+  }
+}
+
+/// `NIZK` holds a proof produced by Spartan NIZK
+#[derive(Serialize, Deserialize, Debug)]
+pub struct NIZK {
+  r1cs_sat_proof: R1CSProof,
+  r: (Vec<Scalar>, Vec<Scalar>),
+}
+
+impl NIZK {
+  fn protocol_name() -> &'static [u8] {
+    b"Spartan NIZK proof"
+  }
+
+  /// A method to produce a NIZK proof of the satisfiability of an R1CS instance
+  pub fn prove(
+    inst: &Instance,
+    vars: VarsAssignment,
+    input: &InputsAssignment,
+    gens: &NIZKGens,
+    transcript: &mut Transcript,
+  ) -> Self {
+    let timer_prove = Timer::new("NIZK::prove");
+    // we create a Transcript object seeded with a random Scalar
+    // to aid the prover produce its randomness
+    let mut random_tape = RandomTape::new(b"proof");
+
+    transcript.append_protocol_name(NIZK::protocol_name());
+    transcript.append_message(b"R1CSInstanceDigest", &inst.digest);
+
+    let (r1cs_sat_proof, rx, ry) = {
+      // we might need to pad variables
+      let padded_vars = {
+        let num_padded_vars = inst.inst.get_num_vars();
+        let num_vars = vars.assignment.len();
+        if num_padded_vars > num_vars {
+          vars.pad(num_padded_vars)
+        } else {
+          vars
+        }
+      };
+
+      let (proof, rx, ry) = R1CSProof::prove(
+        &inst.inst,
+        padded_vars.assignment,
+        &input.assignment,
+        &gens.gens_r1cs_sat,
+        transcript,
+        &mut random_tape,
+      );
+      let proof_encoded: Vec<u8> = bincode::serialize(&proof).unwrap();
+      Timer::print(&format!("len_r1cs_sat_proof {:?}", proof_encoded.len()));
+      (proof, rx, ry)
+    };
+
+    timer_prove.stop();
+    NIZK {
+      r1cs_sat_proof,
+      r: (rx, ry),
+    }
+  }
+
+  /// A method to verify a NIZK proof of the satisfiability of an R1CS instance
+  pub fn verify(
+    &self,
+    inst: &Instance,
+    input: &InputsAssignment,
+    transcript: &mut Transcript,
+    gens: &NIZKGens,
+  ) -> Result<(), ProofVerifyError> {
+    let timer_verify = Timer::new("NIZK::verify");
+
+    transcript.append_protocol_name(NIZK::protocol_name());
+    transcript.append_message(b"R1CSInstanceDigest", &inst.digest);
+
+    // We send evaluations of A, B, C at r = (rx, ry) as claims
+    // to enable the verifier complete the first sum-check
+    let timer_eval = Timer::new("eval_sparse_polys");
+    let (claimed_rx, claimed_ry) = &self.r;
+    let inst_evals = inst.inst.evaluate(claimed_rx, claimed_ry);
+    timer_eval.stop();
+
+    let timer_sat_proof = Timer::new("verify_sat_proof");
+    assert_eq!(input.assignment.len(), inst.inst.get_num_inputs());
+    let (rx, ry) = self.r1cs_sat_proof.verify(
+      inst.inst.get_num_vars(),
+      inst.inst.get_num_cons(),
+      &input.assignment,
+      &inst_evals,
+      transcript,
+      &gens.gens_r1cs_sat,
+    )?;
+
+    // verify if claimed rx and ry are correct
+    assert_eq!(rx, *claimed_rx);
+    assert_eq!(ry, *claimed_ry);
+    timer_sat_proof.stop();
+    timer_verify.stop();
+
+    Ok(())
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::*;
+
+  #[test]
+  pub fn check_snark() {
+    let num_vars = 256;
+    let num_cons = num_vars;
+    let num_inputs = 10;
+
+    // produce public generators
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_cons);
+
+    // produce a synthetic R1CSInstance
+    let (inst, vars, inputs) = Instance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    // create a commitment to R1CSInstance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a proof
+    let mut prover_transcript = Transcript::new(b"example");
+    let proof = SNARK::prove(
+      &inst,
+      &comm,
+      &decomm,
+      vars,
+      &inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the proof
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(&comm, &inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+  }
+
+  #[test]
+  pub fn check_r1cs_invalid_index() {
+    let num_cons = 4;
+    let num_vars = 8;
+    let num_inputs = 1;
+
+    let zero: [u8; 32] = [
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+      0,
+    ];
+
+    let A = vec![(0, 0, zero)];
+    let B = vec![(100, 1, zero)];
+    let C = vec![(1, 1, zero)];
+
+    let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
+    assert!(inst.is_err());
+    assert_eq!(inst.err(), Some(R1CSError::InvalidIndex));
+  }
+
+  #[test]
+  pub fn check_r1cs_invalid_scalar() {
+    let num_cons = 4;
+    let num_vars = 8;
+    let num_inputs = 1;
+
+    let zero: [u8; 32] = [
+      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+      0,
+    ];
+
+    let larger_than_mod = [255; 32];
+
+    let A = vec![(0, 0, zero)];
+    let B = vec![(1, 1, larger_than_mod)];
+    let C = vec![(1, 1, zero)];
+
+    let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
+    assert!(inst.is_err());
+    assert_eq!(inst.err(), Some(R1CSError::InvalidScalar));
+  }
+
+  #[test]
+  fn test_padded_constraints() {
+    // parameters of the R1CS instance
+    let num_cons = 1;
+    let num_vars = 0;
+    let num_inputs = 3;
+    let num_non_zero_entries = 3;
+
+    // We will encode the above constraints into three matrices, where
+    // the coefficients in the matrix are in the little-endian byte order
+    let mut A: Vec<(usize, usize, [u8; 32])> = Vec::new();
+    let mut B: Vec<(usize, usize, [u8; 32])> = Vec::new();
+    let mut C: Vec<(usize, usize, [u8; 32])> = Vec::new();
+
+    // Create a^2 + b + 13
+    A.push((0, num_vars + 2, Scalar::one().to_bytes())); // 1*a
+    B.push((0, num_vars + 2, Scalar::one().to_bytes())); // 1*a
+    C.push((0, num_vars + 1, Scalar::one().to_bytes())); // 1*z
+    C.push((0, num_vars, (-Scalar::from(13u64)).to_bytes())); // -13*1
+    C.push((0, num_vars + 3, (-Scalar::one()).to_bytes())); // -1*b
+
+    // Var Assignments (Z_0 = 16 is the only output)
+    let vars = vec![Scalar::zero().to_bytes(); num_vars];
+
+    // create an InputsAssignment (a = 1, b = 2)
+    let mut inputs = vec![Scalar::zero().to_bytes(); num_inputs];
+    inputs[0] = Scalar::from(16u64).to_bytes();
+    inputs[1] = Scalar::from(1u64).to_bytes();
+    inputs[2] = Scalar::from(2u64).to_bytes();
+
+    let assignment_inputs = InputsAssignment::new(&inputs).unwrap();
+    let assignment_vars = VarsAssignment::new(&vars).unwrap();
+
+    // Check if instance is satisfiable
+    let inst = Instance::new(num_cons, num_vars, num_inputs, &A, &B, &C).unwrap();
+    let res = inst.is_sat(&assignment_vars, &assignment_inputs);
+    assert!(res.unwrap(), "should be satisfied");
+
+    // SNARK public params
+    let gens = SNARKGens::new(num_cons, num_vars, num_inputs, num_non_zero_entries);
+
+    // create a commitment to the R1CS instance
+    let (comm, decomm) = SNARK::encode(&inst, &gens);
+
+    // produce a SNARK
+    let mut prover_transcript = Transcript::new(b"snark_example");
+    let proof = SNARK::prove(
+      &inst,
+      &comm,
+      &decomm,
+      assignment_vars.clone(),
+      &assignment_inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the SNARK
+    let mut verifier_transcript = Transcript::new(b"snark_example");
+    assert!(proof
+      .verify(&comm, &assignment_inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+
+    // NIZK public params
+    let gens = NIZKGens::new(num_cons, num_vars, num_inputs);
+
+    // produce a NIZK
+    let mut prover_transcript = Transcript::new(b"nizk_example");
+    let proof = NIZK::prove(
+      &inst,
+      assignment_vars,
+      &assignment_inputs,
+      &gens,
+      &mut prover_transcript,
+    );
+
+    // verify the NIZK
+    let mut verifier_transcript = Transcript::new(b"nizk_example");
+    assert!(proof
+      .verify(&inst, &assignment_inputs, &mut verifier_transcript, &gens)
+      .is_ok());
+  }
+}

packages/Spartan-secq/src/math.rs

@@ -0,0 +1,36 @@
+pub trait Math {
+  fn square_root(self) -> usize;
+  fn pow2(self) -> usize;
+  fn get_bits(self, num_bits: usize) -> Vec<bool>;
+  fn log_2(self) -> usize;
+}
+
+impl Math for usize {
+  #[inline]
+  fn square_root(self) -> usize {
+    (self as f64).sqrt() as usize
+  }
+
+  #[inline]
+  fn pow2(self) -> usize {
+    let base: usize = 2;
+    base.pow(self as u32)
+  }
+
+  /// Returns the num_bits from n in a canonical order
+  fn get_bits(self, num_bits: usize) -> Vec<bool> {
+    (0..num_bits)
+      .map(|shift_amount| ((self & (1 << (num_bits - shift_amount - 1))) > 0))
+      .collect::<Vec<bool>>()
+  }
+
+  fn log_2(self) -> usize {
+    assert_ne!(self, 0);
+
+    if self.is_power_of_two() {
+      (1usize.leading_zeros() - self.leading_zeros()) as usize
+    } else {
+      (0usize.leading_zeros() - self.leading_zeros()) as usize
+    }
+  }
+}

packages/Spartan-secq/src/nizk/bullet.rs

@@ -0,0 +1,267 @@
+//! This module is an adaptation of code from the bulletproofs crate.
+//! See NOTICE.md for more details
+#![allow(non_snake_case)]
+#![allow(clippy::type_complexity)]
+#![allow(clippy::too_many_arguments)]
+use super::super::errors::ProofVerifyError;
+use super::super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
+use super::super::math::Math;
+use super::super::scalar::Scalar;
+use super::super::transcript::ProofTranscript;
+use crate::group::DecompressEncodedPoint;
+use core::iter;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct BulletReductionProof {
+  L_vec: Vec<CompressedGroup>,
+  R_vec: Vec<CompressedGroup>,
+}
+
+impl BulletReductionProof {
+  /// Create an inner-product proof.
+  ///
+  /// The proof is created with respect to the bases \\(G\\).
+  ///
+  /// The `transcript` is passed in as a parameter so that the
+  /// challenges depend on the *entire* transcript (including parent
+  /// protocols).
+  ///
+  /// The lengths of the vectors must all be the same, and must all be
+  /// either 0 or a power of 2.
+  pub fn prove(
+    transcript: &mut Transcript,
+    Q: &GroupElement,
+    G_vec: &[GroupElement],
+    H: &GroupElement,
+    a_vec: &[Scalar],
+    b_vec: &[Scalar],
+    blind: &Scalar,
+    blinds_vec: &[(Scalar, Scalar)],
+  ) -> (
+    BulletReductionProof,
+    GroupElement,
+    Scalar,
+    Scalar,
+    GroupElement,
+    Scalar,
+  ) {
+    // Create slices G, H, a, b backed by their respective
+    // vectors.  This lets us reslice as we compress the lengths
+    // of the vectors in the main loop below.
+    let mut G = &mut G_vec.to_owned()[..];
+    let mut a = &mut a_vec.to_owned()[..];
+    let mut b = &mut b_vec.to_owned()[..];
+
+    // All of the input vectors must have a length that is a power of two.
+    let mut n = G.len();
+    assert!(n.is_power_of_two());
+    let lg_n = n.log_2();
+
+    // All of the input vectors must have the same length.
+    assert_eq!(G.len(), n);
+    assert_eq!(a.len(), n);
+    assert_eq!(b.len(), n);
+    assert_eq!(blinds_vec.len(), 2 * lg_n);
+
+    let mut L_vec = Vec::with_capacity(lg_n);
+    let mut R_vec = Vec::with_capacity(lg_n);
+    let mut blinds_iter = blinds_vec.iter();
+    let mut blind_fin = *blind;
+
+    while n != 1 {
+      n /= 2;
+      let (a_L, a_R) = a.split_at_mut(n);
+      let (b_L, b_R) = b.split_at_mut(n);
+      let (G_L, G_R) = G.split_at_mut(n);
+
+      let c_L = inner_product(a_L, b_R);
+      let c_R = inner_product(a_R, b_L);
+
+      let (blind_L, blind_R) = blinds_iter.next().unwrap();
+
+      let L = GroupElement::vartime_multiscalar_mul(
+        a_L
+          .iter()
+          .chain(iter::once(&c_L))
+          .chain(iter::once(blind_L))
+          .map(|s| *s)
+          .collect(),
+        G_R
+          .iter()
+          .chain(iter::once(Q))
+          .chain(iter::once(H))
+          .map(|s| *s)
+          .collect(),
+      );
+
+      let R = GroupElement::vartime_multiscalar_mul(
+        a_R
+          .iter()
+          .chain(iter::once(&c_R))
+          .chain(iter::once(blind_R))
+          .map(|s| *s)
+          .collect(),
+        G_L
+          .iter()
+          .chain(iter::once(Q))
+          .chain(iter::once(H))
+          .map(|s| *s)
+          .collect(),
+      );
+
+      transcript.append_point(b"L", &L.compress());
+      transcript.append_point(b"R", &R.compress());
+
+      let u = transcript.challenge_scalar(b"u");
+      let u_inv = u.invert().unwrap();
+
+      for i in 0..n {
+        a_L[i] = a_L[i] * u + u_inv * a_R[i];
+        b_L[i] = b_L[i] * u_inv + u * b_R[i];
+        G_L[i] =
+          GroupElement::vartime_multiscalar_mul([u_inv, u].to_vec(), [G_L[i], G_R[i]].to_vec());
+      }
+
+      blind_fin = blind_fin + blind_L * u * u + blind_R * u_inv * u_inv;
+
+      L_vec.push(L.compress());
+      R_vec.push(R.compress());
+
+      a = a_L;
+      b = b_L;
+      G = G_L;
+    }
+
+    let Gamma_hat = GroupElement::vartime_multiscalar_mul(
+      [a[0], a[0] * b[0], blind_fin].to_vec(),
+      [G[0], *Q, *H].to_vec(),
+    );
+
+    (
+      BulletReductionProof { L_vec, R_vec },
+      Gamma_hat,
+      a[0],
+      b[0],
+      G[0],
+      blind_fin,
+    )
+  }
+
+  /// Computes three vectors of verification scalars \\([u\_{i}^{2}]\\), \\([u\_{i}^{-2}]\\) and \\([s\_{i}]\\) for combined multiscalar multiplication
+  /// in a parent protocol. See [inner product protocol notes](index.html#verification-equation) for details.
+  /// The verifier must provide the input length \\(n\\) explicitly to avoid unbounded allocation within the inner product proof.
+  fn verification_scalars(
+    &self,
+    n: usize,
+    transcript: &mut Transcript,
+  ) -> Result<(Vec<Scalar>, Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
+    let lg_n = self.L_vec.len();
+    if lg_n >= 32 {
+      // 4 billion multiplications should be enough for anyone
+      // and this check prevents overflow in 1<<lg_n below.
+      return Err(ProofVerifyError::InternalError);
+    }
+    if n != (1 << lg_n) {
+      return Err(ProofVerifyError::InternalError);
+    }
+
+    // 1. Recompute x_k,...,x_1 based on the proof transcript
+    let mut challenges = Vec::with_capacity(lg_n);
+    for (L, R) in self.L_vec.iter().zip(self.R_vec.iter()) {
+      transcript.append_point(b"L", L);
+      transcript.append_point(b"R", R);
+      challenges.push(transcript.challenge_scalar(b"u"));
+    }
+
+    // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
+    let mut challenges_inv = challenges.clone();
+    let allinv = Scalar::batch_invert(&mut challenges_inv);
+
+    // 3. Compute u_i^2 and (1/u_i)^2
+    for i in 0..lg_n {
+      challenges[i] = challenges[i].square();
+      challenges_inv[i] = challenges_inv[i].square();
+    }
+    let challenges_sq = challenges;
+    let challenges_inv_sq = challenges_inv;
+
+    // 4. Compute s values inductively.
+    let mut s = Vec::with_capacity(n);
+    s.push(allinv);
+    for i in 1..n {
+      let lg_i = (32 - 1 - (i as u32).leading_zeros()) as usize;
+      let k = 1 << lg_i;
+      // The challenges are stored in "creation order" as [u_k,...,u_1],
+      // so u_{lg(i)+1} = is indexed by (lg_n-1) - lg_i
+      let u_lg_i_sq = challenges_sq[(lg_n - 1) - lg_i];
+      s.push(s[i - k] * u_lg_i_sq);
+    }
+
+    Ok((challenges_sq, challenges_inv_sq, s))
+  }
+
+  /// This method is for testing that proof generation work,
+  /// but for efficiency the actual protocols would use `verification_scalars`
+  /// method to combine inner product verification with other checks
+  /// in a single multiscalar multiplication.
+  pub fn verify(
+    &self,
+    n: usize,
+    a: &[Scalar],
+    transcript: &mut Transcript,
+    Gamma: &GroupElement,
+    G: &[GroupElement],
+  ) -> Result<(GroupElement, GroupElement, Scalar), ProofVerifyError> {
+    let (u_sq, u_inv_sq, s) = self.verification_scalars(n, transcript)?;
+
+    let Ls = self
+      .L_vec
+      .iter()
+      .map(|p| p.decompress().ok_or(ProofVerifyError::InternalError))
+      .collect::<Result<Vec<_>, _>>()?;
+
+    let Rs = self
+      .R_vec
+      .iter()
+      .map(|p| p.decompress().ok_or(ProofVerifyError::InternalError))
+      .collect::<Result<Vec<_>, _>>()?;
+
+    let G_hat = GroupElement::vartime_multiscalar_mul(s.clone(), G.to_vec());
+    let a_hat = inner_product(a, &s);
+
+    let Gamma_hat = GroupElement::vartime_multiscalar_mul(
+      u_sq
+        .iter()
+        .chain(u_inv_sq.iter())
+        .chain(iter::once(&Scalar::one()))
+        .map(|s| *s)
+        .collect(),
+      Ls.iter()
+        .chain(Rs.iter())
+        .chain(iter::once(Gamma))
+        .map(|p| *p)
+        .collect(),
+    );
+
+    Ok((G_hat, Gamma_hat, a_hat))
+  }
+}
+
+/// Computes an inner product of two vectors
+/// \\[
+///    {\langle {\mathbf{a}}, {\mathbf{b}} \rangle} = \sum\_{i=0}^{n-1} a\_i \cdot b\_i.
+/// \\]
+/// Panics if the lengths of \\(\mathbf{a}\\) and \\(\mathbf{b}\\) are not equal.
+pub fn inner_product(a: &[Scalar], b: &[Scalar]) -> Scalar {
+  assert!(
+    a.len() == b.len(),
+    "inner_product(a,b): lengths of vectors do not match"
+  );
+  let mut out = Scalar::zero();
+  for i in 0..a.len() {
+    out += a[i] * b[i];
+  }
+  out
+}

packages/Spartan-secq/src/nizk/mod.rs

@@ -0,0 +1,735 @@
+#![allow(clippy::too_many_arguments)]
+use super::commitments::{Commitments, MultiCommitGens};
+use super::errors::ProofVerifyError;
+use super::group::{CompressedGroup, CompressedGroupExt};
+use super::math::Math;
+use super::random::RandomTape;
+use super::scalar::Scalar;
+use super::transcript::{AppendToTranscript, ProofTranscript};
+use crate::group::DecompressEncodedPoint;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+mod bullet;
+use bullet::BulletReductionProof;
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct KnowledgeProof {
+  alpha: CompressedGroup,
+  z1: Scalar,
+  z2: Scalar,
+}
+
+impl KnowledgeProof {
+  fn protocol_name() -> &'static [u8] {
+    b"knowledge proof"
+  }
+
+  pub fn prove(
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+    x: &Scalar,
+    r: &Scalar,
+  ) -> (KnowledgeProof, CompressedGroup) {
+    transcript.append_protocol_name(KnowledgeProof::protocol_name());
+
+    // produce two random Scalars
+    let t1 = random_tape.random_scalar(b"t1");
+    let t2 = random_tape.random_scalar(b"t2");
+
+    let C = x.commit(r, gens_n).compress();
+    C.append_to_transcript(b"C", transcript);
+
+    let alpha = t1.commit(&t2, gens_n).compress();
+    alpha.append_to_transcript(b"alpha", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let z1 = x * c + t1;
+    let z2 = r * c + t2;
+
+    (KnowledgeProof { alpha, z1, z2 }, C)
+  }
+
+  pub fn verify(
+    &self,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    C: &CompressedGroup,
+  ) -> Result<(), ProofVerifyError> {
+    transcript.append_protocol_name(KnowledgeProof::protocol_name());
+    C.append_to_transcript(b"C", transcript);
+    self.alpha.append_to_transcript(b"alpha", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let lhs = self.z1.commit(&self.z2, gens_n).compress();
+    let rhs = (c * C.unpack()? + self.alpha.unpack()?).compress();
+
+    if lhs == rhs {
+      Ok(())
+    } else {
+      Err(ProofVerifyError::InternalError)
+    }
+  }
+}
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct EqualityProof {
+  alpha: CompressedGroup,
+  z: Scalar,
+}
+
+impl EqualityProof {
+  fn protocol_name() -> &'static [u8] {
+    b"equality proof"
+  }
+
+  pub fn prove(
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+    v1: &Scalar,
+    s1: &Scalar,
+    v2: &Scalar,
+    s2: &Scalar,
+  ) -> (EqualityProof, CompressedGroup, CompressedGroup) {
+    transcript.append_protocol_name(EqualityProof::protocol_name());
+
+    // produce a random Scalar
+    let r = random_tape.random_scalar(b"r");
+
+    let C1 = v1.commit(s1, gens_n).compress();
+    C1.append_to_transcript(b"C1", transcript);
+
+    let C2 = v2.commit(s2, gens_n).compress();
+    C2.append_to_transcript(b"C2", transcript);
+
+    let alpha = (r * gens_n.h).compress();
+    alpha.append_to_transcript(b"alpha", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let z = c * (s1 - s2) + r;
+
+    (EqualityProof { alpha, z }, C1, C2)
+  }
+
+  pub fn verify(
+    &self,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    C1: &CompressedGroup,
+    C2: &CompressedGroup,
+  ) -> Result<(), ProofVerifyError> {
+    transcript.append_protocol_name(EqualityProof::protocol_name());
+    C1.append_to_transcript(b"C1", transcript);
+    C2.append_to_transcript(b"C2", transcript);
+    self.alpha.append_to_transcript(b"alpha", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+    let rhs = {
+      let C = C1.unpack()? - C2.unpack()?;
+      (c * C + self.alpha.unpack()?).compress()
+    };
+
+    let lhs = (self.z * gens_n.h).compress();
+
+    if lhs == rhs {
+      Ok(())
+    } else {
+      Err(ProofVerifyError::InternalError)
+    }
+  }
+}
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct ProductProof {
+  alpha: CompressedGroup,
+  beta: CompressedGroup,
+  delta: CompressedGroup,
+  z: [Scalar; 5],
+}
+
+impl ProductProof {
+  fn protocol_name() -> &'static [u8] {
+    b"product proof"
+  }
+
+  pub fn prove(
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+    x: &Scalar,
+    rX: &Scalar,
+    y: &Scalar,
+    rY: &Scalar,
+    z: &Scalar,
+    rZ: &Scalar,
+  ) -> (
+    ProductProof,
+    CompressedGroup,
+    CompressedGroup,
+    CompressedGroup,
+  ) {
+    transcript.append_protocol_name(ProductProof::protocol_name());
+
+    // produce five random Scalar
+    let b1 = random_tape.random_scalar(b"b1");
+    let b2 = random_tape.random_scalar(b"b2");
+    let b3 = random_tape.random_scalar(b"b3");
+    let b4 = random_tape.random_scalar(b"b4");
+    let b5 = random_tape.random_scalar(b"b5");
+
+    let X = x.commit(rX, gens_n).compress();
+    X.append_to_transcript(b"X", transcript);
+
+    let Y = y.commit(rY, gens_n).compress();
+    Y.append_to_transcript(b"Y", transcript);
+
+    let Z = z.commit(rZ, gens_n).compress();
+    Z.append_to_transcript(b"Z", transcript);
+
+    let alpha = b1.commit(&b2, gens_n).compress();
+    alpha.append_to_transcript(b"alpha", transcript);
+
+    let beta = b3.commit(&b4, gens_n).compress();
+    beta.append_to_transcript(b"beta", transcript);
+
+    let delta = {
+      let gens_X = &MultiCommitGens {
+        n: 1,
+        G: vec![X.decompress().unwrap()],
+        h: gens_n.h,
+      };
+      b3.commit(&b5, gens_X).compress()
+    };
+    delta.append_to_transcript(b"delta", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let z1 = b1 + c * x;
+    let z2 = b2 + c * rX;
+    let z3 = b3 + c * y;
+    let z4 = b4 + c * rY;
+    let z5 = b5 + c * (rZ - rX * y);
+    let z = [z1, z2, z3, z4, z5];
+
+    (
+      ProductProof {
+        alpha,
+        beta,
+        delta,
+        z,
+      },
+      X,
+      Y,
+      Z,
+    )
+  }
+
+  fn check_equality(
+    P: &CompressedGroup,
+    X: &CompressedGroup,
+    c: &Scalar,
+    gens_n: &MultiCommitGens,
+    z1: &Scalar,
+    z2: &Scalar,
+  ) -> bool {
+    let lhs = (P.decompress().unwrap() + c * X.decompress().unwrap()).compress();
+    let rhs = z1.commit(z2, gens_n).compress();
+
+    lhs == rhs
+  }
+
+  pub fn verify(
+    &self,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    X: &CompressedGroup,
+    Y: &CompressedGroup,
+    Z: &CompressedGroup,
+  ) -> Result<(), ProofVerifyError> {
+    transcript.append_protocol_name(ProductProof::protocol_name());
+
+    X.append_to_transcript(b"X", transcript);
+    Y.append_to_transcript(b"Y", transcript);
+    Z.append_to_transcript(b"Z", transcript);
+    self.alpha.append_to_transcript(b"alpha", transcript);
+    self.beta.append_to_transcript(b"beta", transcript);
+    self.delta.append_to_transcript(b"delta", transcript);
+
+    let z1 = self.z[0];
+    let z2 = self.z[1];
+    let z3 = self.z[2];
+    let z4 = self.z[3];
+    let z5 = self.z[4];
+
+    let c = transcript.challenge_scalar(b"c");
+
+    if ProductProof::check_equality(&self.alpha, X, &c, gens_n, &z1, &z2)
+      && ProductProof::check_equality(&self.beta, Y, &c, gens_n, &z3, &z4)
+      && ProductProof::check_equality(
+        &self.delta,
+        Z,
+        &c,
+        &MultiCommitGens {
+          n: 1,
+          G: vec![X.unpack()?],
+          h: gens_n.h,
+        },
+        &z3,
+        &z5,
+      )
+    {
+      Ok(())
+    } else {
+      Err(ProofVerifyError::InternalError)
+    }
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct DotProductProof {
+  delta: CompressedGroup,
+  beta: CompressedGroup,
+  z: Vec<Scalar>,
+  z_delta: Scalar,
+  z_beta: Scalar,
+}
+
+impl DotProductProof {
+  fn protocol_name() -> &'static [u8] {
+    b"dot product proof"
+  }
+
+  pub fn compute_dotproduct(a: &[Scalar], b: &[Scalar]) -> Scalar {
+    assert_eq!(a.len(), b.len());
+    (0..a.len()).map(|i| a[i] * b[i]).sum()
+  }
+
+  pub fn prove(
+    gens_1: &MultiCommitGens,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+    x_vec: &[Scalar],
+    blind_x: &Scalar,
+    a_vec: &[Scalar],
+    y: &Scalar,
+    blind_y: &Scalar,
+  ) -> (DotProductProof, CompressedGroup, CompressedGroup) {
+    transcript.append_protocol_name(DotProductProof::protocol_name());
+
+    let n = x_vec.len();
+    assert_eq!(x_vec.len(), a_vec.len());
+    assert_eq!(gens_n.n, a_vec.len());
+    assert_eq!(gens_1.n, 1);
+
+    // produce randomness for the proofs
+    let d_vec = random_tape.random_vector(b"d_vec", n);
+    let r_delta = random_tape.random_scalar(b"r_delta");
+    let r_beta = random_tape.random_scalar(b"r_beta");
+
+    let Cx = x_vec.commit(blind_x, gens_n).compress();
+    Cx.append_to_transcript(b"Cx", transcript);
+
+    let Cy = y.commit(blind_y, gens_1).compress();
+    Cy.append_to_transcript(b"Cy", transcript);
+
+    a_vec.append_to_transcript(b"a", transcript);
+
+    let delta = d_vec.commit(&r_delta, gens_n).compress();
+    delta.append_to_transcript(b"delta", transcript);
+
+    let dotproduct_a_d = DotProductProof::compute_dotproduct(a_vec, &d_vec);
+
+    let beta = dotproduct_a_d.commit(&r_beta, gens_1).compress();
+    beta.append_to_transcript(b"beta", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let z = (0..d_vec.len())
+      .map(|i| c * x_vec[i] + d_vec[i])
+      .collect::<Vec<Scalar>>();
+
+    let z_delta = c * blind_x + r_delta;
+    let z_beta = c * blind_y + r_beta;
+
+    (
+      DotProductProof {
+        delta,
+        beta,
+        z,
+        z_delta,
+        z_beta,
+      },
+      Cx,
+      Cy,
+    )
+  }
+
+  pub fn verify(
+    &self,
+    gens_1: &MultiCommitGens,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    a: &[Scalar],
+    Cx: &CompressedGroup,
+    Cy: &CompressedGroup,
+  ) -> Result<(), ProofVerifyError> {
+    assert_eq!(gens_n.n, a.len());
+    assert_eq!(gens_1.n, 1);
+
+    transcript.append_protocol_name(DotProductProof::protocol_name());
+    Cx.append_to_transcript(b"Cx", transcript);
+    Cy.append_to_transcript(b"Cy", transcript);
+    a.append_to_transcript(b"a", transcript);
+    self.delta.append_to_transcript(b"delta", transcript);
+    self.beta.append_to_transcript(b"beta", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let mut result =
+      c * Cx.unpack()? + self.delta.unpack()? == self.z.commit(&self.z_delta, gens_n);
+
+    let dotproduct_z_a = DotProductProof::compute_dotproduct(&self.z, a);
+    result &= c * Cy.unpack()? + self.beta.unpack()? == dotproduct_z_a.commit(&self.z_beta, gens_1);
+
+    if result {
+      Ok(())
+    } else {
+      Err(ProofVerifyError::InternalError)
+    }
+  }
+}
+
+pub struct DotProductProofGens {
+  n: usize,
+  pub gens_n: MultiCommitGens,
+  pub gens_1: MultiCommitGens,
+}
+
+impl DotProductProofGens {
+  pub fn new(n: usize, label: &[u8]) -> Self {
+    let (gens_n, gens_1) = MultiCommitGens::new(n + 1, label).split_at(n);
+    DotProductProofGens { n, gens_n, gens_1 }
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct DotProductProofLog {
+  bullet_reduction_proof: BulletReductionProof,
+  delta: CompressedGroup,
+  beta: CompressedGroup,
+  z1: Scalar,
+  z2: Scalar,
+}
+
+impl DotProductProofLog {
+  fn protocol_name() -> &'static [u8] {
+    b"dot product proof (log)"
+  }
+
+  pub fn compute_dotproduct(a: &[Scalar], b: &[Scalar]) -> Scalar {
+    assert_eq!(a.len(), b.len());
+    (0..a.len()).map(|i| a[i] * b[i]).sum()
+  }
+
+  pub fn prove(
+    gens: &DotProductProofGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+    x_vec: &[Scalar],
+    blind_x: &Scalar,
+    a_vec: &[Scalar],
+    y: &Scalar,
+    blind_y: &Scalar,
+  ) -> (DotProductProofLog, CompressedGroup, CompressedGroup) {
+    transcript.append_protocol_name(DotProductProofLog::protocol_name());
+
+    let n = x_vec.len();
+    assert_eq!(x_vec.len(), a_vec.len());
+    assert_eq!(gens.n, n);
+
+    // produce randomness for generating a proof
+    let d = random_tape.random_scalar(b"d");
+    let r_delta = random_tape.random_scalar(b"r_delta");
+    let r_beta = random_tape.random_scalar(b"r_delta");
+    let blinds_vec = {
+      let v1 = random_tape.random_vector(b"blinds_vec_1", 2 * n.log_2());
+      let v2 = random_tape.random_vector(b"blinds_vec_2", 2 * n.log_2());
+      (0..v1.len())
+        .map(|i| (v1[i], v2[i]))
+        .collect::<Vec<(Scalar, Scalar)>>()
+    };
+
+    let Cx = x_vec.commit(blind_x, &gens.gens_n).compress();
+    Cx.append_to_transcript(b"Cx", transcript);
+
+    let Cy = y.commit(blind_y, &gens.gens_1).compress();
+    Cy.append_to_transcript(b"Cy", transcript);
+
+    a_vec.append_to_transcript(b"a", transcript);
+
+    // sample a random base and scale the generator used for
+    // the output of the inner product
+    let r = transcript.challenge_scalar(b"r");
+    let gens_1_scaled = gens.gens_1.scale(&r);
+
+    let blind_Gamma = blind_x + r * blind_y;
+    let (bullet_reduction_proof, _Gamma_hat, x_hat, a_hat, g_hat, rhat_Gamma) =
+      BulletReductionProof::prove(
+        transcript,
+        &gens_1_scaled.G[0],
+        &gens.gens_n.G,
+        &gens.gens_n.h,
+        x_vec,
+        a_vec,
+        &blind_Gamma,
+        &blinds_vec,
+      );
+    let y_hat = x_hat * a_hat;
+
+    let delta = {
+      let gens_hat = MultiCommitGens {
+        n: 1,
+        G: vec![g_hat],
+        h: gens.gens_1.h,
+      };
+      d.commit(&r_delta, &gens_hat).compress()
+    };
+    delta.append_to_transcript(b"delta", transcript);
+
+    let beta = d.commit(&r_beta, &gens_1_scaled).compress();
+    beta.append_to_transcript(b"beta", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let z1 = d + c * y_hat;
+    let z2 = a_hat * (c * rhat_Gamma + r_beta) + r_delta;
+
+    (
+      DotProductProofLog {
+        bullet_reduction_proof,
+        delta,
+        beta,
+        z1,
+        z2,
+      },
+      Cx,
+      Cy,
+    )
+  }
+
+  pub fn verify(
+    &self,
+    n: usize,
+    gens: &DotProductProofGens,
+    transcript: &mut Transcript,
+    a: &[Scalar],
+    Cx: &CompressedGroup,
+    Cy: &CompressedGroup,
+  ) -> Result<(), ProofVerifyError> {
+    assert_eq!(gens.n, n);
+    assert_eq!(a.len(), n);
+
+    transcript.append_protocol_name(DotProductProofLog::protocol_name());
+    Cx.append_to_transcript(b"Cx", transcript);
+    Cy.append_to_transcript(b"Cy", transcript);
+    a.append_to_transcript(b"a", transcript);
+
+    // sample a random base and scale the generator used for
+    // the output of the inner product
+    let r = transcript.challenge_scalar(b"r");
+    let gens_1_scaled = gens.gens_1.scale(&r);
+
+    let Gamma = Cx.unpack()? + r * Cy.unpack()?;
+
+    let (g_hat, Gamma_hat, a_hat) =
+      self
+        .bullet_reduction_proof
+        .verify(n, a, transcript, &Gamma, &gens.gens_n.G)?;
+    self.delta.append_to_transcript(b"delta", transcript);
+    self.beta.append_to_transcript(b"beta", transcript);
+
+    let c = transcript.challenge_scalar(b"c");
+
+    let c_s = &c;
+    let beta_s = self.beta.unpack()?;
+    let a_hat_s = &a_hat;
+    let delta_s = self.delta.unpack()?;
+    let z1_s = &self.z1;
+    let z2_s = &self.z2;
+
+    let lhs = ((Gamma_hat * c_s + beta_s) * a_hat_s + delta_s).compress();
+    let rhs = ((g_hat + gens_1_scaled.G[0] * a_hat_s) * z1_s + gens_1_scaled.h * z2_s).compress();
+
+    assert_eq!(lhs, rhs);
+
+    if lhs == rhs {
+      Ok(())
+    } else {
+      Err(ProofVerifyError::InternalError)
+    }
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::*;
+  use rand_core::OsRng;
+  #[test]
+  fn check_knowledgeproof() {
+    let mut csprng: OsRng = OsRng;
+
+    let gens_1 = MultiCommitGens::new(1, b"test-knowledgeproof");
+
+    let x = Scalar::random(&mut csprng);
+    let r = Scalar::random(&mut csprng);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, committed_value) =
+      KnowledgeProof::prove(&gens_1, &mut prover_transcript, &mut random_tape, &x, &r);
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(&gens_1, &mut verifier_transcript, &committed_value)
+      .is_ok());
+  }
+
+  #[test]
+  fn check_equalityproof() {
+    let mut csprng: OsRng = OsRng;
+
+    let gens_1 = MultiCommitGens::new(1, b"test-equalityproof");
+    let v1 = Scalar::random(&mut csprng);
+    let v2 = v1;
+    let s1 = Scalar::random(&mut csprng);
+    let s2 = Scalar::random(&mut csprng);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, C1, C2) = EqualityProof::prove(
+      &gens_1,
+      &mut prover_transcript,
+      &mut random_tape,
+      &v1,
+      &s1,
+      &v2,
+      &s2,
+    );
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(&gens_1, &mut verifier_transcript, &C1, &C2)
+      .is_ok());
+  }
+
+  #[test]
+  fn check_productproof() {
+    let mut csprng: OsRng = OsRng;
+
+    let gens_1 = MultiCommitGens::new(1, b"test-productproof");
+    let x = Scalar::random(&mut csprng);
+    let rX = Scalar::random(&mut csprng);
+    let y = Scalar::random(&mut csprng);
+    let rY = Scalar::random(&mut csprng);
+    let z = x * y;
+    let rZ = Scalar::random(&mut csprng);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, X, Y, Z) = ProductProof::prove(
+      &gens_1,
+      &mut prover_transcript,
+      &mut random_tape,
+      &x,
+      &rX,
+      &y,
+      &rY,
+      &z,
+      &rZ,
+    );
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(&gens_1, &mut verifier_transcript, &X, &Y, &Z)
+      .is_ok());
+  }
+
+  #[test]
+  fn check_dotproductproof() {
+    let mut csprng: OsRng = OsRng;
+
+    let n = 1024;
+
+    let gens_1 = MultiCommitGens::new(1, b"test-two");
+    let gens_1024 = MultiCommitGens::new(n, b"test-1024");
+
+    let mut x: Vec<Scalar> = Vec::new();
+    let mut a: Vec<Scalar> = Vec::new();
+    for _ in 0..n {
+      x.push(Scalar::random(&mut csprng));
+      a.push(Scalar::random(&mut csprng));
+    }
+    let y = DotProductProofLog::compute_dotproduct(&x, &a);
+    let r_x = Scalar::random(&mut csprng);
+    let r_y = Scalar::random(&mut csprng);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, Cx, Cy) = DotProductProof::prove(
+      &gens_1,
+      &gens_1024,
+      &mut prover_transcript,
+      &mut random_tape,
+      &x,
+      &r_x,
+      &a,
+      &y,
+      &r_y,
+    );
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(&gens_1, &gens_1024, &mut verifier_transcript, &a, &Cx, &Cy)
+      .is_ok());
+  }
+
+  #[test]
+  fn check_dotproductproof_log() {
+    let mut csprng: OsRng = OsRng;
+
+    let n = 1024;
+
+    let gens = DotProductProofGens::new(n, b"test-1024");
+
+    let x: Vec<Scalar> = (0..n).map(|_i| Scalar::random(&mut csprng)).collect();
+    let a: Vec<Scalar> = (0..n).map(|_i| Scalar::random(&mut csprng)).collect();
+    let y = DotProductProof::compute_dotproduct(&x, &a);
+
+    let r_x = Scalar::random(&mut csprng);
+    let r_y = Scalar::random(&mut csprng);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, Cx, Cy) = DotProductProofLog::prove(
+      &gens,
+      &mut prover_transcript,
+      &mut random_tape,
+      &x,
+      &r_x,
+      &a,
+      &y,
+      &r_y,
+    );
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(n, &gens, &mut verifier_transcript, &a, &Cx, &Cy)
+      .is_ok());
+  }
+}

packages/Spartan-secq/src/product_tree.rs

@@ -0,0 +1,486 @@
+#![allow(dead_code)]
+use super::dense_mlpoly::DensePolynomial;
+use super::dense_mlpoly::EqPolynomial;
+use super::math::Math;
+use super::scalar::Scalar;
+use super::sumcheck::SumcheckInstanceProof;
+use super::transcript::ProofTranscript;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+#[derive(Debug)]
+pub struct ProductCircuit {
+  left_vec: Vec<DensePolynomial>,
+  right_vec: Vec<DensePolynomial>,
+}
+
+impl ProductCircuit {
+  fn compute_layer(
+    inp_left: &DensePolynomial,
+    inp_right: &DensePolynomial,
+  ) -> (DensePolynomial, DensePolynomial) {
+    let len = inp_left.len() + inp_right.len();
+    let outp_left = (0..len / 4)
+      .map(|i| inp_left[i] * inp_right[i])
+      .collect::<Vec<Scalar>>();
+    let outp_right = (len / 4..len / 2)
+      .map(|i| inp_left[i] * inp_right[i])
+      .collect::<Vec<Scalar>>();
+
+    (
+      DensePolynomial::new(outp_left),
+      DensePolynomial::new(outp_right),
+    )
+  }
+
+  pub fn new(poly: &DensePolynomial) -> Self {
+    let mut left_vec: Vec<DensePolynomial> = Vec::new();
+    let mut right_vec: Vec<DensePolynomial> = Vec::new();
+
+    let num_layers = poly.len().log_2();
+    let (outp_left, outp_right) = poly.split(poly.len() / 2);
+
+    left_vec.push(outp_left);
+    right_vec.push(outp_right);
+
+    for i in 0..num_layers - 1 {
+      let (outp_left, outp_right) = ProductCircuit::compute_layer(&left_vec[i], &right_vec[i]);
+      left_vec.push(outp_left);
+      right_vec.push(outp_right);
+    }
+
+    ProductCircuit {
+      left_vec,
+      right_vec,
+    }
+  }
+
+  pub fn evaluate(&self) -> Scalar {
+    let len = self.left_vec.len();
+    assert_eq!(self.left_vec[len - 1].get_num_vars(), 0);
+    assert_eq!(self.right_vec[len - 1].get_num_vars(), 0);
+    self.left_vec[len - 1][0] * self.right_vec[len - 1][0]
+  }
+}
+
+pub struct DotProductCircuit {
+  left: DensePolynomial,
+  right: DensePolynomial,
+  weight: DensePolynomial,
+}
+
+impl DotProductCircuit {
+  pub fn new(left: DensePolynomial, right: DensePolynomial, weight: DensePolynomial) -> Self {
+    assert_eq!(left.len(), right.len());
+    assert_eq!(left.len(), weight.len());
+    DotProductCircuit {
+      left,
+      right,
+      weight,
+    }
+  }
+
+  pub fn evaluate(&self) -> Scalar {
+    (0..self.left.len())
+      .map(|i| self.left[i] * self.right[i] * self.weight[i])
+      .sum()
+  }
+
+  pub fn split(&mut self) -> (DotProductCircuit, DotProductCircuit) {
+    let idx = self.left.len() / 2;
+    assert_eq!(idx * 2, self.left.len());
+    let (l1, l2) = self.left.split(idx);
+    let (r1, r2) = self.right.split(idx);
+    let (w1, w2) = self.weight.split(idx);
+    (
+      DotProductCircuit {
+        left: l1,
+        right: r1,
+        weight: w1,
+      },
+      DotProductCircuit {
+        left: l2,
+        right: r2,
+        weight: w2,
+      },
+    )
+  }
+}
+
+#[allow(dead_code)]
+#[derive(Debug, Serialize, Deserialize)]
+pub struct LayerProof {
+  pub proof: SumcheckInstanceProof,
+  pub claims: Vec<Scalar>,
+}
+
+#[allow(dead_code)]
+impl LayerProof {
+  pub fn verify(
+    &self,
+    claim: Scalar,
+    num_rounds: usize,
+    degree_bound: usize,
+    transcript: &mut Transcript,
+  ) -> (Scalar, Vec<Scalar>) {
+    self
+      .proof
+      .verify(claim, num_rounds, degree_bound, transcript)
+      .unwrap()
+  }
+}
+
+#[allow(dead_code)]
+#[derive(Debug, Serialize, Deserialize)]
+pub struct LayerProofBatched {
+  pub proof: SumcheckInstanceProof,
+  pub claims_prod_left: Vec<Scalar>,
+  pub claims_prod_right: Vec<Scalar>,
+}
+
+#[allow(dead_code)]
+impl LayerProofBatched {
+  pub fn verify(
+    &self,
+    claim: Scalar,
+    num_rounds: usize,
+    degree_bound: usize,
+    transcript: &mut Transcript,
+  ) -> (Scalar, Vec<Scalar>) {
+    self
+      .proof
+      .verify(claim, num_rounds, degree_bound, transcript)
+      .unwrap()
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct ProductCircuitEvalProof {
+  proof: Vec<LayerProof>,
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct ProductCircuitEvalProofBatched {
+  proof: Vec<LayerProofBatched>,
+  claims_dotp: (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>),
+}
+
+impl ProductCircuitEvalProof {
+  #![allow(dead_code)]
+  pub fn prove(
+    circuit: &mut ProductCircuit,
+    transcript: &mut Transcript,
+  ) -> (Self, Scalar, Vec<Scalar>) {
+    let mut proof: Vec<LayerProof> = Vec::new();
+    let num_layers = circuit.left_vec.len();
+
+    let mut claim = circuit.evaluate();
+    let mut rand = Vec::new();
+    for layer_id in (0..num_layers).rev() {
+      let len = circuit.left_vec[layer_id].len() + circuit.right_vec[layer_id].len();
+
+      let mut poly_C = DensePolynomial::new(EqPolynomial::new(rand.clone()).evals());
+      assert_eq!(poly_C.len(), len / 2);
+
+      let num_rounds_prod = poly_C.len().log_2();
+      let comb_func_prod = |poly_A_comp: &Scalar,
+                            poly_B_comp: &Scalar,
+                            poly_C_comp: &Scalar|
+       -> Scalar { poly_A_comp * poly_B_comp * poly_C_comp };
+      let (proof_prod, rand_prod, claims_prod) = SumcheckInstanceProof::prove_cubic(
+        &claim,
+        num_rounds_prod,
+        &mut circuit.left_vec[layer_id],
+        &mut circuit.right_vec[layer_id],
+        &mut poly_C,
+        comb_func_prod,
+        transcript,
+      );
+
+      transcript.append_scalar(b"claim_prod_left", &claims_prod[0]);
+      transcript.append_scalar(b"claim_prod_right", &claims_prod[1]);
+
+      // produce a random challenge
+      let r_layer = transcript.challenge_scalar(b"challenge_r_layer");
+      claim = claims_prod[0] + r_layer * (claims_prod[1] - claims_prod[0]);
+
+      let mut ext = vec![r_layer];
+      ext.extend(rand_prod);
+      rand = ext;
+
+      proof.push(LayerProof {
+        proof: proof_prod,
+        claims: claims_prod[0..claims_prod.len() - 1].to_vec(),
+      });
+    }
+
+    (ProductCircuitEvalProof { proof }, claim, rand)
+  }
+
+  pub fn verify(
+    &self,
+    eval: Scalar,
+    len: usize,
+    transcript: &mut Transcript,
+  ) -> (Scalar, Vec<Scalar>) {
+    let num_layers = len.log_2();
+    let mut claim = eval;
+    let mut rand: Vec<Scalar> = Vec::new();
+    //let mut num_rounds = 0;
+    assert_eq!(self.proof.len(), num_layers);
+    for (num_rounds, i) in (0..num_layers).enumerate() {
+      let (claim_last, rand_prod) = self.proof[i].verify(claim, num_rounds, 3, transcript);
+
+      let claims_prod = &self.proof[i].claims;
+      transcript.append_scalar(b"claim_prod_left", &claims_prod[0]);
+      transcript.append_scalar(b"claim_prod_right", &claims_prod[1]);
+
+      assert_eq!(rand.len(), rand_prod.len());
+      let eq: Scalar = (0..rand.len())
+        .map(|i| {
+          rand[i] * rand_prod[i] + (Scalar::one() - rand[i]) * (Scalar::one() - rand_prod[i])
+        })
+        .product();
+      assert_eq!(claims_prod[0] * claims_prod[1] * eq, claim_last);
+
+      // produce a random challenge
+      let r_layer = transcript.challenge_scalar(b"challenge_r_layer");
+      claim = (Scalar::one() - r_layer) * claims_prod[0] + r_layer * claims_prod[1];
+      let mut ext = vec![r_layer];
+      ext.extend(rand_prod);
+      rand = ext;
+    }
+
+    (claim, rand)
+  }
+}
+
+impl ProductCircuitEvalProofBatched {
+  pub fn prove(
+    prod_circuit_vec: &mut Vec<&mut ProductCircuit>,
+    dotp_circuit_vec: &mut Vec<&mut DotProductCircuit>,
+    transcript: &mut Transcript,
+  ) -> (Self, Vec<Scalar>) {
+    assert!(!prod_circuit_vec.is_empty());
+
+    let mut claims_dotp_final = (Vec::new(), Vec::new(), Vec::new());
+
+    let mut proof_layers: Vec<LayerProofBatched> = Vec::new();
+    let num_layers = prod_circuit_vec[0].left_vec.len();
+    let mut claims_to_verify = (0..prod_circuit_vec.len())
+      .map(|i| prod_circuit_vec[i].evaluate())
+      .collect::<Vec<Scalar>>();
+    let mut rand = Vec::new();
+    for layer_id in (0..num_layers).rev() {
+      // prepare paralell instance that share poly_C first
+      let len = prod_circuit_vec[0].left_vec[layer_id].len()
+        + prod_circuit_vec[0].right_vec[layer_id].len();
+
+      let mut poly_C_par = DensePolynomial::new(EqPolynomial::new(rand.clone()).evals());
+      assert_eq!(poly_C_par.len(), len / 2);
+
+      let num_rounds_prod = poly_C_par.len().log_2();
+      let comb_func_prod = |poly_A_comp: &Scalar,
+                            poly_B_comp: &Scalar,
+                            poly_C_comp: &Scalar|
+       -> Scalar { poly_A_comp * poly_B_comp * poly_C_comp };
+
+      let mut poly_A_batched_par: Vec<&mut DensePolynomial> = Vec::new();
+      let mut poly_B_batched_par: Vec<&mut DensePolynomial> = Vec::new();
+      for prod_circuit in prod_circuit_vec.iter_mut() {
+        poly_A_batched_par.push(&mut prod_circuit.left_vec[layer_id]);
+        poly_B_batched_par.push(&mut prod_circuit.right_vec[layer_id])
+      }
+      let poly_vec_par = (
+        &mut poly_A_batched_par,
+        &mut poly_B_batched_par,
+        &mut poly_C_par,
+      );
+
+      // prepare sequential instances that don't share poly_C
+      let mut poly_A_batched_seq: Vec<&mut DensePolynomial> = Vec::new();
+      let mut poly_B_batched_seq: Vec<&mut DensePolynomial> = Vec::new();
+      let mut poly_C_batched_seq: Vec<&mut DensePolynomial> = Vec::new();
+      if layer_id == 0 && !dotp_circuit_vec.is_empty() {
+        // add additional claims
+        for item in dotp_circuit_vec.iter() {
+          claims_to_verify.push(item.evaluate());
+          assert_eq!(len / 2, item.left.len());
+          assert_eq!(len / 2, item.right.len());
+          assert_eq!(len / 2, item.weight.len());
+        }
+
+        for dotp_circuit in dotp_circuit_vec.iter_mut() {
+          poly_A_batched_seq.push(&mut dotp_circuit.left);
+          poly_B_batched_seq.push(&mut dotp_circuit.right);
+          poly_C_batched_seq.push(&mut dotp_circuit.weight);
+        }
+      }
+      let poly_vec_seq = (
+        &mut poly_A_batched_seq,
+        &mut poly_B_batched_seq,
+        &mut poly_C_batched_seq,
+      );
+
+      // produce a fresh set of coeffs and a joint claim
+      let coeff_vec =
+        transcript.challenge_vector(b"rand_coeffs_next_layer", claims_to_verify.len());
+      let claim = (0..claims_to_verify.len())
+        .map(|i| claims_to_verify[i] * coeff_vec[i])
+        .sum();
+
+      let (proof, rand_prod, claims_prod, claims_dotp) = SumcheckInstanceProof::prove_cubic_batched(
+        &claim,
+        num_rounds_prod,
+        poly_vec_par,
+        poly_vec_seq,
+        &coeff_vec,
+        comb_func_prod,
+        transcript,
+      );
+
+      let (claims_prod_left, claims_prod_right, _claims_eq) = claims_prod;
+      for i in 0..prod_circuit_vec.len() {
+        transcript.append_scalar(b"claim_prod_left", &claims_prod_left[i]);
+        transcript.append_scalar(b"claim_prod_right", &claims_prod_right[i]);
+      }
+
+      if layer_id == 0 && !dotp_circuit_vec.is_empty() {
+        let (claims_dotp_left, claims_dotp_right, claims_dotp_weight) = claims_dotp;
+        for i in 0..dotp_circuit_vec.len() {
+          transcript.append_scalar(b"claim_dotp_left", &claims_dotp_left[i]);
+          transcript.append_scalar(b"claim_dotp_right", &claims_dotp_right[i]);
+          transcript.append_scalar(b"claim_dotp_weight", &claims_dotp_weight[i]);
+        }
+        claims_dotp_final = (claims_dotp_left, claims_dotp_right, claims_dotp_weight);
+      }
+
+      // produce a random challenge to condense two claims into a single claim
+      let r_layer = transcript.challenge_scalar(b"challenge_r_layer");
+
+      claims_to_verify = (0..prod_circuit_vec.len())
+        .map(|i| claims_prod_left[i] + r_layer * (claims_prod_right[i] - claims_prod_left[i]))
+        .collect::<Vec<Scalar>>();
+
+      let mut ext = vec![r_layer];
+      ext.extend(rand_prod);
+      rand = ext;
+
+      proof_layers.push(LayerProofBatched {
+        proof,
+        claims_prod_left,
+        claims_prod_right,
+      });
+    }
+
+    (
+      ProductCircuitEvalProofBatched {
+        proof: proof_layers,
+        claims_dotp: claims_dotp_final,
+      },
+      rand,
+    )
+  }
+
+  pub fn verify(
+    &self,
+    claims_prod_vec: &[Scalar],
+    claims_dotp_vec: &[Scalar],
+    len: usize,
+    transcript: &mut Transcript,
+  ) -> (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>) {
+    let num_layers = len.log_2();
+    let mut rand: Vec<Scalar> = Vec::new();
+    //let mut num_rounds = 0;
+    assert_eq!(self.proof.len(), num_layers);
+
+    let mut claims_to_verify = claims_prod_vec.to_owned();
+    let mut claims_to_verify_dotp: Vec<Scalar> = Vec::new();
+    for (num_rounds, i) in (0..num_layers).enumerate() {
+      if i == num_layers - 1 {
+        claims_to_verify.extend(claims_dotp_vec);
+      }
+
+      // produce random coefficients, one for each instance
+      let coeff_vec =
+        transcript.challenge_vector(b"rand_coeffs_next_layer", claims_to_verify.len());
+
+      // produce a joint claim
+      let claim = (0..claims_to_verify.len())
+        .map(|i| claims_to_verify[i] * coeff_vec[i])
+        .sum();
+
+      let (claim_last, rand_prod) = self.proof[i].verify(claim, num_rounds, 3, transcript);
+
+      let claims_prod_left = &self.proof[i].claims_prod_left;
+      let claims_prod_right = &self.proof[i].claims_prod_right;
+      assert_eq!(claims_prod_left.len(), claims_prod_vec.len());
+      assert_eq!(claims_prod_right.len(), claims_prod_vec.len());
+
+      for i in 0..claims_prod_vec.len() {
+        transcript.append_scalar(b"claim_prod_left", &claims_prod_left[i]);
+        transcript.append_scalar(b"claim_prod_right", &claims_prod_right[i]);
+      }
+
+      assert_eq!(rand.len(), rand_prod.len());
+      let eq: Scalar = (0..rand.len())
+        .map(|i| {
+          rand[i] * rand_prod[i] + (Scalar::one() - rand[i]) * (Scalar::one() - rand_prod[i])
+        })
+        .product();
+      let mut claim_expected: Scalar = (0..claims_prod_vec.len())
+        .map(|i| coeff_vec[i] * (claims_prod_left[i] * claims_prod_right[i] * eq))
+        .sum();
+
+      // add claims from the dotp instances
+      if i == num_layers - 1 {
+        let num_prod_instances = claims_prod_vec.len();
+        let (claims_dotp_left, claims_dotp_right, claims_dotp_weight) = &self.claims_dotp;
+        for i in 0..claims_dotp_left.len() {
+          transcript.append_scalar(b"claim_dotp_left", &claims_dotp_left[i]);
+          transcript.append_scalar(b"claim_dotp_right", &claims_dotp_right[i]);
+          transcript.append_scalar(b"claim_dotp_weight", &claims_dotp_weight[i]);
+
+          claim_expected += coeff_vec[i + num_prod_instances]
+            * claims_dotp_left[i]
+            * claims_dotp_right[i]
+            * claims_dotp_weight[i];
+        }
+      }
+
+      assert_eq!(claim_expected, claim_last);
+
+      // produce a random challenge
+      let r_layer = transcript.challenge_scalar(b"challenge_r_layer");
+
+      claims_to_verify = (0..claims_prod_left.len())
+        .map(|i| claims_prod_left[i] + r_layer * (claims_prod_right[i] - claims_prod_left[i]))
+        .collect::<Vec<Scalar>>();
+
+      // add claims to verify for dotp circuit
+      if i == num_layers - 1 {
+        let (claims_dotp_left, claims_dotp_right, claims_dotp_weight) = &self.claims_dotp;
+
+        for i in 0..claims_dotp_vec.len() / 2 {
+          // combine left claims
+          let claim_left = claims_dotp_left[2 * i]
+            + r_layer * (claims_dotp_left[2 * i + 1] - claims_dotp_left[2 * i]);
+
+          let claim_right = claims_dotp_right[2 * i]
+            + r_layer * (claims_dotp_right[2 * i + 1] - claims_dotp_right[2 * i]);
+
+          let claim_weight = claims_dotp_weight[2 * i]
+            + r_layer * (claims_dotp_weight[2 * i + 1] - claims_dotp_weight[2 * i]);
+          claims_to_verify_dotp.push(claim_left);
+          claims_to_verify_dotp.push(claim_right);
+          claims_to_verify_dotp.push(claim_weight);
+        }
+      }
+
+      let mut ext = vec![r_layer];
+      ext.extend(rand_prod);
+      rand = ext;
+    }
+    (claims_to_verify, claims_to_verify_dotp, rand)
+  }
+}

packages/Spartan-secq/src/r1csinstance.rs

@@ -0,0 +1,367 @@
+use crate::transcript::AppendToTranscript;
+
+use super::dense_mlpoly::DensePolynomial;
+use super::errors::ProofVerifyError;
+use super::math::Math;
+use super::random::RandomTape;
+use super::scalar::Scalar;
+use super::sparse_mlpoly::{
+  MultiSparseMatPolynomialAsDense, SparseMatEntry, SparseMatPolyCommitment,
+  SparseMatPolyCommitmentGens, SparseMatPolyEvalProof, SparseMatPolynomial,
+};
+use super::timer::Timer;
+use flate2::{write::ZlibEncoder, Compression};
+use merlin::Transcript;
+use rand_core::OsRng;
+use serde::{Deserialize, Serialize};
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct R1CSInstance {
+  num_cons: usize,
+  num_vars: usize,
+  num_inputs: usize,
+  A: SparseMatPolynomial,
+  B: SparseMatPolynomial,
+  C: SparseMatPolynomial,
+}
+
+pub struct R1CSCommitmentGens {
+  gens: SparseMatPolyCommitmentGens,
+}
+
+impl R1CSCommitmentGens {
+  pub fn new(
+    label: &'static [u8],
+    num_cons: usize,
+    num_vars: usize,
+    num_inputs: usize,
+    num_nz_entries: usize,
+  ) -> R1CSCommitmentGens {
+    assert!(num_inputs < num_vars);
+    let num_poly_vars_x = num_cons.log_2();
+    let num_poly_vars_y = (2 * num_vars).log_2();
+    let gens =
+      SparseMatPolyCommitmentGens::new(label, num_poly_vars_x, num_poly_vars_y, num_nz_entries, 3);
+    R1CSCommitmentGens { gens }
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct R1CSCommitment {
+  num_cons: usize,
+  num_vars: usize,
+  num_inputs: usize,
+  comm: SparseMatPolyCommitment,
+}
+
+impl AppendToTranscript for R1CSCommitment {
+  fn append_to_transcript(&self, _label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_u64(b"num_cons", self.num_cons as u64);
+    transcript.append_u64(b"num_vars", self.num_vars as u64);
+    transcript.append_u64(b"num_inputs", self.num_inputs as u64);
+    self.comm.append_to_transcript(b"comm", transcript);
+  }
+}
+
+pub struct R1CSDecommitment {
+  dense: MultiSparseMatPolynomialAsDense,
+}
+
+impl R1CSCommitment {
+  pub fn get_num_cons(&self) -> usize {
+    self.num_cons
+  }
+
+  pub fn get_num_vars(&self) -> usize {
+    self.num_vars
+  }
+
+  pub fn get_num_inputs(&self) -> usize {
+    self.num_inputs
+  }
+}
+
+impl R1CSInstance {
+  pub fn new(
+    num_cons: usize,
+    num_vars: usize,
+    num_inputs: usize,
+    A: &[(usize, usize, Scalar)],
+    B: &[(usize, usize, Scalar)],
+    C: &[(usize, usize, Scalar)],
+  ) -> R1CSInstance {
+    Timer::print(&format!("number_of_constraints {}", num_cons));
+    Timer::print(&format!("number_of_variables {}", num_vars));
+    Timer::print(&format!("number_of_inputs {}", num_inputs));
+    Timer::print(&format!("number_non-zero_entries_A {}", A.len()));
+    Timer::print(&format!("number_non-zero_entries_B {}", B.len()));
+    Timer::print(&format!("number_non-zero_entries_C {}", C.len()));
+
+    // check that num_cons is a power of 2
+    assert_eq!(num_cons.next_power_of_two(), num_cons);
+
+    // check that num_vars is a power of 2
+    assert_eq!(num_vars.next_power_of_two(), num_vars);
+
+    // check that number_inputs + 1 <= num_vars
+    assert!(num_inputs < num_vars);
+
+    // no errors, so create polynomials
+    let num_poly_vars_x = num_cons.log_2();
+    let num_poly_vars_y = (2 * num_vars).log_2();
+
+    let mat_A = (0..A.len())
+      .map(|i| SparseMatEntry::new(A[i].0, A[i].1, A[i].2))
+      .collect::<Vec<SparseMatEntry>>();
+    let mat_B = (0..B.len())
+      .map(|i| SparseMatEntry::new(B[i].0, B[i].1, B[i].2))
+      .collect::<Vec<SparseMatEntry>>();
+    let mat_C = (0..C.len())
+      .map(|i| SparseMatEntry::new(C[i].0, C[i].1, C[i].2))
+      .collect::<Vec<SparseMatEntry>>();
+
+    let poly_A = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_A);
+    let poly_B = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_B);
+    let poly_C = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, mat_C);
+
+    R1CSInstance {
+      num_cons,
+      num_vars,
+      num_inputs,
+      A: poly_A,
+      B: poly_B,
+      C: poly_C,
+    }
+  }
+
+  pub fn get_num_vars(&self) -> usize {
+    self.num_vars
+  }
+
+  pub fn get_num_cons(&self) -> usize {
+    self.num_cons
+  }
+
+  pub fn get_num_inputs(&self) -> usize {
+    self.num_inputs
+  }
+
+  pub fn get_digest(&self) -> Vec<u8> {
+    let mut encoder = ZlibEncoder::new(Vec::new(), Compression::default());
+    bincode::serialize_into(&mut encoder, &self).unwrap();
+    encoder.finish().unwrap()
+  }
+
+  pub fn produce_synthetic_r1cs(
+    num_cons: usize,
+    num_vars: usize,
+    num_inputs: usize,
+  ) -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
+    Timer::print(&format!("number_of_constraints {}", num_cons));
+    Timer::print(&format!("number_of_variables {}", num_vars));
+    Timer::print(&format!("number_of_inputs {}", num_inputs));
+
+    let mut csprng: OsRng = OsRng;
+
+    // assert num_cons and num_vars are power of 2
+    assert_eq!((num_cons.log_2()).pow2(), num_cons);
+    assert_eq!((num_vars.log_2()).pow2(), num_vars);
+
+    // num_inputs + 1 <= num_vars
+    assert!(num_inputs < num_vars);
+
+    // z is organized as [vars,1,io]
+    let size_z = num_vars + num_inputs + 1;
+
+    // produce a random satisfying assignment
+    let Z = {
+      let mut Z: Vec<Scalar> = (0..size_z)
+        .map(|_i| Scalar::random(&mut csprng))
+        .collect::<Vec<Scalar>>();
+      Z[num_vars] = Scalar::one(); // set the constant term to 1
+      Z
+    };
+
+    // three sparse matrices
+    let mut A: Vec<SparseMatEntry> = Vec::new();
+    let mut B: Vec<SparseMatEntry> = Vec::new();
+    let mut C: Vec<SparseMatEntry> = Vec::new();
+    let one = Scalar::one();
+    for i in 0..num_cons {
+      let A_idx = i % size_z;
+      let B_idx = (i + 2) % size_z;
+      A.push(SparseMatEntry::new(i, A_idx, one));
+      B.push(SparseMatEntry::new(i, B_idx, one));
+      let AB_val = Z[A_idx] * Z[B_idx];
+
+      let C_idx = (i + 3) % size_z;
+      let C_val = Z[C_idx];
+
+      if C_val == Scalar::zero() {
+        C.push(SparseMatEntry::new(i, num_vars, AB_val));
+      } else {
+        C.push(SparseMatEntry::new(
+          i,
+          C_idx,
+          AB_val * C_val.invert().unwrap(),
+        ));
+      }
+    }
+
+    Timer::print(&format!("number_non-zero_entries_A {}", A.len()));
+    Timer::print(&format!("number_non-zero_entries_B {}", B.len()));
+    Timer::print(&format!("number_non-zero_entries_C {}", C.len()));
+
+    let num_poly_vars_x = num_cons.log_2();
+    let num_poly_vars_y = (2 * num_vars).log_2();
+    let poly_A = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, A);
+    let poly_B = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, B);
+    let poly_C = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, C);
+
+    let inst = R1CSInstance {
+      num_cons,
+      num_vars,
+      num_inputs,
+      A: poly_A,
+      B: poly_B,
+      C: poly_C,
+    };
+
+    assert!(inst.is_sat(&Z[..num_vars], &Z[num_vars + 1..]));
+
+    (inst, Z[..num_vars].to_vec(), Z[num_vars + 1..].to_vec())
+  }
+
+  pub fn is_sat(&self, vars: &[Scalar], input: &[Scalar]) -> bool {
+    assert_eq!(vars.len(), self.num_vars);
+    assert_eq!(input.len(), self.num_inputs);
+
+    let z = {
+      let mut z = vars.to_vec();
+      z.extend(&vec![Scalar::one()]);
+      z.extend(input);
+      z
+    };
+
+    // verify if Az * Bz - Cz = [0...]
+    let Az = self
+      .A
+      .multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
+    let Bz = self
+      .B
+      .multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
+    let Cz = self
+      .C
+      .multiply_vec(self.num_cons, self.num_vars + self.num_inputs + 1, &z);
+
+    assert_eq!(Az.len(), self.num_cons);
+    assert_eq!(Bz.len(), self.num_cons);
+    assert_eq!(Cz.len(), self.num_cons);
+    let res: usize = (0..self.num_cons)
+      .map(|i| usize::from(Az[i] * Bz[i] != Cz[i]))
+      .sum();
+
+    res == 0
+  }
+
+  pub fn multiply_vec(
+    &self,
+    num_rows: usize,
+    num_cols: usize,
+    z: &[Scalar],
+  ) -> (DensePolynomial, DensePolynomial, DensePolynomial) {
+    assert_eq!(num_rows, self.num_cons);
+    assert_eq!(z.len(), num_cols);
+    assert!(num_cols > self.num_vars);
+    (
+      DensePolynomial::new(self.A.multiply_vec(num_rows, num_cols, z)),
+      DensePolynomial::new(self.B.multiply_vec(num_rows, num_cols, z)),
+      DensePolynomial::new(self.C.multiply_vec(num_rows, num_cols, z)),
+    )
+  }
+
+  pub fn compute_eval_table_sparse(
+    &self,
+    num_rows: usize,
+    num_cols: usize,
+    evals: &[Scalar],
+  ) -> (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>) {
+    assert_eq!(num_rows, self.num_cons);
+    assert!(num_cols > self.num_vars);
+
+    let evals_A = self.A.compute_eval_table_sparse(evals, num_rows, num_cols);
+    let evals_B = self.B.compute_eval_table_sparse(evals, num_rows, num_cols);
+    let evals_C = self.C.compute_eval_table_sparse(evals, num_rows, num_cols);
+
+    (evals_A, evals_B, evals_C)
+  }
+
+  pub fn evaluate(&self, rx: &[Scalar], ry: &[Scalar]) -> (Scalar, Scalar, Scalar) {
+    let evals = SparseMatPolynomial::multi_evaluate(&[&self.A, &self.B, &self.C], rx, ry);
+    (evals[0], evals[1], evals[2])
+  }
+
+  pub fn commit(&self, gens: &R1CSCommitmentGens) -> (R1CSCommitment, R1CSDecommitment) {
+    let (comm, dense) = SparseMatPolynomial::multi_commit(&[&self.A, &self.B, &self.C], &gens.gens);
+    let r1cs_comm = R1CSCommitment {
+      num_cons: self.num_cons,
+      num_vars: self.num_vars,
+      num_inputs: self.num_inputs,
+      comm,
+    };
+
+    let r1cs_decomm = R1CSDecommitment { dense };
+
+    (r1cs_comm, r1cs_decomm)
+  }
+}
+
+#[derive(Debug, Serialize, Deserialize)]
+pub struct R1CSEvalProof {
+  proof: SparseMatPolyEvalProof,
+}
+
+impl R1CSEvalProof {
+  pub fn prove(
+    decomm: &R1CSDecommitment,
+    rx: &[Scalar], // point at which the polynomial is evaluated
+    ry: &[Scalar],
+    evals: &(Scalar, Scalar, Scalar),
+    gens: &R1CSCommitmentGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> R1CSEvalProof {
+    let timer = Timer::new("R1CSEvalProof::prove");
+    let proof = SparseMatPolyEvalProof::prove(
+      &decomm.dense,
+      rx,
+      ry,
+      &[evals.0, evals.1, evals.2],
+      &gens.gens,
+      transcript,
+      random_tape,
+    );
+    timer.stop();
+
+    R1CSEvalProof { proof }
+  }
+
+  pub fn verify(
+    &self,
+    comm: &R1CSCommitment,
+    rx: &[Scalar], // point at which the R1CS matrix polynomials are evaluated
+    ry: &[Scalar],
+    evals: &(Scalar, Scalar, Scalar),
+    gens: &R1CSCommitmentGens,
+    transcript: &mut Transcript,
+  ) -> Result<(), ProofVerifyError> {
+    self.proof.verify(
+      &comm.comm,
+      rx,
+      ry,
+      &[evals.0, evals.1, evals.2],
+      &gens.gens,
+      transcript,
+    )
+  }
+}

packages/Spartan-secq/src/r1csproof.rs

@@ -0,0 +1,608 @@
+#![allow(clippy::too_many_arguments)]
+use super::commitments::{Commitments, MultiCommitGens};
+use super::dense_mlpoly::{
+  DensePolynomial, EqPolynomial, PolyCommitment, PolyCommitmentGens, PolyEvalProof,
+};
+use super::errors::ProofVerifyError;
+use super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
+use super::math::Math;
+use super::nizk::{EqualityProof, KnowledgeProof, ProductProof};
+use super::r1csinstance::R1CSInstance;
+use super::random::RandomTape;
+use super::scalar::Scalar;
+use super::sparse_mlpoly::{SparsePolyEntry, SparsePolynomial};
+use super::sumcheck::ZKSumcheckInstanceProof;
+use super::timer::Timer;
+use super::transcript::{AppendToTranscript, ProofTranscript};
+use crate::group::DecompressEncodedPoint;
+use core::iter;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct R1CSProof {
+  comm_vars: PolyCommitment,
+  sc_proof_phase1: ZKSumcheckInstanceProof,
+  claims_phase2: (
+    CompressedGroup,
+    CompressedGroup,
+    CompressedGroup,
+    CompressedGroup,
+  ),
+  pok_claims_phase2: (KnowledgeProof, ProductProof),
+  proof_eq_sc_phase1: EqualityProof,
+  sc_proof_phase2: ZKSumcheckInstanceProof,
+  comm_vars_at_ry: CompressedGroup,
+  proof_eval_vars_at_ry: PolyEvalProof,
+  proof_eq_sc_phase2: EqualityProof,
+}
+
+pub struct R1CSSumcheckGens {
+  gens_1: MultiCommitGens,
+  gens_3: MultiCommitGens,
+  gens_4: MultiCommitGens,
+}
+
+// TODO: fix passing gens_1_ref
+impl R1CSSumcheckGens {
+  pub fn new(label: &'static [u8], gens_1_ref: &MultiCommitGens) -> Self {
+    let gens_1 = gens_1_ref.clone();
+    let gens_3 = MultiCommitGens::new(3, label);
+    let gens_4 = MultiCommitGens::new(4, label);
+
+    R1CSSumcheckGens {
+      gens_1,
+      gens_3,
+      gens_4,
+    }
+  }
+}
+
+pub struct R1CSGens {
+  gens_sc: R1CSSumcheckGens,
+  gens_pc: PolyCommitmentGens,
+}
+
+impl R1CSGens {
+  pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
+    let num_poly_vars = num_vars.log_2();
+    let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
+    let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
+    R1CSGens { gens_sc, gens_pc }
+  }
+}
+
+impl R1CSProof {
+  fn prove_phase_one(
+    num_rounds: usize,
+    evals_tau: &mut DensePolynomial,
+    evals_Az: &mut DensePolynomial,
+    evals_Bz: &mut DensePolynomial,
+    evals_Cz: &mut DensePolynomial,
+    gens: &R1CSSumcheckGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (ZKSumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>, Scalar) {
+    let comb_func = |poly_A_comp: &Scalar,
+                     poly_B_comp: &Scalar,
+                     poly_C_comp: &Scalar,
+                     poly_D_comp: &Scalar|
+     -> Scalar { poly_A_comp * (poly_B_comp * poly_C_comp - poly_D_comp) };
+
+    let (sc_proof_phase_one, r, claims, blind_claim_postsc) =
+      ZKSumcheckInstanceProof::prove_cubic_with_additive_term(
+        &Scalar::zero(), // claim is zero
+        &Scalar::zero(), // blind for claim is also zero
+        num_rounds,
+        evals_tau,
+        evals_Az,
+        evals_Bz,
+        evals_Cz,
+        comb_func,
+        &gens.gens_1,
+        &gens.gens_4,
+        transcript,
+        random_tape,
+      );
+
+    (sc_proof_phase_one, r, claims, blind_claim_postsc)
+  }
+
+  fn prove_phase_two(
+    num_rounds: usize,
+    claim: &Scalar,
+    blind_claim: &Scalar,
+    evals_z: &mut DensePolynomial,
+    evals_ABC: &mut DensePolynomial,
+    gens: &R1CSSumcheckGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (ZKSumcheckInstanceProof, Vec<Scalar>, Vec<Scalar>, Scalar) {
+    let comb_func =
+      |poly_A_comp: &Scalar, poly_B_comp: &Scalar| -> Scalar { poly_A_comp * poly_B_comp };
+    let (sc_proof_phase_two, r, claims, blind_claim_postsc) = ZKSumcheckInstanceProof::prove_quad(
+      claim,
+      blind_claim,
+      num_rounds,
+      evals_z,
+      evals_ABC,
+      comb_func,
+      &gens.gens_1,
+      &gens.gens_3,
+      transcript,
+      random_tape,
+    );
+
+    (sc_proof_phase_two, r, claims, blind_claim_postsc)
+  }
+
+  fn protocol_name() -> &'static [u8] {
+    b"R1CS proof"
+  }
+
+  pub fn prove(
+    inst: &R1CSInstance,
+    vars: Vec<Scalar>,
+    input: &[Scalar],
+    gens: &R1CSGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (R1CSProof, Vec<Scalar>, Vec<Scalar>) {
+    let timer_prove = Timer::new("R1CSProof::prove");
+    transcript.append_protocol_name(R1CSProof::protocol_name());
+
+    // we currently require the number of |inputs| + 1 to be at most number of vars
+    assert!(input.len() < vars.len());
+
+    input.append_to_transcript(b"input", transcript);
+
+    let timer_commit = Timer::new("polycommit");
+    let (poly_vars, comm_vars, blinds_vars) = {
+      // create a multilinear polynomial using the supplied assignment for variables
+      let poly_vars = DensePolynomial::new(vars.clone());
+
+      // produce a commitment to the satisfying assignment
+      let (comm_vars, blinds_vars) = poly_vars.commit(&gens.gens_pc, Some(random_tape));
+
+      // add the commitment to the prover's transcript
+      comm_vars.append_to_transcript(b"poly_commitment", transcript);
+      (poly_vars, comm_vars, blinds_vars)
+    };
+    timer_commit.stop();
+
+    let timer_sc_proof_phase1 = Timer::new("prove_sc_phase_one");
+
+    // append input to variables to create a single vector z
+    let z = {
+      let num_inputs = input.len();
+      let num_vars = vars.len();
+      let mut z = vars;
+      z.extend(&vec![Scalar::one()]); // add constant term in z
+      z.extend(input);
+      z.extend(&vec![Scalar::zero(); num_vars - num_inputs - 1]); // we will pad with zeros
+      z
+    };
+
+    // derive the verifier's challenge tau
+    let (num_rounds_x, num_rounds_y) = (inst.get_num_cons().log_2(), z.len().log_2());
+    let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
+    // compute the initial evaluation table for R(\tau, x)
+    let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
+    let (mut poly_Az, mut poly_Bz, mut poly_Cz) =
+      inst.multiply_vec(inst.get_num_cons(), z.len(), &z);
+
+    let (sc_proof_phase1, rx, _claims_phase1, blind_claim_postsc1) = R1CSProof::prove_phase_one(
+      num_rounds_x,
+      &mut poly_tau,
+      &mut poly_Az,
+      &mut poly_Bz,
+      &mut poly_Cz,
+      &gens.gens_sc,
+      transcript,
+      random_tape,
+    );
+    assert_eq!(poly_tau.len(), 1);
+    assert_eq!(poly_Az.len(), 1);
+    assert_eq!(poly_Bz.len(), 1);
+    assert_eq!(poly_Cz.len(), 1);
+    timer_sc_proof_phase1.stop();
+
+    let (tau_claim, Az_claim, Bz_claim, Cz_claim) =
+      (&poly_tau[0], &poly_Az[0], &poly_Bz[0], &poly_Cz[0]);
+    let (Az_blind, Bz_blind, Cz_blind, prod_Az_Bz_blind) = (
+      random_tape.random_scalar(b"Az_blind"),
+      random_tape.random_scalar(b"Bz_blind"),
+      random_tape.random_scalar(b"Cz_blind"),
+      random_tape.random_scalar(b"prod_Az_Bz_blind"),
+    );
+
+    let (pok_Cz_claim, comm_Cz_claim) = {
+      KnowledgeProof::prove(
+        &gens.gens_sc.gens_1,
+        transcript,
+        random_tape,
+        Cz_claim,
+        &Cz_blind,
+      )
+    };
+
+    let (proof_prod, comm_Az_claim, comm_Bz_claim, comm_prod_Az_Bz_claims) = {
+      let prod = Az_claim * Bz_claim;
+      ProductProof::prove(
+        &gens.gens_sc.gens_1,
+        transcript,
+        random_tape,
+        Az_claim,
+        &Az_blind,
+        Bz_claim,
+        &Bz_blind,
+        &prod,
+        &prod_Az_Bz_blind,
+      )
+    };
+
+    comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
+    comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
+    comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
+    comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
+
+    // prove the final step of sum-check #1
+    let taus_bound_rx = tau_claim;
+    let blind_expected_claim_postsc1 = taus_bound_rx * (prod_Az_Bz_blind - Cz_blind);
+    let claim_post_phase1 = (Az_claim * Bz_claim - Cz_claim) * taus_bound_rx;
+    let (proof_eq_sc_phase1, _C1, _C2) = EqualityProof::prove(
+      &gens.gens_sc.gens_1,
+      transcript,
+      random_tape,
+      &claim_post_phase1,
+      &blind_expected_claim_postsc1,
+      &claim_post_phase1,
+      &blind_claim_postsc1,
+    );
+
+    let timer_sc_proof_phase2 = Timer::new("prove_sc_phase_two");
+    // combine the three claims into a single claim
+    let r_A = transcript.challenge_scalar(b"challenege_Az");
+    let r_B = transcript.challenge_scalar(b"challenege_Bz");
+    let r_C = transcript.challenge_scalar(b"challenege_Cz");
+    let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
+    let blind_claim_phase2 = r_A * Az_blind + r_B * Bz_blind + r_C * Cz_blind;
+
+    let evals_ABC = {
+      // compute the initial evaluation table for R(\tau, x)
+      let evals_rx = EqPolynomial::new(rx.clone()).evals();
+      let (evals_A, evals_B, evals_C) =
+        inst.compute_eval_table_sparse(inst.get_num_cons(), z.len(), &evals_rx);
+
+      assert_eq!(evals_A.len(), evals_B.len());
+      assert_eq!(evals_A.len(), evals_C.len());
+      (0..evals_A.len())
+        .map(|i| r_A * evals_A[i] + r_B * evals_B[i] + r_C * evals_C[i])
+        .collect::<Vec<Scalar>>()
+    };
+
+    // another instance of the sum-check protocol
+    let (sc_proof_phase2, ry, claims_phase2, blind_claim_postsc2) = R1CSProof::prove_phase_two(
+      num_rounds_y,
+      &claim_phase2,
+      &blind_claim_phase2,
+      &mut DensePolynomial::new(z),
+      &mut DensePolynomial::new(evals_ABC),
+      &gens.gens_sc,
+      transcript,
+      random_tape,
+    );
+    timer_sc_proof_phase2.stop();
+
+    let timer_polyeval = Timer::new("polyeval");
+    let eval_vars_at_ry = poly_vars.evaluate(&ry[1..]);
+    let blind_eval = random_tape.random_scalar(b"blind_eval");
+    let (proof_eval_vars_at_ry, comm_vars_at_ry) = PolyEvalProof::prove(
+      &poly_vars,
+      Some(&blinds_vars),
+      &ry[1..],
+      &eval_vars_at_ry,
+      Some(&blind_eval),
+      &gens.gens_pc,
+      transcript,
+      random_tape,
+    );
+    timer_polyeval.stop();
+
+    // prove the final step of sum-check #2
+    let blind_eval_Z_at_ry = (Scalar::one() - ry[0]) * blind_eval;
+    let blind_expected_claim_postsc2 = claims_phase2[1] * blind_eval_Z_at_ry;
+    let claim_post_phase2 = claims_phase2[0] * claims_phase2[1];
+    let (proof_eq_sc_phase2, _C1, _C2) = EqualityProof::prove(
+      &gens.gens_pc.gens.gens_1,
+      transcript,
+      random_tape,
+      &claim_post_phase2,
+      &blind_expected_claim_postsc2,
+      &claim_post_phase2,
+      &blind_claim_postsc2,
+    );
+
+    timer_prove.stop();
+
+    (
+      R1CSProof {
+        comm_vars,
+        sc_proof_phase1,
+        claims_phase2: (
+          comm_Az_claim,
+          comm_Bz_claim,
+          comm_Cz_claim,
+          comm_prod_Az_Bz_claims,
+        ),
+        pok_claims_phase2: (pok_Cz_claim, proof_prod),
+        proof_eq_sc_phase1,
+        sc_proof_phase2,
+        comm_vars_at_ry,
+        proof_eval_vars_at_ry,
+        proof_eq_sc_phase2,
+      },
+      rx,
+      ry,
+    )
+  }
+
+  pub fn verify(
+    &self,
+    num_vars: usize,
+    num_cons: usize,
+    input: &[Scalar],
+    evals: &(Scalar, Scalar, Scalar),
+    transcript: &mut Transcript,
+    gens: &R1CSGens,
+  ) -> Result<(Vec<Scalar>, Vec<Scalar>), ProofVerifyError> {
+    transcript.append_protocol_name(R1CSProof::protocol_name());
+
+    input.append_to_transcript(b"input", transcript);
+
+    let n = num_vars;
+    // add the commitment to the verifier's transcript
+    self
+      .comm_vars
+      .append_to_transcript(b"poly_commitment", transcript);
+
+    let (num_rounds_x, num_rounds_y) = (num_cons.log_2(), (2 * num_vars).log_2());
+
+    // derive the verifier's challenge tau
+    let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
+
+    // verify the first sum-check instance
+    let claim_phase1 = Scalar::zero()
+      .commit(&Scalar::zero(), &gens.gens_sc.gens_1)
+      .compress();
+    let (comm_claim_post_phase1, rx) = self.sc_proof_phase1.verify(
+      &claim_phase1,
+      num_rounds_x,
+      3,
+      &gens.gens_sc.gens_1,
+      &gens.gens_sc.gens_4,
+      transcript,
+    )?;
+    // perform the intermediate sum-check test with claimed Az, Bz, and Cz
+    let (comm_Az_claim, comm_Bz_claim, comm_Cz_claim, comm_prod_Az_Bz_claims) = &self.claims_phase2;
+    let (pok_Cz_claim, proof_prod) = &self.pok_claims_phase2;
+
+    pok_Cz_claim.verify(&gens.gens_sc.gens_1, transcript, comm_Cz_claim)?;
+    proof_prod.verify(
+      &gens.gens_sc.gens_1,
+      transcript,
+      comm_Az_claim,
+      comm_Bz_claim,
+      comm_prod_Az_Bz_claims,
+    )?;
+
+    comm_Az_claim.append_to_transcript(b"comm_Az_claim", transcript);
+    comm_Bz_claim.append_to_transcript(b"comm_Bz_claim", transcript);
+    comm_Cz_claim.append_to_transcript(b"comm_Cz_claim", transcript);
+    comm_prod_Az_Bz_claims.append_to_transcript(b"comm_prod_Az_Bz_claims", transcript);
+
+    let taus_bound_rx: Scalar = (0..rx.len())
+      .map(|i| rx[i] * tau[i] + (Scalar::one() - rx[i]) * (Scalar::one() - tau[i]))
+      .product();
+    let expected_claim_post_phase1 = (taus_bound_rx
+      * (comm_prod_Az_Bz_claims.decompress().unwrap() - comm_Cz_claim.decompress().unwrap()))
+    .compress();
+
+    // verify proof that expected_claim_post_phase1 == claim_post_phase1
+    self.proof_eq_sc_phase1.verify(
+      &gens.gens_sc.gens_1,
+      transcript,
+      &expected_claim_post_phase1,
+      &comm_claim_post_phase1,
+    )?;
+
+    // derive three public challenges and then derive a joint claim
+    let r_A = transcript.challenge_scalar(b"challenege_Az");
+    let r_B = transcript.challenge_scalar(b"challenege_Bz");
+    let r_C = transcript.challenge_scalar(b"challenege_Cz");
+
+    // r_A * comm_Az_claim + r_B * comm_Bz_claim + r_C * comm_Cz_claim;
+    let comm_claim_phase2 = GroupElement::vartime_multiscalar_mul(
+      iter::once(r_A)
+        .chain(iter::once(r_B))
+        .chain(iter::once(r_C))
+        .collect(),
+      iter::once(&comm_Az_claim)
+        .chain(iter::once(&comm_Bz_claim))
+        .chain(iter::once(&comm_Cz_claim))
+        .map(|pt| pt.decompress().unwrap())
+        .collect(),
+    )
+    .compress();
+
+    // verify the joint claim with a sum-check protocol
+    let (comm_claim_post_phase2, ry) = self.sc_proof_phase2.verify(
+      &comm_claim_phase2,
+      num_rounds_y,
+      2,
+      &gens.gens_sc.gens_1,
+      &gens.gens_sc.gens_3,
+      transcript,
+    )?;
+
+    // verify Z(ry) proof against the initial commitment
+    self.proof_eval_vars_at_ry.verify(
+      &gens.gens_pc,
+      transcript,
+      &ry[1..],
+      &self.comm_vars_at_ry,
+      &self.comm_vars,
+    )?;
+
+    let poly_input_eval = {
+      // constant term
+      let mut input_as_sparse_poly_entries = vec![SparsePolyEntry::new(0, Scalar::one())];
+      //remaining inputs
+      input_as_sparse_poly_entries.extend(
+        (0..input.len())
+          .map(|i| SparsePolyEntry::new(i + 1, input[i]))
+          .collect::<Vec<SparsePolyEntry>>(),
+      );
+      SparsePolynomial::new(n.log_2(), input_as_sparse_poly_entries).evaluate(&ry[1..])
+    };
+
+    // compute commitment to eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval
+    let comm_eval_Z_at_ry = GroupElement::vartime_multiscalar_mul(
+      iter::once(Scalar::one() - ry[0])
+        .chain(iter::once(ry[0]))
+        .map(|s| s)
+        .collect(),
+      iter::once(self.comm_vars_at_ry.decompress().unwrap())
+        .chain(iter::once(
+          poly_input_eval.commit(&Scalar::zero(), &gens.gens_pc.gens.gens_1),
+        ))
+        .collect(),
+    );
+
+    // perform the final check in the second sum-check protocol
+    let (eval_A_r, eval_B_r, eval_C_r) = evals;
+    let expected_claim_post_phase2 =
+      ((r_A * eval_A_r + r_B * eval_B_r + r_C * eval_C_r) * comm_eval_Z_at_ry).compress();
+    // verify proof that expected_claim_post_phase1 == claim_post_phase1
+    self.proof_eq_sc_phase2.verify(
+      &gens.gens_sc.gens_1,
+      transcript,
+      &expected_claim_post_phase2,
+      &comm_claim_post_phase2,
+    )?;
+
+    Ok((rx, ry))
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::*;
+  use rand_core::OsRng;
+
+  fn produce_tiny_r1cs() -> (R1CSInstance, Vec<Scalar>, Vec<Scalar>) {
+    // three constraints over five variables Z1, Z2, Z3, Z4, and Z5
+    // rounded to the nearest power of two
+    let num_cons = 128;
+    let num_vars = 256;
+    let num_inputs = 2;
+
+    // encode the above constraints into three matrices
+    let mut A: Vec<(usize, usize, Scalar)> = Vec::new();
+    let mut B: Vec<(usize, usize, Scalar)> = Vec::new();
+    let mut C: Vec<(usize, usize, Scalar)> = Vec::new();
+
+    let one = Scalar::one();
+    // constraint 0 entries
+    // (Z1 + Z2) * I0 - Z3 = 0;
+    A.push((0, 0, one));
+    A.push((0, 1, one));
+    B.push((0, num_vars + 1, one));
+    C.push((0, 2, one));
+
+    // constraint 1 entries
+    // (Z1 + I1) * (Z3) - Z4 = 0
+    A.push((1, 0, one));
+    A.push((1, num_vars + 2, one));
+    B.push((1, 2, one));
+    C.push((1, 3, one));
+    // constraint 3 entries
+    // Z5 * 1 - 0 = 0
+    A.push((2, 4, one));
+    B.push((2, num_vars, one));
+
+    let inst = R1CSInstance::new(num_cons, num_vars, num_inputs, &A, &B, &C);
+
+    // compute a satisfying assignment
+    let mut csprng: OsRng = OsRng;
+    let i0 = Scalar::random(&mut csprng);
+    let i1 = Scalar::random(&mut csprng);
+    let z1 = Scalar::random(&mut csprng);
+    let z2 = Scalar::random(&mut csprng);
+    let z3 = (z1 + z2) * i0; // constraint 1: (Z1 + Z2) * I0 - Z3 = 0;
+    let z4 = (z1 + i1) * z3; // constraint 2: (Z1 + I1) * (Z3) - Z4 = 0
+    let z5 = Scalar::zero(); //constraint 3
+
+    let mut vars = vec![Scalar::zero(); num_vars];
+    vars[0] = z1;
+    vars[1] = z2;
+    vars[2] = z3;
+    vars[3] = z4;
+    vars[4] = z5;
+
+    let mut input = vec![Scalar::zero(); num_inputs];
+    input[0] = i0;
+    input[1] = i1;
+
+    (inst, vars, input)
+  }
+
+  #[test]
+  fn test_tiny_r1cs() {
+    let (inst, vars, input) = tests::produce_tiny_r1cs();
+    let is_sat = inst.is_sat(&vars, &input);
+    assert!(is_sat);
+  }
+
+  #[test]
+  fn test_synthetic_r1cs() {
+    let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(1024, 1024, 10);
+    let is_sat = inst.is_sat(&vars, &input);
+    assert!(is_sat);
+  }
+
+  #[test]
+  pub fn check_r1cs_proof() {
+    let num_vars = 1024;
+    let num_cons = num_vars;
+    let num_inputs = 10;
+    let (inst, vars, input) = R1CSInstance::produce_synthetic_r1cs(num_cons, num_vars, num_inputs);
+
+    let gens = R1CSGens::new(b"test-m", num_cons, num_vars);
+
+    let mut random_tape = RandomTape::new(b"proof");
+    let mut prover_transcript = Transcript::new(b"example");
+    let (proof, rx, ry) = R1CSProof::prove(
+      &inst,
+      vars,
+      &input,
+      &gens,
+      &mut prover_transcript,
+      &mut random_tape,
+    );
+
+    let inst_evals = inst.evaluate(&rx, &ry);
+
+    let mut verifier_transcript = Transcript::new(b"example");
+    assert!(proof
+      .verify(
+        inst.get_num_vars(),
+        inst.get_num_cons(),
+        &input,
+        &inst_evals,
+        &mut verifier_transcript,
+        &gens,
+      )
+      .is_ok());
+  }
+}

packages/Spartan-secq/src/random.rs

@@ -0,0 +1,27 @@
+use super::scalar::Scalar;
+use super::transcript::ProofTranscript;
+use merlin::Transcript;
+use rand_core::OsRng;
+pub struct RandomTape {
+  tape: Transcript,
+}
+
+impl RandomTape {
+  pub fn new(name: &'static [u8]) -> Self {
+    let tape = {
+      let mut rng = OsRng::default();
+      let mut tape = Transcript::new(name);
+      tape.append_scalar(b"init_randomness", &Scalar::random(&mut rng));
+      tape
+    };
+    Self { tape }
+  }
+
+  pub fn random_scalar(&mut self, label: &'static [u8]) -> Scalar {
+    self.tape.challenge_scalar(label)
+  }
+
+  pub fn random_vector(&mut self, label: &'static [u8], len: usize) -> Vec<Scalar> {
+    self.tape.challenge_vector(label, len)
+  }
+}

packages/Spartan-secq/src/scalar/mod.rs

@@ -0,0 +1,46 @@
+use secq256k1::elliptic_curve::ops::Reduce;
+use secq256k1::U256;
+
+mod scalar;
+
+pub type Scalar = scalar::Scalar;
+pub type ScalarBytes = secq256k1::Scalar;
+
+pub trait ScalarFromPrimitives {
+  fn to_scalar(self) -> Scalar;
+}
+
+impl ScalarFromPrimitives for usize {
+  #[inline]
+  fn to_scalar(self) -> Scalar {
+    (0..self).map(|_i| Scalar::one()).sum()
+  }
+}
+
+impl ScalarFromPrimitives for bool {
+  #[inline]
+  fn to_scalar(self) -> Scalar {
+    if self {
+      Scalar::one()
+    } else {
+      Scalar::zero()
+    }
+  }
+}
+
+pub trait ScalarBytesFromScalar {
+  fn decompress_scalar(s: &Scalar) -> ScalarBytes;
+  fn decompress_vector(s: &[Scalar]) -> Vec<ScalarBytes>;
+}
+
+impl ScalarBytesFromScalar for Scalar {
+  fn decompress_scalar(s: &Scalar) -> ScalarBytes {
+    ScalarBytes::from_uint_reduced(U256::from_le_slice(&s.to_bytes()))
+  }
+
+  fn decompress_vector(s: &[Scalar]) -> Vec<ScalarBytes> {
+    (0..s.len())
+      .map(|i| Scalar::decompress_scalar(&s[i]))
+      .collect::<Vec<ScalarBytes>>()
+  }
+}

packages/Spartan-secq/src/sumcheck.rs

@@ -0,0 +1,778 @@
+#![allow(clippy::too_many_arguments)]
+#![allow(clippy::type_complexity)]
+use super::commitments::{Commitments, MultiCommitGens};
+use super::dense_mlpoly::DensePolynomial;
+use super::errors::ProofVerifyError;
+use super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul};
+use super::nizk::DotProductProof;
+use super::random::RandomTape;
+use super::scalar::Scalar;
+use super::transcript::{AppendToTranscript, ProofTranscript};
+use super::unipoly::{CompressedUniPoly, UniPoly};
+use crate::group::DecompressEncodedPoint;
+use core::iter;
+use itertools::izip;
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct SumcheckInstanceProof {
+  compressed_polys: Vec<CompressedUniPoly>,
+}
+
+impl SumcheckInstanceProof {
+  pub fn new(compressed_polys: Vec<CompressedUniPoly>) -> SumcheckInstanceProof {
+    SumcheckInstanceProof { compressed_polys }
+  }
+
+  pub fn verify(
+    &self,
+    claim: Scalar,
+    num_rounds: usize,
+    degree_bound: usize,
+    transcript: &mut Transcript,
+  ) -> Result<(Scalar, Vec<Scalar>), ProofVerifyError> {
+    let mut e = claim;
+    let mut r: Vec<Scalar> = Vec::new();
+
+    // verify that there is a univariate polynomial for each round
+    assert_eq!(self.compressed_polys.len(), num_rounds);
+    for i in 0..self.compressed_polys.len() {
+      let poly = self.compressed_polys[i].decompress(&e);
+
+      // verify degree bound
+      assert_eq!(poly.degree(), degree_bound);
+
+      // check if G_k(0) + G_k(1) = e
+      assert_eq!(poly.eval_at_zero() + poly.eval_at_one(), e);
+
+      // append the prover's message to the transcript
+      poly.append_to_transcript(b"poly", transcript);
+
+      //derive the verifier's challenge for the next round
+      let r_i = transcript.challenge_scalar(b"challenge_nextround");
+
+      r.push(r_i);
+
+      // evaluate the claimed degree-ell polynomial at r_i
+      e = poly.evaluate(&r_i);
+    }
+
+    Ok((e, r))
+  }
+}
+
+#[derive(Serialize, Deserialize, Debug)]
+pub struct ZKSumcheckInstanceProof {
+  comm_polys: Vec<CompressedGroup>,
+  comm_evals: Vec<CompressedGroup>,
+  proofs: Vec<DotProductProof>,
+}
+
+impl ZKSumcheckInstanceProof {
+  pub fn new(
+    comm_polys: Vec<CompressedGroup>,
+    comm_evals: Vec<CompressedGroup>,
+    proofs: Vec<DotProductProof>,
+  ) -> Self {
+    ZKSumcheckInstanceProof {
+      comm_polys,
+      comm_evals,
+      proofs,
+    }
+  }
+
+  pub fn verify(
+    &self,
+    comm_claim: &CompressedGroup,
+    num_rounds: usize,
+    degree_bound: usize,
+    gens_1: &MultiCommitGens,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+  ) -> Result<(CompressedGroup, Vec<Scalar>), ProofVerifyError> {
+    // verify degree bound
+    assert_eq!(gens_n.n, degree_bound + 1);
+
+    // verify that there is a univariate polynomial for each round
+    assert_eq!(self.comm_polys.len(), num_rounds);
+    assert_eq!(self.comm_evals.len(), num_rounds);
+
+    let mut r: Vec<Scalar> = Vec::new();
+    for i in 0..self.comm_polys.len() {
+      let comm_poly = &self.comm_polys[i];
+
+      // append the prover's polynomial to the transcript
+      comm_poly.append_to_transcript(b"comm_poly", transcript);
+
+      //derive the verifier's challenge for the next round
+      let r_i = transcript.challenge_scalar(b"challenge_nextround");
+
+      // verify the proof of sum-check and evals
+      let res = {
+        let comm_claim_per_round = if i == 0 {
+          comm_claim
+        } else {
+          &self.comm_evals[i - 1]
+        };
+        let comm_eval = &self.comm_evals[i];
+
+        // add two claims to transcript
+        comm_claim_per_round.append_to_transcript(b"comm_claim_per_round", transcript);
+        comm_eval.append_to_transcript(b"comm_eval", transcript);
+
+        // produce two weights
+        let w = transcript.challenge_vector(b"combine_two_claims_to_one", 2);
+
+        // compute a weighted sum of the RHS
+        let comm_target = GroupElement::vartime_multiscalar_mul(
+          w.clone(),
+          iter::once(&comm_claim_per_round)
+            .chain(iter::once(&comm_eval))
+            .map(|pt| pt.decompress().unwrap())
+            .collect(),
+        )
+        .compress();
+
+        let a = {
+          // the vector to use to decommit for sum-check test
+          let a_sc = {
+            let mut a = vec![Scalar::one(); degree_bound + 1];
+            a[0] += Scalar::one();
+            a
+          };
+
+          // the vector to use to decommit for evaluation
+          let a_eval = {
+            let mut a = vec![Scalar::one(); degree_bound + 1];
+            for j in 1..a.len() {
+              a[j] = a[j - 1] * r_i;
+            }
+            a
+          };
+
+          // take weighted sum of the two vectors using w
+          assert_eq!(a_sc.len(), a_eval.len());
+          (0..a_sc.len())
+            .map(|i| w[0] * a_sc[i] + w[1] * a_eval[i])
+            .collect::<Vec<Scalar>>()
+        };
+
+        self.proofs[i]
+          .verify(
+            gens_1,
+            gens_n,
+            transcript,
+            &a,
+            &self.comm_polys[i],
+            &comm_target,
+          )
+          .is_ok()
+      };
+      if !res {
+        return Err(ProofVerifyError::InternalError);
+      }
+
+      r.push(r_i);
+    }
+
+    Ok((self.comm_evals[self.comm_evals.len() - 1], r))
+  }
+}
+
+impl SumcheckInstanceProof {
+  pub fn prove_cubic<F>(
+    claim: &Scalar,
+    num_rounds: usize,
+    poly_A: &mut DensePolynomial,
+    poly_B: &mut DensePolynomial,
+    poly_C: &mut DensePolynomial,
+    comb_func: F,
+    transcript: &mut Transcript,
+  ) -> (Self, Vec<Scalar>, Vec<Scalar>)
+  where
+    F: Fn(&Scalar, &Scalar, &Scalar) -> Scalar,
+  {
+    let mut e = *claim;
+    let mut r: Vec<Scalar> = Vec::new();
+    let mut cubic_polys: Vec<CompressedUniPoly> = Vec::new();
+    for _j in 0..num_rounds {
+      let mut eval_point_0 = Scalar::zero();
+      let mut eval_point_2 = Scalar::zero();
+      let mut eval_point_3 = Scalar::zero();
+
+      let len = poly_A.len() / 2;
+      for i in 0..len {
+        // eval 0: bound_func is A(low)
+        eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C[i]);
+
+        // eval 2: bound_func is -A(low) + 2*A(high)
+        let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+        let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+        let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
+        eval_point_2 += comb_func(
+          &poly_A_bound_point,
+          &poly_B_bound_point,
+          &poly_C_bound_point,
+        );
+
+        // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
+        let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
+        let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
+        let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
+
+        eval_point_3 += comb_func(
+          &poly_A_bound_point,
+          &poly_B_bound_point,
+          &poly_C_bound_point,
+        );
+      }
+
+      let evals = vec![eval_point_0, e - eval_point_0, eval_point_2, eval_point_3];
+      let poly = UniPoly::from_evals(&evals);
+
+      // append the prover's message to the transcript
+      poly.append_to_transcript(b"poly", transcript);
+
+      //derive the verifier's challenge for the next round
+      let r_j = transcript.challenge_scalar(b"challenge_nextround");
+      r.push(r_j);
+      // bound all tables to the verifier's challenege
+      poly_A.bound_poly_var_top(&r_j);
+      poly_B.bound_poly_var_top(&r_j);
+      poly_C.bound_poly_var_top(&r_j);
+      e = poly.evaluate(&r_j);
+      cubic_polys.push(poly.compress());
+    }
+
+    (
+      SumcheckInstanceProof::new(cubic_polys),
+      r,
+      vec![poly_A[0], poly_B[0], poly_C[0]],
+    )
+  }
+
+  pub fn prove_cubic_batched<F>(
+    claim: &Scalar,
+    num_rounds: usize,
+    poly_vec_par: (
+      &mut Vec<&mut DensePolynomial>,
+      &mut Vec<&mut DensePolynomial>,
+      &mut DensePolynomial,
+    ),
+    poly_vec_seq: (
+      &mut Vec<&mut DensePolynomial>,
+      &mut Vec<&mut DensePolynomial>,
+      &mut Vec<&mut DensePolynomial>,
+    ),
+    coeffs: &[Scalar],
+    comb_func: F,
+    transcript: &mut Transcript,
+  ) -> (
+    Self,
+    Vec<Scalar>,
+    (Vec<Scalar>, Vec<Scalar>, Scalar),
+    (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>),
+  )
+  where
+    F: Fn(&Scalar, &Scalar, &Scalar) -> Scalar,
+  {
+    let (poly_A_vec_par, poly_B_vec_par, poly_C_par) = poly_vec_par;
+    let (poly_A_vec_seq, poly_B_vec_seq, poly_C_vec_seq) = poly_vec_seq;
+
+    //let (poly_A_vec_seq, poly_B_vec_seq, poly_C_vec_seq) = poly_vec_seq;
+    let mut e = *claim;
+    let mut r: Vec<Scalar> = Vec::new();
+    let mut cubic_polys: Vec<CompressedUniPoly> = Vec::new();
+
+    for _j in 0..num_rounds {
+      let mut evals: Vec<(Scalar, Scalar, Scalar)> = Vec::new();
+
+      for (poly_A, poly_B) in poly_A_vec_par.iter().zip(poly_B_vec_par.iter()) {
+        let mut eval_point_0 = Scalar::zero();
+        let mut eval_point_2 = Scalar::zero();
+        let mut eval_point_3 = Scalar::zero();
+
+        let len = poly_A.len() / 2;
+        for i in 0..len {
+          // eval 0: bound_func is A(low)
+          eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C_par[i]);
+
+          // eval 2: bound_func is -A(low) + 2*A(high)
+          let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C_par[len + i] + poly_C_par[len + i] - poly_C_par[i];
+          eval_point_2 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+          );
+
+          // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
+          let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C_bound_point + poly_C_par[len + i] - poly_C_par[i];
+
+          eval_point_3 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+          );
+        }
+
+        evals.push((eval_point_0, eval_point_2, eval_point_3));
+      }
+
+      for (poly_A, poly_B, poly_C) in izip!(
+        poly_A_vec_seq.iter(),
+        poly_B_vec_seq.iter(),
+        poly_C_vec_seq.iter()
+      ) {
+        let mut eval_point_0 = Scalar::zero();
+        let mut eval_point_2 = Scalar::zero();
+        let mut eval_point_3 = Scalar::zero();
+        let len = poly_A.len() / 2;
+        for i in 0..len {
+          // eval 0: bound_func is A(low)
+          eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C[i]);
+          // eval 2: bound_func is -A(low) + 2*A(high)
+          let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
+          eval_point_2 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+          );
+          // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
+          let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
+          eval_point_3 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+          );
+        }
+        evals.push((eval_point_0, eval_point_2, eval_point_3));
+      }
+
+      let evals_combined_0 = (0..evals.len()).map(|i| evals[i].0 * coeffs[i]).sum();
+      let evals_combined_2 = (0..evals.len()).map(|i| evals[i].1 * coeffs[i]).sum();
+      let evals_combined_3 = (0..evals.len()).map(|i| evals[i].2 * coeffs[i]).sum();
+
+      let evals = vec![
+        evals_combined_0,
+        e - evals_combined_0,
+        evals_combined_2,
+        evals_combined_3,
+      ];
+      let poly = UniPoly::from_evals(&evals);
+
+      // append the prover's message to the transcript
+      poly.append_to_transcript(b"poly", transcript);
+
+      //derive the verifier's challenge for the next round
+      let r_j = transcript.challenge_scalar(b"challenge_nextround");
+      r.push(r_j);
+
+      // bound all tables to the verifier's challenege
+      for (poly_A, poly_B) in poly_A_vec_par.iter_mut().zip(poly_B_vec_par.iter_mut()) {
+        poly_A.bound_poly_var_top(&r_j);
+        poly_B.bound_poly_var_top(&r_j);
+      }
+      poly_C_par.bound_poly_var_top(&r_j);
+
+      for (poly_A, poly_B, poly_C) in izip!(
+        poly_A_vec_seq.iter_mut(),
+        poly_B_vec_seq.iter_mut(),
+        poly_C_vec_seq.iter_mut()
+      ) {
+        poly_A.bound_poly_var_top(&r_j);
+        poly_B.bound_poly_var_top(&r_j);
+        poly_C.bound_poly_var_top(&r_j);
+      }
+
+      e = poly.evaluate(&r_j);
+      cubic_polys.push(poly.compress());
+    }
+
+    let poly_A_par_final = (0..poly_A_vec_par.len())
+      .map(|i| poly_A_vec_par[i][0])
+      .collect();
+    let poly_B_par_final = (0..poly_B_vec_par.len())
+      .map(|i| poly_B_vec_par[i][0])
+      .collect();
+    let claims_prod = (poly_A_par_final, poly_B_par_final, poly_C_par[0]);
+
+    let poly_A_seq_final = (0..poly_A_vec_seq.len())
+      .map(|i| poly_A_vec_seq[i][0])
+      .collect();
+    let poly_B_seq_final = (0..poly_B_vec_seq.len())
+      .map(|i| poly_B_vec_seq[i][0])
+      .collect();
+    let poly_C_seq_final = (0..poly_C_vec_seq.len())
+      .map(|i| poly_C_vec_seq[i][0])
+      .collect();
+    let claims_dotp = (poly_A_seq_final, poly_B_seq_final, poly_C_seq_final);
+
+    (
+      SumcheckInstanceProof::new(cubic_polys),
+      r,
+      claims_prod,
+      claims_dotp,
+    )
+  }
+}
+
+impl ZKSumcheckInstanceProof {
+  pub fn prove_quad<F>(
+    claim: &Scalar,
+    blind_claim: &Scalar,
+    num_rounds: usize,
+    poly_A: &mut DensePolynomial,
+    poly_B: &mut DensePolynomial,
+    comb_func: F,
+    gens_1: &MultiCommitGens,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (Self, Vec<Scalar>, Vec<Scalar>, Scalar)
+  where
+    F: Fn(&Scalar, &Scalar) -> Scalar,
+  {
+    let (blinds_poly, blinds_evals) = (
+      random_tape.random_vector(b"blinds_poly", num_rounds),
+      random_tape.random_vector(b"blinds_evals", num_rounds),
+    );
+    let mut claim_per_round = *claim;
+    let mut comm_claim_per_round = claim_per_round.commit(blind_claim, gens_1).compress();
+
+    let mut r: Vec<Scalar> = Vec::new();
+    let mut comm_polys: Vec<CompressedGroup> = Vec::new();
+    let mut comm_evals: Vec<CompressedGroup> = Vec::new();
+    let mut proofs: Vec<DotProductProof> = Vec::new();
+
+    for j in 0..num_rounds {
+      let (poly, comm_poly) = {
+        let mut eval_point_0 = Scalar::zero();
+        let mut eval_point_2 = Scalar::zero();
+
+        let len = poly_A.len() / 2;
+        for i in 0..len {
+          // eval 0: bound_func is A(low)
+          eval_point_0 += comb_func(&poly_A[i], &poly_B[i]);
+
+          // eval 2: bound_func is -A(low) + 2*A(high)
+          let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+          eval_point_2 += comb_func(&poly_A_bound_point, &poly_B_bound_point);
+        }
+
+        let evals = vec![eval_point_0, claim_per_round - eval_point_0, eval_point_2];
+        let poly = UniPoly::from_evals(&evals);
+        let comm_poly = poly.commit(gens_n, &blinds_poly[j]).compress();
+        (poly, comm_poly)
+      };
+
+      // append the prover's message to the transcript
+      comm_poly.append_to_transcript(b"comm_poly", transcript);
+      comm_polys.push(comm_poly);
+
+      //derive the verifier's challenge for the next round
+      let r_j = transcript.challenge_scalar(b"challenge_nextround");
+
+      // bound all tables to the verifier's challenege
+      poly_A.bound_poly_var_top(&r_j);
+      poly_B.bound_poly_var_top(&r_j);
+
+      // produce a proof of sum-check and of evaluation
+      let (proof, claim_next_round, comm_claim_next_round) = {
+        let eval = poly.evaluate(&r_j);
+        let comm_eval = eval.commit(&blinds_evals[j], gens_1).compress();
+
+        // we need to prove the following under homomorphic commitments:
+        // (1) poly(0) + poly(1) = claim_per_round
+        // (2) poly(r_j) = eval
+
+        // Our technique is to leverage dot product proofs:
+        // (1) we can prove: <poly_in_coeffs_form, (2, 1, 1, 1)> = claim_per_round
+        // (2) we can prove: <poly_in_coeffs_form, (1, r_j, r^2_j, ..) = eval
+        // for efficiency we batch them using random weights
+
+        // add two claims to transcript
+        comm_claim_per_round.append_to_transcript(b"comm_claim_per_round", transcript);
+        comm_eval.append_to_transcript(b"comm_eval", transcript);
+
+        // produce two weights
+        let w = transcript.challenge_vector(b"combine_two_claims_to_one", 2);
+
+        // compute a weighted sum of the RHS
+        let target = w[0] * claim_per_round + w[1] * eval;
+        let comm_target = GroupElement::vartime_multiscalar_mul(
+          w.clone(),
+          iter::once(&comm_claim_per_round)
+            .chain(iter::once(&comm_eval))
+            .map(|pt| pt.decompress().unwrap())
+            .collect(),
+        )
+        .compress();
+
+        let blind = {
+          let blind_sc = if j == 0 {
+            blind_claim
+          } else {
+            &blinds_evals[j - 1]
+          };
+
+          let blind_eval = &blinds_evals[j];
+
+          w[0] * blind_sc + w[1] * blind_eval
+        };
+        assert_eq!(target.commit(&blind, gens_1).compress(), comm_target);
+
+        let a = {
+          // the vector to use to decommit for sum-check test
+          let a_sc = {
+            let mut a = vec![Scalar::one(); poly.degree() + 1];
+            a[0] += Scalar::one();
+            a
+          };
+
+          // the vector to use to decommit for evaluation
+          let a_eval = {
+            let mut a = vec![Scalar::one(); poly.degree() + 1];
+            for j in 1..a.len() {
+              a[j] = a[j - 1] * r_j;
+            }
+            a
+          };
+
+          // take weighted sum of the two vectors using w
+          assert_eq!(a_sc.len(), a_eval.len());
+          (0..a_sc.len())
+            .map(|i| w[0] * a_sc[i] + w[1] * a_eval[i])
+            .collect::<Vec<Scalar>>()
+        };
+
+        let (proof, _comm_poly, _comm_sc_eval) = DotProductProof::prove(
+          gens_1,
+          gens_n,
+          transcript,
+          random_tape,
+          &poly.as_vec(),
+          &blinds_poly[j],
+          &a,
+          &target,
+          &blind,
+        );
+
+        (proof, eval, comm_eval)
+      };
+
+      claim_per_round = claim_next_round;
+      comm_claim_per_round = comm_claim_next_round;
+
+      proofs.push(proof);
+      r.push(r_j);
+      comm_evals.push(comm_claim_per_round);
+    }
+
+    (
+      ZKSumcheckInstanceProof::new(comm_polys, comm_evals, proofs),
+      r,
+      vec![poly_A[0], poly_B[0]],
+      blinds_evals[num_rounds - 1],
+    )
+  }
+
+  pub fn prove_cubic_with_additive_term<F>(
+    claim: &Scalar,
+    blind_claim: &Scalar,
+    num_rounds: usize,
+    poly_A: &mut DensePolynomial,
+    poly_B: &mut DensePolynomial,
+    poly_C: &mut DensePolynomial,
+    poly_D: &mut DensePolynomial,
+    comb_func: F,
+    gens_1: &MultiCommitGens,
+    gens_n: &MultiCommitGens,
+    transcript: &mut Transcript,
+    random_tape: &mut RandomTape,
+  ) -> (Self, Vec<Scalar>, Vec<Scalar>, Scalar)
+  where
+    F: Fn(&Scalar, &Scalar, &Scalar, &Scalar) -> Scalar,
+  {
+    let (blinds_poly, blinds_evals) = (
+      random_tape.random_vector(b"blinds_poly", num_rounds),
+      random_tape.random_vector(b"blinds_evals", num_rounds),
+    );
+
+    let mut claim_per_round = *claim;
+    let mut comm_claim_per_round = claim_per_round.commit(blind_claim, gens_1).compress();
+
+    let mut r: Vec<Scalar> = Vec::new();
+    let mut comm_polys: Vec<CompressedGroup> = Vec::new();
+    let mut comm_evals: Vec<CompressedGroup> = Vec::new();
+    let mut proofs: Vec<DotProductProof> = Vec::new();
+
+    for j in 0..num_rounds {
+      let (poly, comm_poly) = {
+        let mut eval_point_0 = Scalar::zero();
+        let mut eval_point_2 = Scalar::zero();
+        let mut eval_point_3 = Scalar::zero();
+
+        let len = poly_A.len() / 2;
+        for i in 0..len {
+          // eval 0: bound_func is A(low)
+          eval_point_0 += comb_func(&poly_A[i], &poly_B[i], &poly_C[i], &poly_D[i]);
+
+          // eval 2: bound_func is -A(low) + 2*A(high)
+          let poly_A_bound_point = poly_A[len + i] + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B[len + i] + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C[len + i] + poly_C[len + i] - poly_C[i];
+          let poly_D_bound_point = poly_D[len + i] + poly_D[len + i] - poly_D[i];
+          eval_point_2 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+            &poly_D_bound_point,
+          );
+
+          // eval 3: bound_func is -2A(low) + 3A(high); computed incrementally with bound_func applied to eval(2)
+          let poly_A_bound_point = poly_A_bound_point + poly_A[len + i] - poly_A[i];
+          let poly_B_bound_point = poly_B_bound_point + poly_B[len + i] - poly_B[i];
+          let poly_C_bound_point = poly_C_bound_point + poly_C[len + i] - poly_C[i];
+          let poly_D_bound_point = poly_D_bound_point + poly_D[len + i] - poly_D[i];
+          eval_point_3 += comb_func(
+            &poly_A_bound_point,
+            &poly_B_bound_point,
+            &poly_C_bound_point,
+            &poly_D_bound_point,
+          );
+        }
+
+        let evals = vec![
+          eval_point_0,
+          claim_per_round - eval_point_0,
+          eval_point_2,
+          eval_point_3,
+        ];
+        let poly = UniPoly::from_evals(&evals);
+        let comm_poly = poly.commit(gens_n, &blinds_poly[j]).compress();
+        (poly, comm_poly)
+      };
+
+      // append the prover's message to the transcript
+      comm_poly.append_to_transcript(b"comm_poly", transcript);
+      comm_polys.push(comm_poly);
+
+      //derive the verifier's challenge for the next round
+      let r_j = transcript.challenge_scalar(b"challenge_nextround");
+
+      // bound all tables to the verifier's challenege
+      poly_A.bound_poly_var_top(&r_j);
+      poly_B.bound_poly_var_top(&r_j);
+      poly_C.bound_poly_var_top(&r_j);
+      poly_D.bound_poly_var_top(&r_j);
+
+      // produce a proof of sum-check and of evaluation
+      let (proof, claim_next_round, comm_claim_next_round) = {
+        let eval = poly.evaluate(&r_j);
+        let comm_eval = eval.commit(&blinds_evals[j], gens_1).compress();
+
+        // we need to prove the following under homomorphic commitments:
+        // (1) poly(0) + poly(1) = claim_per_round
+        // (2) poly(r_j) = eval
+
+        // Our technique is to leverage dot product proofs:
+        // (1) we can prove: <poly_in_coeffs_form, (2, 1, 1, 1)> = claim_per_round
+        // (2) we can prove: <poly_in_coeffs_form, (1, r_j, r^2_j, ..) = eval
+        // for efficiency we batch them using random weights
+
+        // add two claims to transcript
+        comm_claim_per_round.append_to_transcript(b"comm_claim_per_round", transcript);
+        comm_eval.append_to_transcript(b"comm_eval", transcript);
+
+        // produce two weights
+        let w = transcript.challenge_vector(b"combine_two_claims_to_one", 2);
+
+        // compute a weighted sum of the RHS
+        let target = w[0] * claim_per_round + w[1] * eval;
+        let comm_target = GroupElement::vartime_multiscalar_mul(
+          w.clone(),
+          iter::once(&comm_claim_per_round)
+            .chain(iter::once(&comm_eval))
+            .map(|pt| pt.decompress().unwrap())
+            .collect::<Vec<GroupElement>>(),
+        )
+        .compress();
+
+        let blind = {
+          let blind_sc = if j == 0 {
+            blind_claim
+          } else {
+            &blinds_evals[j - 1]
+          };
+
+          let blind_eval = &blinds_evals[j];
+
+          w[0] * blind_sc + w[1] * blind_eval
+        };
+
+        assert_eq!(target.commit(&blind, gens_1).compress(), comm_target);
+
+        let a = {
+          // the vector to use to decommit for sum-check test
+          let a_sc = {
+            let mut a = vec![Scalar::one(); poly.degree() + 1];
+            a[0] += Scalar::one();
+            a
+          };
+
+          // the vector to use to decommit for evaluation
+          let a_eval = {
+            let mut a = vec![Scalar::one(); poly.degree() + 1];
+            for j in 1..a.len() {
+              a[j] = a[j - 1] * r_j;
+            }
+            a
+          };
+
+          // take weighted sum of the two vectors using w
+          assert_eq!(a_sc.len(), a_eval.len());
+          (0..a_sc.len())
+            .map(|i| w[0] * a_sc[i] + w[1] * a_eval[i])
+            .collect::<Vec<Scalar>>()
+        };
+
+        let (proof, _comm_poly, _comm_sc_eval) = DotProductProof::prove(
+          gens_1,
+          gens_n,
+          transcript,
+          random_tape,
+          &poly.as_vec(),
+          &blinds_poly[j],
+          &a,
+          &target,
+          &blind,
+        );
+
+        (proof, eval, comm_eval)
+      };
+
+      proofs.push(proof);
+      claim_per_round = claim_next_round;
+      comm_claim_per_round = comm_claim_next_round;
+      r.push(r_j);
+      comm_evals.push(comm_claim_per_round);
+    }
+
+    (
+      ZKSumcheckInstanceProof::new(comm_polys, comm_evals, proofs),
+      r,
+      vec![poly_A[0], poly_B[0], poly_C[0], poly_D[0]],
+      blinds_evals[num_rounds - 1],
+    )
+  }
+}

packages/Spartan-secq/src/timer.rs

@@ -0,0 +1,88 @@
+#[cfg(feature = "profile")]
+use colored::Colorize;
+#[cfg(feature = "profile")]
+use core::sync::atomic::AtomicUsize;
+#[cfg(feature = "profile")]
+use core::sync::atomic::Ordering;
+#[cfg(feature = "profile")]
+use std::time::Instant;
+
+#[cfg(feature = "profile")]
+pub static CALL_DEPTH: AtomicUsize = AtomicUsize::new(0);
+
+#[cfg(feature = "profile")]
+pub struct Timer {
+  label: String,
+  timer: Instant,
+}
+
+#[cfg(feature = "profile")]
+impl Timer {
+  #[inline(always)]
+  pub fn new(label: &str) -> Self {
+    let timer = Instant::now();
+    CALL_DEPTH.fetch_add(1, Ordering::Relaxed);
+    let star = "* ";
+    println!(
+      "{:indent$}{}{}",
+      "",
+      star,
+      label.yellow().bold(),
+      indent = 2 * CALL_DEPTH.fetch_add(0, Ordering::Relaxed)
+    );
+    Self {
+      label: label.to_string(),
+      timer,
+    }
+  }
+
+  #[inline(always)]
+  pub fn stop(&self) {
+    let duration = self.timer.elapsed();
+    let star = "* ";
+    println!(
+      "{:indent$}{}{} {:?}",
+      "",
+      star,
+      self.label.blue().bold(),
+      duration,
+      indent = 2 * CALL_DEPTH.fetch_add(0, Ordering::Relaxed)
+    );
+    CALL_DEPTH.fetch_sub(1, Ordering::Relaxed);
+  }
+
+  #[inline(always)]
+  pub fn print(msg: &str) {
+    CALL_DEPTH.fetch_add(1, Ordering::Relaxed);
+    let star = "* ";
+    println!(
+      "{:indent$}{}{}",
+      "",
+      star,
+      msg.to_string().green().bold(),
+      indent = 2 * CALL_DEPTH.fetch_add(0, Ordering::Relaxed)
+    );
+    CALL_DEPTH.fetch_sub(1, Ordering::Relaxed);
+  }
+}
+
+#[cfg(not(feature = "profile"))]
+pub struct Timer {
+  _label: String,
+}
+
+#[cfg(not(feature = "profile"))]
+impl Timer {
+  #[inline(always)]
+  pub fn new(label: &str) -> Self {
+    Self {
+      _label: label.to_string(),
+    }
+  }
+
+  #[inline(always)]
+  pub fn stop(&self) {}
+
+  #[inline(always)]
+  pub fn print(_msg: &str) {}
+}

packages/Spartan-secq/src/transcript.rs

@@ -0,0 +1,63 @@
+use super::group::CompressedGroup;
+use super::scalar::Scalar;
+use merlin::Transcript;
+
+pub trait ProofTranscript {
+  fn append_protocol_name(&mut self, protocol_name: &'static [u8]);
+  fn append_scalar(&mut self, label: &'static [u8], scalar: &Scalar);
+  fn append_point(&mut self, label: &'static [u8], point: &CompressedGroup);
+  fn challenge_scalar(&mut self, label: &'static [u8]) -> Scalar;
+  fn challenge_vector(&mut self, label: &'static [u8], len: usize) -> Vec<Scalar>;
+}
+
+impl ProofTranscript for Transcript {
+  fn append_protocol_name(&mut self, protocol_name: &'static [u8]) {
+    self.append_message(b"protocol-name", protocol_name);
+  }
+
+  fn append_scalar(&mut self, label: &'static [u8], scalar: &Scalar) {
+    self.append_message(label, &scalar.to_bytes());
+  }
+
+  fn append_point(&mut self, label: &'static [u8], point: &CompressedGroup) {
+    self.append_message(label, point.as_bytes());
+  }
+
+  fn challenge_scalar(&mut self, label: &'static [u8]) -> Scalar {
+    let mut buf = [0u8; 64];
+    self.challenge_bytes(label, &mut buf);
+    Scalar::from_bytes_wide(&buf)
+  }
+
+  fn challenge_vector(&mut self, label: &'static [u8], len: usize) -> Vec<Scalar> {
+    (0..len)
+      .map(|_i| self.challenge_scalar(label))
+      .collect::<Vec<Scalar>>()
+  }
+}
+
+pub trait AppendToTranscript {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript);
+}
+
+impl AppendToTranscript for Scalar {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_scalar(label, self);
+  }
+}
+
+impl AppendToTranscript for [Scalar] {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_message(label, b"begin_append_vector");
+    for item in self {
+      transcript.append_scalar(label, item);
+    }
+    transcript.append_message(label, b"end_append_vector");
+  }
+}
+
+impl AppendToTranscript for CompressedGroup {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_point(label, self);
+  }
+}

packages/Spartan-secq/src/unipoly.rs

@@ -0,0 +1,182 @@
+use super::commitments::{Commitments, MultiCommitGens};
+use super::group::GroupElement;
+use super::scalar::{Scalar, ScalarFromPrimitives};
+use super::transcript::{AppendToTranscript, ProofTranscript};
+use merlin::Transcript;
+use serde::{Deserialize, Serialize};
+
+// ax^2 + bx + c stored as vec![c,b,a]
+// ax^3 + bx^2 + cx + d stored as vec![d,c,b,a]
+#[derive(Debug)]
+pub struct UniPoly {
+  coeffs: Vec<Scalar>,
+}
+
+// ax^2 + bx + c stored as vec![c,a]
+// ax^3 + bx^2 + cx + d stored as vec![d,b,a]
+#[derive(Serialize, Deserialize, Debug)]
+pub struct CompressedUniPoly {
+  coeffs_except_linear_term: Vec<Scalar>,
+}
+
+impl UniPoly {
+  pub fn from_evals(evals: &[Scalar]) -> Self {
+    // we only support degree-2 or degree-3 univariate polynomials
+    assert!(evals.len() == 3 || evals.len() == 4);
+    let coeffs = if evals.len() == 3 {
+      // ax^2 + bx + c
+      let two_inv = (2_usize).to_scalar().invert().unwrap();
+
+      let c = evals[0];
+      let a = two_inv * (evals[2] - evals[1] - evals[1] + c);
+      let b = evals[1] - c - a;
+      vec![c, b, a]
+    } else {
+      // ax^3 + bx^2 + cx + d
+      let two_inv = (2_usize).to_scalar().invert().unwrap();
+      let six_inv = (6_usize).to_scalar().invert().unwrap();
+
+      let d = evals[0];
+      let a = six_inv
+        * (evals[3] - evals[2] - evals[2] - evals[2] + evals[1] + evals[1] + evals[1] - evals[0]);
+      let b = two_inv
+        * (evals[0] + evals[0] - evals[1] - evals[1] - evals[1] - evals[1] - evals[1]
+          + evals[2]
+          + evals[2]
+          + evals[2]
+          + evals[2]
+          - evals[3]);
+      let c = evals[1] - d - a - b;
+      vec![d, c, b, a]
+    };
+
+    UniPoly { coeffs }
+  }
+
+  pub fn degree(&self) -> usize {
+    self.coeffs.len() - 1
+  }
+
+  pub fn as_vec(&self) -> Vec<Scalar> {
+    self.coeffs.clone()
+  }
+
+  pub fn eval_at_zero(&self) -> Scalar {
+    self.coeffs[0]
+  }
+
+  pub fn eval_at_one(&self) -> Scalar {
+    (0..self.coeffs.len()).map(|i| self.coeffs[i]).sum()
+  }
+
+  pub fn evaluate(&self, r: &Scalar) -> Scalar {
+    let mut eval = self.coeffs[0];
+    let mut power = *r;
+    for i in 1..self.coeffs.len() {
+      eval += power * self.coeffs[i];
+      power *= r;
+    }
+    eval
+  }
+
+  pub fn compress(&self) -> CompressedUniPoly {
+    let coeffs_except_linear_term = [&self.coeffs[..1], &self.coeffs[2..]].concat();
+    assert_eq!(coeffs_except_linear_term.len() + 1, self.coeffs.len());
+    CompressedUniPoly {
+      coeffs_except_linear_term,
+    }
+  }
+
+  pub fn commit(&self, gens: &MultiCommitGens, blind: &Scalar) -> GroupElement {
+    self.coeffs.commit(blind, gens)
+  }
+}
+
+impl CompressedUniPoly {
+  // we require eval(0) + eval(1) = hint, so we can solve for the linear term as:
+  // linear_term = hint - 2 * constant_term - deg2 term - deg3 term
+  pub fn decompress(&self, hint: &Scalar) -> UniPoly {
+    let mut linear_term =
+      hint - self.coeffs_except_linear_term[0] - self.coeffs_except_linear_term[0];
+    for i in 1..self.coeffs_except_linear_term.len() {
+      linear_term -= self.coeffs_except_linear_term[i];
+    }
+
+    let mut coeffs = vec![self.coeffs_except_linear_term[0], linear_term];
+    coeffs.extend(&self.coeffs_except_linear_term[1..]);
+    assert_eq!(self.coeffs_except_linear_term.len() + 1, coeffs.len());
+    UniPoly { coeffs }
+  }
+}
+
+impl AppendToTranscript for UniPoly {
+  fn append_to_transcript(&self, label: &'static [u8], transcript: &mut Transcript) {
+    transcript.append_message(label, b"UniPoly_begin");
+    for i in 0..self.coeffs.len() {
+      transcript.append_scalar(b"coeff", &self.coeffs[i]);
+    }
+    transcript.append_message(label, b"UniPoly_end");
+  }
+}
+
+#[cfg(test)]
+mod tests {
+
+  use super::*;
+
+  #[test]
+  fn test_from_evals_quad() {
+    // polynomial is 2x^2 + 3x + 1
+    let e0 = Scalar::one();
+    let e1 = (6_usize).to_scalar();
+    let e2 = (15_usize).to_scalar();
+    let evals = vec![e0, e1, e2];
+    let poly = UniPoly::from_evals(&evals);
+
+    assert_eq!(poly.eval_at_zero(), e0);
+    assert_eq!(poly.eval_at_one(), e1);
+    assert_eq!(poly.coeffs.len(), 3);
+    assert_eq!(poly.coeffs[0], Scalar::one());
+    assert_eq!(poly.coeffs[1], (3_usize).to_scalar());
+    assert_eq!(poly.coeffs[2], (2_usize).to_scalar());
+
+    let hint = e0 + e1;
+    let compressed_poly = poly.compress();
+    let decompressed_poly = compressed_poly.decompress(&hint);
+    for i in 0..decompressed_poly.coeffs.len() {
+      assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
+    }
+
+    let e3 = (28_usize).to_scalar();
+    assert_eq!(poly.evaluate(&(3_usize).to_scalar()), e3);
+  }
+
+  #[test]
+  fn test_from_evals_cubic() {
+    // polynomial is x^3 + 2x^2 + 3x + 1
+    let e0 = Scalar::one();
+    let e1 = (7_usize).to_scalar();
+    let e2 = (23_usize).to_scalar();
+    let e3 = (55_usize).to_scalar();
+    let evals = vec![e0, e1, e2, e3];
+    let poly = UniPoly::from_evals(&evals);
+
+    assert_eq!(poly.eval_at_zero(), e0);
+    assert_eq!(poly.eval_at_one(), e1);
+    assert_eq!(poly.coeffs.len(), 4);
+    assert_eq!(poly.coeffs[0], Scalar::one());
+    assert_eq!(poly.coeffs[1], (3_usize).to_scalar());
+    assert_eq!(poly.coeffs[2], (2_usize).to_scalar());
+    assert_eq!(poly.coeffs[3], (1_usize).to_scalar());
+
+    let hint = e0 + e1;
+    let compressed_poly = poly.compress();
+    let decompressed_poly = compressed_poly.decompress(&hint);
+    for i in 0..decompressed_poly.coeffs.len() {
+      assert_eq!(decompressed_poly.coeffs[i], poly.coeffs[i]);
+    }
+
+    let e4 = (109_usize).to_scalar();
+    assert_eq!(poly.evaluate(&(4_usize).to_scalar()), e4);
+  }
+}

packages/benchmark/node/package.json

@@ -8,7 +8,7 @@
   },
   "dependencies": {
     "@ethereumjs/util": "^8.0.3",
-    "@personaelabs/spartan-ecdsa": "*"
+    "@personaelabs/spartan-ecdsa": "file:./../../lib"
   },
   "devDependencies": {
     "ts-node": "^10.9.1",

packages/benchmark/web/package.json

@@ -9,7 +9,7 @@
     "lint": "next lint"
   },
   "dependencies": {
-    "@personaelabs/spartan-ecdsa": "*",
+    "@personaelabs/spartan-ecdsa": "file:./../../lib",
     "@ethereumjs/util": "^8.0.3",
     "comlink": "^4.3.1",
     "elliptic": "^6.5.4",
@@ -17,8 +17,7 @@
     "next": "13.0.0",
     "react": "18.2.0",
     "react-dom": "18.2.0",
-    "readline": "^1.3.0",
-    "snarkjs": "^0.5.0"
+    "readline": "^1.3.0"
   },
   "devDependencies": {
     "@types/node": "18.11.7",

packages/circuit_reader/Cargo.toml

@@ -0,0 +1,22 @@
+[package]
+name = "circuit_reader"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+bincode = "1.3.3"
+secq256k1 = { path = "../secq256k1" }
+spartan = { path = "../Spartan-secq" }
+ff = "0.12.0"
+byteorder = "1.4.3"
+group = "0.12.0"
+itertools = "0.9.0"
+
+[[bin]]
+name = "gen_spartan_inst"
+path = "src/bin/gen_spartan_inst.rs"
+
+
+

packages/circuit_reader/src/bin/gen_spartan_inst.rs

@@ -0,0 +1,24 @@
+#![allow(non_snake_case)]
+use bincode;
+use circuit_reader::load_as_spartan_inst;
+use std::env::{args, current_dir};
+use std::fs::File;
+use std::io::Write;
+
+fn main() {
+    let circom_r1cs_path = args().nth(1).unwrap();
+    let output_path = args().nth(2).unwrap();
+    let num_pub_inputs = args().nth(3).unwrap().parse::<usize>().unwrap();
+
+    let root = current_dir().unwrap();
+    let circom_r1cs_path = root.join(circom_r1cs_path);
+    let spartan_inst = load_as_spartan_inst(circom_r1cs_path, num_pub_inputs);
+    let sparta_inst_bytes = bincode::serialize(&spartan_inst).unwrap();
+
+    File::create(root.join(output_path.clone()))
+        .unwrap()
+        .write_all(sparta_inst_bytes.as_slice())
+        .unwrap();
+
+    println!("Written Spartan circuit to {}", output_path);
+}

packages/circuit_reader/src/lib.rs

@@ -1,41 +1,15 @@
-#![allow(non_snake_case)]
-use bincode;
+mod circom_reader;
+
+use circom_reader::{load_r1cs_from_bin_file, R1CS};
 use ff::PrimeField;
 use libspartan::Instance;
 use secq256k1::AffinePoint;
 use secq256k1::FieldBytes;
-use spartan_wasm::circom_reader::{load_r1cs_from_bin_file, R1CS};
-use std::env::{args, current_dir};
-use std::fs::File;
-use std::io::Write;
 use std::path::PathBuf;
 
-fn main() {
-    let circuit_path = args().nth(1).unwrap();
-    let output_path = args().nth(2).unwrap();
-    let num_pub_inputs = args().nth(3).unwrap().parse::<usize>().unwrap();
-
-    let root = current_dir().unwrap();
-    let circuit_path = root.join(circuit_path);
-    let spartan_inst = load_as_spartan_inst(circuit_path, num_pub_inputs);
-    let sparta_inst_bytes = bincode::serialize(&spartan_inst).unwrap();
-
-    File::create(root.join(output_path.clone()))
-        .unwrap()
-        .write_all(sparta_inst_bytes.as_slice())
-        .unwrap();
-
-    println!("Written Spartan circuit to {}", output_path);
-}
-
 pub fn load_as_spartan_inst(circuit_file: PathBuf, num_pub_inputs: usize) -> Instance {
-    let root = current_dir().unwrap();
-
-    let circuit_file = root.join(circuit_file);
     let (r1cs, _) = load_r1cs_from_bin_file::<AffinePoint>(&circuit_file);
-
     let spartan_inst = convert_to_spartan_r1cs(&r1cs, num_pub_inputs);
-
     spartan_inst
 }
 

packages/circuits/package.json

@@ -1,6 +1,6 @@
 {
-  "name": "circuits",
-  "version": "1.0.0",
+  "name": "@personaelabs/spartan-ecdsa-circuits",
+  "version": "0.1.0",
   "main": "index.js",
   "license": "MIT",
   "dependencies": {
@@ -18,4 +18,4 @@
     "ts-jest": "^29.0.3",
     "typescript": "^4.9.4"
   }
-}
+}

packages/circuits/poseidon/poseidon_constants.circom

@@ -1,3 +1,5 @@
+pragma circom 2.1.2;
+
 function ROUND_KEYS() {
     return [
     15180568604901803243989155929934437997245952775071395385994322939386074967328,
@@ -213,4 +215,4 @@ function MDS_MATRIX() {
             70274477372358662369456035572054501601454406272695978931839980644925236550307
         ]
     ];
-}
+}

packages/lib/embedWasmBytes.ts

@@ -12,7 +12,7 @@ const embedWasmBytes = async () => {
     export const wasmBytes = new Uint8Array([${bytes.toString()}]);
   `;
 
-  fs.writeFileSync("./src/wasm/wasm_bytes.ts", file);
+  fs.writeFileSync("./src/wasm/wasmBytes.ts", file);
 };
 
 embedWasmBytes();

packages/lib/jest.config.js

@@ -3,7 +3,10 @@ module.exports = {
   preset: 'ts-jest',
   testEnvironment: 'node',
   transform: {
-    "^.+\\.js?$": "ts-jest"
+    "^.+\\.(ts|js)?$": "ts-jest"
+  },
+  moduleNameMapper: {
+    "@src/(.*)$": "<rootDir>/src/$1",
   },
   testTimeout: 600000,
 };

packages/lib/package.json

@@ -1,17 +1,32 @@
 {
   "name": "@personaelabs/spartan-ecdsa",
-  "version": "1.0.2",
-  "main": "./build/lib.js",
-  "types": "./build/lib.d.ts",
+  "version": "2.3.1",
+  "description": "Spartan-ecdsa (which to our knowledge) is the fastest open-source method to verify ECDSA (secp256k1) signatures in zero-knowledge.",
+  "keywords": [
+    "spartan",
+    "spartan-ecdsa",
+    "zk",
+    "efficient-ecdsa"
+  ],
+  "author": "Personae Labs",
+  "main": "./dist/index.js",
+  "types": "./dist/index.d.ts",
   "license": "MIT",
+  "bugs": {
+    "url": "https://github.com/personaelabs/spartan-ecdsa/issues/new"
+  },
+  "homepage": "https://github.com/personaelabs/spartan-ecdsa",
+  "publishConfig": {
+    "access": "public"
+  },
   "files": [
-    "build/**/*"
+    "dist/**/*"
   ],
   "scripts": {
-    "build": "rm -rf ./build && yarn embedWasmBytes && tsc",
+    "build": "rm -rf ./dist && yarn embedWasmBytes && tsc --project tsconfig.build.json",
     "prepublishOnly": "yarn build",
     "prepare": "yarn embedWasmBytes",
-    "embedWasmBytes": "ts-node ./embed_wasm_bytes.ts",
+    "embedWasmBytes": "ts-node ./embedWasmBytes.ts",
     "test": "jest"
   },
   "devDependencies": {
@@ -25,6 +40,6 @@
     "@ethereumjs/util": "^8.0.3",
     "@zk-kit/incremental-merkle-tree": "^1.0.0",
     "elliptic": "^6.5.4",
-    "snarkjs": "^0.5.0"
+    "snarkjs": "^0.7.1"
   }
-}
+}

packages/lib/src/config.ts

@@ -1,25 +0,0 @@
-import { ProverConfig, VerifyConfig } from "./types";
-
-// Default configs for pubkey membership proving/verifying
-export const defaultPubkeyMembershipPConfig: ProverConfig = {
-  witnessGenWasm:
-    "https://storage.googleapis.com/personae-proving-keys/membership/pubkey_membership.wasm",
-  circuit:
-    "https://storage.googleapis.com/personae-proving-keys/membership/pubkey_membership.circuit"
-};
-
-export const defaultPubkeyMembershipVConfig: VerifyConfig = {
-  circuit: defaultPubkeyMembershipPConfig.circuit
-};
-
-// Default configs for address membership proving/verifyign
-export const defaultAddressMembershipPConfig: ProverConfig = {
-  witnessGenWasm:
-    "https://storage.googleapis.com/personae-proving-keys/membership/addr_membership.wasm",
-  circuit:
-    "https://storage.googleapis.com/personae-proving-keys/membership/addr_membership.circuit"
-};
-
-export const defaultAddressMembershipVConfig: VerifyConfig = {
-  circuit: defaultAddressMembershipPConfig.circuit
-};

packages/lib/src/config/index.ts

@@ -0,0 +1,25 @@
+import { ProverConfig, VerifyConfig } from "@src/types";
+
+// Default configs for pubkey membership proving/verifying
+export const defaultPubkeyProverConfig: ProverConfig = {
+    witnessGenWasm:
+        "https://storage.googleapis.com/personae-proving-keys/membership/pubkey_membership.wasm",
+    circuit:
+        "https://storage.googleapis.com/personae-proving-keys/membership/pubkey_membership.circuit"
+};
+
+export const defaultPubkeyVerifierConfig: VerifyConfig = {
+    circuit: defaultPubkeyProverConfig.circuit
+};
+
+// Default configs for address membership proving/verifyign
+export const defaultAddressProverConfig: ProverConfig = {
+    witnessGenWasm:
+        "https://storage.googleapis.com/personae-proving-keys/membership/addr_membership.wasm",
+    circuit:
+        "https://storage.googleapis.com/personae-proving-keys/membership/addr_membership.circuit"
+};
+
+export const defaultAddressVerifierConfig: VerifyConfig = {
+    circuit: defaultAddressProverConfig.circuit
+};

packages/lib/src/core/prover.ts

@@ -1,16 +1,16 @@
-import { Profiler } from "../helpers/profiler";
-import { IProver, MerkleProof, NIZK, ProverConfig } from "../types";
-import { loadCircuit, fromSig, snarkJsWitnessGen } from "../helpers/utils";
+import { Profiler } from "@src/helpers/profiler";
+import { IProver, MerkleProof, NIZK, ProveArgs, ProverConfig } from "@src/types";
+import { loadCircuit, fromSig, snarkJsWitnessGen } from "@src/helpers/utils";
 import {
   PublicInput,
   computeEffEcdsaPubInput,
   CircuitPubInput
-} from "../helpers/public_input";
-import wasm, { init } from "../wasm";
+} from "@src/helpers/publicInputs";
+import { init, wasm } from "@src/wasm";
 import {
-  defaultPubkeyMembershipPConfig,
-  defaultAddressMembershipPConfig
-} from "../config";
+  defaultPubkeyProverConfig,
+  defaultAddressProverConfig
+} from "@src/config";
 
 /**
  * ECDSA Membership Prover
@@ -18,16 +18,22 @@ import {
 export class MembershipProver extends Profiler implements IProver {
   circuit: string;
   witnessGenWasm: string;
+  useRemoteCircuit: boolean;
 
-  constructor(options: ProverConfig) {
-    super({ enabled: options?.enableProfiler });
+  constructor({
+    enableProfiler,
+    circuit,
+    witnessGenWasm,
+    useRemoteCircuit
+  }: ProverConfig) {
+    super({ enabled: enableProfiler });
 
     if (
-      options.circuit === defaultPubkeyMembershipPConfig.circuit ||
-      options.witnessGenWasm ===
-        defaultPubkeyMembershipPConfig.witnessGenWasm ||
-      options.circuit === defaultAddressMembershipPConfig.circuit ||
-      options.witnessGenWasm === defaultAddressMembershipPConfig.witnessGenWasm
+      circuit === defaultPubkeyProverConfig.circuit ||
+      witnessGenWasm ===
+      defaultPubkeyProverConfig.witnessGenWasm ||
+      circuit === defaultAddressProverConfig.circuit ||
+      witnessGenWasm === defaultAddressProverConfig.witnessGenWasm
     ) {
       console.warn(`
       Spartan-ecdsa default config warning:
@@ -37,33 +43,16 @@ export class MembershipProver extends Profiler implements IProver {
       `);
     }
 
-    const isNode = typeof window === "undefined";
-    if (isNode) {
-      if (
-        options.circuit.includes("http") ||
-        options.witnessGenWasm.includes("http")
-      ) {
-        throw new Error(
-          `An URL was given for circuit/witnessGenWasm in Node.js environment. Please specify a local path.
-          `
-        );
-      }
-    }
-
-    this.circuit = options.circuit;
-    this.witnessGenWasm = options.witnessGenWasm;
+    this.circuit = circuit;
+    this.witnessGenWasm = witnessGenWasm;
+    this.useRemoteCircuit = useRemoteCircuit ?? false;
   }
 
   async initWasm() {
     await init();
   }
 
-  // @ts-ignore
-  async prove(
-    sig: string,
-    msgHash: Buffer,
-    merkleProof: MerkleProof
-  ): Promise<NIZK> {
+  async prove({ sig, msgHash, merkleProof }: ProveArgs): Promise<NIZK> {
     const { r, s, v } = fromSig(sig);
 
     const effEcdsaPubInput = computeEffEcdsaPubInput(r, v, msgHash);
@@ -90,7 +79,9 @@ export class MembershipProver extends Profiler implements IProver {
     this.timeEnd("Generate witness");
 
     this.time("Load circuit");
-    const circuitBin = await loadCircuit(this.circuit);
+    const useRemoteCircuit =
+      this.useRemoteCircuit || typeof window !== "undefined";
+    const circuitBin = await loadCircuit(this.circuit, useRemoteCircuit);
     this.timeEnd("Load circuit");
 
     // Get the public input in bytes

packages/lib/src/core/verifier.ts

@@ -1,25 +1,30 @@
 import {
-  defaultAddressMembershipVConfig,
-  defaultPubkeyMembershipVConfig
-} from "../config";
-import { Profiler } from "../helpers/profiler";
-import { loadCircuit } from "../helpers/utils";
-import { IVerifier, VerifyConfig } from "../types";
-import wasm, { init } from "../wasm";
-import { PublicInput, verifyEffEcdsaPubInput } from "../helpers/public_input";
+  defaultAddressVerifierConfig,
+  defaultPubkeyVerifierConfig
+} from "@src/config";
+import { Profiler } from "@src/helpers/profiler";
+import { loadCircuit } from "@src/helpers/utils";
+import { IVerifier, VerifyArgs, VerifyConfig } from "@src/types";
+import { init, wasm } from "@src/wasm";
+import { PublicInput, verifyEffEcdsaPubInput } from "@src/helpers/publicInputs";
 
 /**
  * ECDSA Membership Verifier
  */
 export class MembershipVerifier extends Profiler implements IVerifier {
   circuit: string;
+  useRemoteCircuit: boolean;
 
-  constructor(options: VerifyConfig) {
-    super({ enabled: options?.enableProfiler });
+  constructor({
+    circuit,
+    enableProfiler,
+    useRemoteCircuit
+  }: VerifyConfig) {
+    super({ enabled: enableProfiler });
 
     if (
-      options.circuit === defaultAddressMembershipVConfig.circuit ||
-      options.circuit === defaultPubkeyMembershipVConfig.circuit
+      circuit === defaultAddressVerifierConfig.circuit ||
+      circuit === defaultPubkeyVerifierConfig.circuit
     ) {
       console.warn(`
       Spartan-ecdsa default config warning:
@@ -29,19 +34,18 @@ export class MembershipVerifier extends Profiler implements IVerifier {
       `);
     }
 
-    this.circuit = options.circuit;
+    this.circuit = circuit;
+    this.useRemoteCircuit =
+      useRemoteCircuit || typeof window !== "undefined";
   }
 
   async initWasm() {
     await init();
   }
 
-  async verify(
-    proof: Uint8Array,
-    publicInputSer: Uint8Array
-  ): Promise<boolean> {
+  async verify({ proof, publicInputSer }: VerifyArgs): Promise<boolean> {
     this.time("Load circuit");
-    const circuitBin = await loadCircuit(this.circuit);
+    const circuitBin = await loadCircuit(this.circuit, this.useRemoteCircuit);
     this.timeEnd("Load circuit");
 
     this.time("Verify public input");

packages/lib/src/helpers/poseidon.ts

@@ -1,5 +1,5 @@
+import { init, wasm } from "@src/wasm";
 import { bigIntToLeBytes, bytesLeToBigInt } from "./utils";
-import wasm, { init } from "../wasm";
 
 export class Poseidon {
   hash(inputs: bigint[]): bigint {

packages/lib/src/helpers/publicInputs.ts

@@ -1,8 +1,8 @@
 var EC = require("elliptic").ec;
 const BN = require("bn.js");
 
+import { EffECDSAPubInput } from "@src/types";
 import { bytesToBigInt, bigIntToBytes } from "./utils";
-import { EffECDSAPubInput } from "../types";
 
 const ec = new EC("secp256k1");
 
@@ -109,7 +109,7 @@ export class PublicInput {
 
 /**
  * Compute the group elements T and U for efficient ecdsa
- * http://localhost:1313/posts/efficient-ecdsa-1/
+ * https://personaelabs.org/posts/efficient-ecdsa-1/
  */
 export const computeEffEcdsaPubInput = (
   r: bigint,
@@ -144,15 +144,18 @@ export const computeEffEcdsaPubInput = (
 /**
  * Verify the public values of the efficient ECDSA circuit
  */
-export const verifyEffEcdsaPubInput = (pubInput: PublicInput): boolean => {
+export const verifyEffEcdsaPubInput = ({
+  r,
+  rV,
+  msgHash,
+  circuitPubInput
+}: PublicInput): boolean => {
   const expectedCircuitInput = computeEffEcdsaPubInput(
-    pubInput.r,
-    pubInput.rV,
-    pubInput.msgHash
+    r,
+    rV,
+    msgHash
   );
 
-  const circuitPubInput = pubInput.circuitPubInput;
-
   const isValid =
     expectedCircuitInput.Tx === circuitPubInput.Tx &&
     expectedCircuitInput.Ty === circuitPubInput.Ty &&

packages/lib/src/helpers/tree.ts

@@ -1,7 +1,6 @@
 import { IncrementalMerkleTree } from "@zk-kit/incremental-merkle-tree";
 import { Poseidon } from "./poseidon";
 import { MerkleProof } from "../types";
-import { bytesToBigInt } from "./utils";
 
 export class Tree {
   depth: number;
@@ -20,6 +19,14 @@ export class Tree {
     this.treeInner.insert(leaf);
   }
 
+  delete(index: number) {
+    this.treeInner.delete(index);
+  }
+
+  leaves(): bigint[] {
+    return this.treeInner.leaves;
+  }
+
   root(): bigint {
     return this.treeInner.root;
   }
@@ -30,17 +37,14 @@ export class Tree {
 
   createProof(index: number): MerkleProof {
     const proof = this.treeInner.createProof(index);
-
-    const siblings = proof.siblings.map(s =>
-      typeof s[0] === "bigint" ? s : bytesToBigInt(s[0])
-    );
-
     return {
-      siblings,
+      siblings: proof.siblings,
       pathIndices: proof.pathIndices,
       root: proof.root
     };
   }
 
-  // TODO: Add more functions that expose the IncrementalMerkleTree API
+  verifyProof(proof: MerkleProof, leaf: bigint): boolean {
+    return this.treeInner.verifyProof({ ...proof, leaf });
+  }
 }

packages/lib/src/helpers/utils.ts

@@ -18,9 +18,11 @@ export const snarkJsWitnessGen = async (input: any, wasmFile: string) => {
 /**
  * Load a circuit from a file or URL
  */
-export const loadCircuit = async (pathOrUrl: string): Promise<Uint8Array> => {
-  const isWeb = typeof window !== "undefined";
-  if (isWeb) {
+export const loadCircuit = async (
+  pathOrUrl: string,
+  useRemoteCircuit: boolean
+): Promise<Uint8Array> => {
+  if (useRemoteCircuit) {
     return await fetchCircuit(pathOrUrl);
   } else {
     return await readCircuitFromFs(pathOrUrl);

packages/lib/src/index.ts

@@ -0,0 +1,8 @@
+export { MembershipProver } from "@src/core/prover";
+export { MembershipVerifier } from "@src/core/verifier";
+export { CircuitPubInput, PublicInput, computeEffEcdsaPubInput, verifyEffEcdsaPubInput } from "@src/helpers/publicInputs";
+export { Tree } from "@src/helpers/tree";
+export { Poseidon } from "@src/helpers/poseidon";
+export { init, wasm } from "@src/wasm/index";
+export { defaultPubkeyProverConfig as defaultPubkeyMembershipPConfig, defaultPubkeyVerifierConfig as defaultPubkeyMembershipVConfig, defaultAddressProverConfig as defaultAddressMembershipPConfig, defaultAddressVerifierConfig as defaultAddressMembershipVConfig } from "@src/config";
+export type { MerkleProof, EffECDSAPubInput, NIZK, ProverConfig, VerifyConfig, IProver, IVerifier } from "@src/types";

packages/lib/src/lib.ts

@@ -1,8 +0,0 @@
-export * from "./types";
-export * from "./helpers/public_input";
-export * from "./core/membership_prover";
-export * from "./core/membership_verifier";
-export * from "./helpers/tree";
-export * from "./helpers/poseidon";
-export * from "./wasm/index";
-export * from "./config";

packages/lib/src/types.ts

@@ -1,45 +0,0 @@
-import { PublicInput } from "./helpers/public_input";
-
-// The same structure as MerkleProof in @zk-kit/incremental-merkle-tree.
-// Not directly using MerkleProof defined in @zk-kit/incremental-merkle-tree so
-// library users can choose whatever merkle tree management method they want.
-export interface MerkleProof {
-  root: bigint;
-  siblings: bigint[];
-  pathIndices: number[];
-}
-export interface EffECDSAPubInput {
-  Tx: bigint;
-  Ty: bigint;
-  Ux: bigint;
-  Uy: bigint;
-}
-
-export interface NIZK {
-  proof: Uint8Array;
-  publicInput: PublicInput;
-}
-
-export interface ProverConfig {
-  witnessGenWasm: string;
-  circuit: string;
-  enableProfiler?: boolean;
-}
-
-export interface VerifyConfig {
-  circuit: string; // Path to circuit file compiled by Nova-Scotia
-  enableProfiler?: boolean;
-}
-
-export interface IProver {
-  circuit: string; // Path to circuit file compiled by Nova-Scotia
-  witnessGenWasm: string; // Path to witness generator wasm file generated by Circom
-
-  prove(...args: any): Promise<NIZK>;
-}
-
-export interface IVerifier {
-  circuit: string; // Path to circuit file compiled by Nova-Scotia
-
-  verify(proof: Uint8Array, publicInput: Uint8Array): Promise<boolean>;
-}

packages/lib/src/types/index.ts

@@ -0,0 +1,58 @@
+import { PublicInput } from "@src/helpers/publicInputs";
+
+// The same structure as MerkleProof in @zk-kit/incremental-merkle-tree.
+// Not directly using MerkleProof defined in @zk-kit/incremental-merkle-tree so
+// library users can choose whatever merkle tree management method they want.
+export interface MerkleProof {
+    root: bigint;
+    siblings: [bigint][];
+    pathIndices: number[];
+}
+export interface EffECDSAPubInput {
+    Tx: bigint;
+    Ty: bigint;
+    Ux: bigint;
+    Uy: bigint;
+}
+
+export interface NIZK {
+    proof: Uint8Array;
+    publicInput: PublicInput;
+}
+
+export interface ProverConfig {
+    witnessGenWasm: string;
+    circuit: string;
+    enableProfiler?: boolean;
+    useRemoteCircuit?: boolean;
+}
+
+export interface ProveArgs {
+    sig: string;
+    msgHash: Buffer,
+    merkleProof: MerkleProof;
+}
+
+export interface VerifyArgs {
+    proof: Uint8Array,
+    publicInputSer: Uint8Array
+}
+
+export interface VerifyConfig {
+    circuit: string; // Path to circuit file compiled by Nova-Scotia
+    enableProfiler?: boolean;
+    useRemoteCircuit?: boolean;
+}
+
+export interface IProver {
+    circuit: string; // Path to circuit file compiled by Nova-Scotia
+    witnessGenWasm: string; // Path to witness generator wasm file generated by Circom
+
+    prove({ sig, msgHash, merkleProof }: ProveArgs): Promise<NIZK>;
+}
+
+export interface IVerifier {
+    circuit: string; // Path to circuit file compiled by Nova-Scotia
+
+    verify({ proof, publicInputSer }: VerifyArgs): Promise<boolean>;
+}

packages/lib/src/wasm/index.ts

@@ -1,10 +1,10 @@
 import * as wasm from "./wasm";
 
-import { wasmBytes } from "./wasm_bytes";
+import { wasmBytes } from "./wasmBytes";
 
 export const init = async () => {
   await wasm.initSync(wasmBytes.buffer);
   wasm.init_panic_hook();
 };
 
-export default wasm;
+export { wasm };

packages/lib/src/wasm/wasm.d.ts

@@ -26,18 +26,16 @@ export function poseidon(input_bytes: Uint8Array): Uint8Array;
 export type InitInput = RequestInfo | URL | Response | BufferSource | WebAssembly.Module;
 
 export interface InitOutput {
+  readonly memory: WebAssembly.Memory;
   readonly prove: (a: number, b: number, c: number, d: number, e: number, f: number, g: number) => void;
   readonly verify: (a: number, b: number, c: number, d: number, e: number, f: number, g: number) => void;
   readonly poseidon: (a: number, b: number, c: number) => void;
   readonly init_panic_hook: () => void;
-  readonly memory: WebAssembly.Memory;
   readonly __wbindgen_add_to_stack_pointer: (a: number) => number;
   readonly __wbindgen_malloc: (a: number) => number;
   readonly __wbindgen_free: (a: number, b: number) => void;
   readonly __wbindgen_exn_store: (a: number) => void;
   readonly __wbindgen_realloc: (a: number, b: number, c: number) => number;
-  readonly __wbindgen_thread_destroy: () => void;
-  readonly __wbindgen_start: () => void;
 }
 
 export type SyncInitInput = BufferSource | WebAssembly.Module;
@@ -46,12 +44,10 @@ export type SyncInitInput = BufferSource | WebAssembly.Module;
 * a precompiled `WebAssembly.Module`.
 *
 * @param {SyncInitInput} module
-* @param {WebAssembly.Memory} maybe_memory
 *
 * @returns {InitOutput}
 */
-export function initSync(module: SyncInitInput, maybe_memory?: WebAssembly.Memory): InitOutput;
-
+export function initSync(module: SyncInitInput): InitOutput;
 /**
 * If `module_or_path` is {RequestInfo} or {URL}, makes a request and
 * for everything else, calls `WebAssembly.instantiate` directly.
@@ -61,4 +57,4 @@ export function initSync(module: SyncInitInput, maybe_memory?: WebAssembly.Memor
 *
 * @returns {Promise<InitOutput>}
 */
-export default function init (module_or_path?: InitInput | Promise<InitInput>, maybe_memory?: WebAssembly.Memory): Promise<InitOutput>;
+export default function __wbg_init (module_or_path?: InitInput | Promise<InitInput>, maybe_memory?: WebAssembly.Memory): Promise<InitOutput>;

packages/lib/src/wasm/wasm.js

@@ -1,7 +1,6 @@
-
 let wasm;
 
-const heap = new Array(32).fill(undefined);
+const heap = new Array(128).fill(undefined);
 
 heap.push(undefined, null, true, false);
 
@@ -10,7 +9,7 @@ function getObject(idx) { return heap[idx]; }
 let heap_next = heap.length;
 
 function dropObject(idx) {
-    if (idx < 36) return;
+    if (idx < 132) return;
     heap[idx] = heap_next;
     heap_next = idx;
 }
@@ -21,21 +20,22 @@ function takeObject(idx) {
     return ret;
 }
 
-const cachedTextDecoder = new TextDecoder('utf-8', { ignoreBOM: true, fatal: true });
+const cachedTextDecoder = (typeof TextDecoder !== 'undefined' ? new TextDecoder('utf-8', { ignoreBOM: true, fatal: true }) : { decode: () => { throw Error('TextDecoder not available') } } );
 
-cachedTextDecoder.decode();
+if (typeof TextDecoder !== 'undefined') { cachedTextDecoder.decode(); };
 
-let cachedUint8Memory0 = new Uint8Array();
+let cachedUint8Memory0 = null;
 
 function getUint8Memory0() {
-    if (cachedUint8Memory0.buffer !== wasm.memory.buffer) {
+    if (cachedUint8Memory0 === null || cachedUint8Memory0.byteLength === 0) {
         cachedUint8Memory0 = new Uint8Array(wasm.memory.buffer);
     }
     return cachedUint8Memory0;
 }
 
 function getStringFromWasm0(ptr, len) {
-    return cachedTextDecoder.decode(getUint8Memory0().slice(ptr, ptr + len));
+    ptr = ptr >>> 0;
+    return cachedTextDecoder.decode(getUint8Memory0().subarray(ptr, ptr + len));
 }
 
 function addHeapObject(obj) {
@@ -55,22 +55,23 @@ export function init_panic_hook() {
 let WASM_VECTOR_LEN = 0;
 
 function passArray8ToWasm0(arg, malloc) {
-    const ptr = malloc(arg.length * 1);
+    const ptr = malloc(arg.length * 1) >>> 0;
     getUint8Memory0().set(arg, ptr / 1);
     WASM_VECTOR_LEN = arg.length;
     return ptr;
 }
 
-let cachedInt32Memory0 = new Int32Array();
+let cachedInt32Memory0 = null;
 
 function getInt32Memory0() {
-    if (cachedInt32Memory0.buffer !== wasm.memory.buffer) {
+    if (cachedInt32Memory0 === null || cachedInt32Memory0.byteLength === 0) {
         cachedInt32Memory0 = new Int32Array(wasm.memory.buffer);
     }
     return cachedInt32Memory0;
 }
 
 function getArrayU8FromWasm0(ptr, len) {
+    ptr = ptr >>> 0;
     return getUint8Memory0().subarray(ptr / 1, ptr / 1 + len);
 }
 /**
@@ -96,9 +97,9 @@ export function prove(circuit, vars, public_inputs) {
         if (r3) {
             throw takeObject(r2);
         }
-        var v3 = getArrayU8FromWasm0(r0, r1).slice();
+        var v4 = getArrayU8FromWasm0(r0, r1).slice();
         wasm.__wbindgen_free(r0, r1 * 1);
-        return v3;
+        return v4;
     } finally {
         wasm.__wbindgen_add_to_stack_pointer(16);
     }
@@ -149,9 +150,9 @@ export function poseidon(input_bytes) {
         if (r3) {
             throw takeObject(r2);
         }
-        var v1 = getArrayU8FromWasm0(r0, r1).slice();
+        var v2 = getArrayU8FromWasm0(r0, r1).slice();
         wasm.__wbindgen_free(r0, r1 * 1);
-        return v1;
+        return v2;
     } finally {
         wasm.__wbindgen_add_to_stack_pointer(16);
     }
@@ -165,29 +166,33 @@ function handleError(f, args) {
     }
 }
 
-const cachedTextEncoder = new TextEncoder('utf-8');
+const cachedTextEncoder = (typeof TextEncoder !== 'undefined' ? new TextEncoder('utf-8') : { encode: () => { throw Error('TextEncoder not available') } } );
 
-const encodeString = function (arg, view) {
+const encodeString = (typeof cachedTextEncoder.encodeInto === 'function'
+    ? function (arg, view) {
+    return cachedTextEncoder.encodeInto(arg, view);
+}
+    : function (arg, view) {
     const buf = cachedTextEncoder.encode(arg);
     view.set(buf);
     return {
         read: arg.length,
         written: buf.length
     };
-};
+});
 
 function passStringToWasm0(arg, malloc, realloc) {
 
     if (realloc === undefined) {
         const buf = cachedTextEncoder.encode(arg);
-        const ptr = malloc(buf.length);
+        const ptr = malloc(buf.length) >>> 0;
         getUint8Memory0().subarray(ptr, ptr + buf.length).set(buf);
         WASM_VECTOR_LEN = buf.length;
         return ptr;
     }
 
     let len = arg.length;
-    let ptr = malloc(len);
+    let ptr = malloc(len) >>> 0;
 
     const mem = getUint8Memory0();
 
@@ -203,7 +208,7 @@ function passStringToWasm0(arg, malloc, realloc) {
         if (offset !== 0) {
             arg = arg.slice(offset);
         }
-        ptr = realloc(ptr, len, len = offset + arg.length * 3);
+        ptr = realloc(ptr, len, len = offset + arg.length * 3) >>> 0;
         const view = getUint8Memory0().subarray(ptr + offset, ptr + len);
         const ret = encodeString(arg, view);
 
@@ -214,7 +219,7 @@ function passStringToWasm0(arg, malloc, realloc) {
     return ptr;
 }
 
-async function load(module, imports) {
+async function __wbg_load(module, imports) {
     if (typeof Response === 'function' && module instanceof Response) {
         if (typeof WebAssembly.instantiateStreaming === 'function') {
             try {
@@ -245,10 +250,10 @@ async function load(module, imports) {
     }
 }
 
-function getImports() {
+function __wbg_get_imports() {
     const imports = {};
     imports.wbg = {};
-    imports.wbg.__wbg_crypto_e1d53a1d73fb10b8 = function(arg0) {
+    imports.wbg.__wbg_crypto_70a96de3b6b73dac = function(arg0) {
         const ret = getObject(arg0).crypto;
         return addHeapObject(ret);
     };
@@ -257,15 +262,15 @@ function getImports() {
         const ret = typeof(val) === 'object' && val !== null;
         return ret;
     };
-    imports.wbg.__wbg_process_038c26bf42b093f8 = function(arg0) {
+    imports.wbg.__wbg_process_dd1577445152112e = function(arg0) {
         const ret = getObject(arg0).process;
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_versions_ab37218d2f0b24a8 = function(arg0) {
+    imports.wbg.__wbg_versions_58036bec3add9e6f = function(arg0) {
         const ret = getObject(arg0).versions;
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_node_080f4b19d15bc1fe = function(arg0) {
+    imports.wbg.__wbg_node_6a9d28205ed5b0d8 = function(arg0) {
         const ret = getObject(arg0).node;
         return addHeapObject(ret);
     };
@@ -276,11 +281,11 @@ function getImports() {
     imports.wbg.__wbindgen_object_drop_ref = function(arg0) {
         takeObject(arg0);
     };
-    imports.wbg.__wbg_msCrypto_6e7d3e1f92610cbb = function(arg0) {
+    imports.wbg.__wbg_msCrypto_adbc770ec9eca9c7 = function(arg0) {
         const ret = getObject(arg0).msCrypto;
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_require_78a3dcfbdba9cbce = function() { return handleError(function () {
+    imports.wbg.__wbg_require_f05d779769764e82 = function() { return handleError(function () {
         const ret = module.require;
         return addHeapObject(ret);
     }, arguments) };
@@ -292,17 +297,17 @@ function getImports() {
         const ret = getStringFromWasm0(arg0, arg1);
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_getRandomValues_805f1c3d65988a5a = function() { return handleError(function (arg0, arg1) {
+    imports.wbg.__wbg_getRandomValues_3774744e221a22ad = function() { return handleError(function (arg0, arg1) {
         getObject(arg0).getRandomValues(getObject(arg1));
     }, arguments) };
-    imports.wbg.__wbg_randomFillSync_6894564c2c334c42 = function() { return handleError(function (arg0, arg1, arg2) {
-        getObject(arg0).randomFillSync(getArrayU8FromWasm0(arg1, arg2));
+    imports.wbg.__wbg_randomFillSync_e950366c42764a07 = function() { return handleError(function (arg0, arg1) {
+        getObject(arg0).randomFillSync(takeObject(arg1));
     }, arguments) };
-    imports.wbg.__wbg_newnoargs_b5b063fc6c2f0376 = function(arg0, arg1) {
+    imports.wbg.__wbg_newnoargs_e643855c6572a4a8 = function(arg0, arg1) {
         const ret = new Function(getStringFromWasm0(arg0, arg1));
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_call_97ae9d8645dc388b = function() { return handleError(function (arg0, arg1) {
+    imports.wbg.__wbg_call_f96b398515635514 = function() { return handleError(function (arg0, arg1) {
         const ret = getObject(arg0).call(getObject(arg1));
         return addHeapObject(ret);
     }, arguments) };
@@ -310,19 +315,19 @@ function getImports() {
         const ret = getObject(arg0);
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_self_6d479506f72c6a71 = function() { return handleError(function () {
+    imports.wbg.__wbg_self_b9aad7f1c618bfaf = function() { return handleError(function () {
         const ret = self.self;
         return addHeapObject(ret);
     }, arguments) };
-    imports.wbg.__wbg_window_f2557cc78490aceb = function() { return handleError(function () {
+    imports.wbg.__wbg_window_55e469842c98b086 = function() { return handleError(function () {
         const ret = window.window;
         return addHeapObject(ret);
     }, arguments) };
-    imports.wbg.__wbg_globalThis_7f206bda628d5286 = function() { return handleError(function () {
+    imports.wbg.__wbg_globalThis_d0957e302752547e = function() { return handleError(function () {
         const ret = globalThis.globalThis;
         return addHeapObject(ret);
     }, arguments) };
-    imports.wbg.__wbg_global_ba75c50d1cf384f4 = function() { return handleError(function () {
+    imports.wbg.__wbg_global_ae2f87312b8987fb = function() { return handleError(function () {
         const ret = global.global;
         return addHeapObject(ret);
     }, arguments) };
@@ -330,30 +335,30 @@ function getImports() {
         const ret = getObject(arg0) === undefined;
         return ret;
     };
-    imports.wbg.__wbg_call_168da88779e35f61 = function() { return handleError(function (arg0, arg1, arg2) {
+    imports.wbg.__wbg_call_35782e9a1aa5e091 = function() { return handleError(function (arg0, arg1, arg2) {
         const ret = getObject(arg0).call(getObject(arg1), getObject(arg2));
         return addHeapObject(ret);
     }, arguments) };
-    imports.wbg.__wbg_buffer_3f3d764d4747d564 = function(arg0) {
+    imports.wbg.__wbg_buffer_fcbfb6d88b2732e9 = function(arg0) {
         const ret = getObject(arg0).buffer;
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_new_8c3f0052272a457a = function(arg0) {
+    imports.wbg.__wbg_newwithbyteoffsetandlength_92c251989c485785 = function(arg0, arg1, arg2) {
+        const ret = new Uint8Array(getObject(arg0), arg1 >>> 0, arg2 >>> 0);
+        return addHeapObject(ret);
+    };
+    imports.wbg.__wbg_new_bc5d9aad3f9ac80e = function(arg0) {
         const ret = new Uint8Array(getObject(arg0));
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_set_83db9690f9353e79 = function(arg0, arg1, arg2) {
+    imports.wbg.__wbg_set_4b3aa8445ac1e91c = function(arg0, arg1, arg2) {
         getObject(arg0).set(getObject(arg1), arg2 >>> 0);
     };
-    imports.wbg.__wbg_length_9e1ae1900cb0fbd5 = function(arg0) {
-        const ret = getObject(arg0).length;
-        return ret;
-    };
-    imports.wbg.__wbg_newwithlength_f5933855e4f48a19 = function(arg0) {
+    imports.wbg.__wbg_newwithlength_89eca18f2603a999 = function(arg0) {
         const ret = new Uint8Array(arg0 >>> 0);
         return addHeapObject(ret);
     };
-    imports.wbg.__wbg_subarray_58ad4efbb5bcb886 = function(arg0, arg1, arg2) {
+    imports.wbg.__wbg_subarray_7649d027b2b141b3 = function(arg0, arg1, arg2) {
         const ret = getObject(arg0).subarray(arg1 >>> 0, arg2 >>> 0);
         return addHeapObject(ret);
     };
@@ -363,16 +368,20 @@ function getImports() {
     };
     imports.wbg.__wbg_stack_658279fe44541cf6 = function(arg0, arg1) {
         const ret = getObject(arg1).stack;
-        const ptr0 = passStringToWasm0(ret, wasm.__wbindgen_malloc, wasm.__wbindgen_realloc);
-        const len0 = WASM_VECTOR_LEN;
-        getInt32Memory0()[arg0 / 4 + 1] = len0;
-        getInt32Memory0()[arg0 / 4 + 0] = ptr0;
+        const ptr1 = passStringToWasm0(ret, wasm.__wbindgen_malloc, wasm.__wbindgen_realloc);
+        const len1 = WASM_VECTOR_LEN;
+        getInt32Memory0()[arg0 / 4 + 1] = len1;
+        getInt32Memory0()[arg0 / 4 + 0] = ptr1;
     };
     imports.wbg.__wbg_error_f851667af71bcfc6 = function(arg0, arg1) {
+        let deferred0_0;
+        let deferred0_1;
         try {
+            deferred0_0 = arg0;
+            deferred0_1 = arg1;
             console.error(getStringFromWasm0(arg0, arg1));
         } finally {
-            wasm.__wbindgen_free(arg0, arg1);
+            wasm.__wbindgen_free(deferred0_0, deferred0_1);
         }
     };
     imports.wbg.__wbindgen_throw = function(arg0, arg1) {
@@ -386,57 +395,60 @@ function getImports() {
     return imports;
 }
 
-function initMemory(imports, maybe_memory) {
-    imports.wbg.memory = maybe_memory || new WebAssembly.Memory({initial:18,maximum:65536,shared:true});
+function __wbg_init_memory(imports, maybe_memory) {
+
 }
 
-function finalizeInit(instance, module) {
+function __wbg_finalize_init(instance, module) {
     wasm = instance.exports;
-    init.__wbindgen_wasm_module = module;
-    cachedInt32Memory0 = new Int32Array();
-    cachedUint8Memory0 = new Uint8Array();
+    __wbg_init.__wbindgen_wasm_module = module;
+    cachedInt32Memory0 = null;
+    cachedUint8Memory0 = null;
+
 
-    wasm.__wbindgen_start();
     return wasm;
 }
 
 async function initSync(module, maybe_memory) {
-    if (!wasm) {
-        const imports = getImports();
+    if (wasm !== undefined) return wasm;
 
-        initMemory(imports, maybe_memory);
-    
-        /*
-        if (!(module instanceof WebAssembly.Module)) {
-            module = new WebAssembly.Module(module);
-        }
-        */
-       const compiled = WebAssembly.compile(module);
-    
-        const instance = await WebAssembly.instantiate(await compiled, imports);
-    
-        return finalizeInit(instance, module);
+    const imports = __wbg_get_imports();
+
+    __wbg_init_memory(imports, maybe_memory);
+
+     /*
+    if (!(module instanceof WebAssembly.Module)) {
+        module = new WebAssembly.Module(module);
     }
+    */
+    const compiled = WebAssembly.compile(module);
+
+    const instance = await WebAssembly.instantiate(await compiled, imports);
+    
+
+    return __wbg_finalize_init(instance, module);
 }
 
-async function init(input, maybe_memory) {
+async function __wbg_init(input, maybe_memory) {
+    if (wasm !== undefined) return wasm;
+
     /*
     if (typeof input === 'undefined') {
         input = new URL('spartan_wasm_bg.wasm', import.meta.url);
     }
     */
-    const imports = getImports();
+    const imports = __wbg_get_imports();
 
     if (typeof input === 'string' || (typeof Request === 'function' && input instanceof Request) || (typeof URL === 'function' && input instanceof URL)) {
         input = fetch(input);
     }
 
-    initMemory(imports, maybe_memory);
+    __wbg_init_memory(imports, maybe_memory);
 
-    const { instance, module } = await load(await input, imports);
+    const { instance, module } = await __wbg_load(await input, imports);
 
-    return finalizeInit(instance, module);
+    return __wbg_finalize_init(instance, module);
 }
 
 export { initSync }
-export default init;
+export default __wbg_init;

packages/lib/tests/efficientEcdsa.test.ts

@@ -1,9 +1,10 @@
+import { hashPersonalMessage } from "@ethereumjs/util";
+
 import {
   CircuitPubInput,
   PublicInput,
   verifyEffEcdsaPubInput
-} from "../src/helpers/public_input";
-import { hashPersonalMessage } from "@ethereumjs/util";
+} from "../src/helpers/publicInputs";
 
 describe("public_input", () => {
   /**

packages/lib/tests/membershipNizk.test.ts

@@ -1,19 +1,20 @@
-import {
-  MembershipProver,
-  MembershipVerifier,
-  Tree,
-  Poseidon,
-  NIZK
-} from "../src/lib";
 import {
   hashPersonalMessage,
   ecsign,
   privateToAddress,
   privateToPublic
 } from "@ethereumjs/util";
-var EC = require("elliptic").ec;
+
 import * as path from "path";
 
+import {
+  MembershipProver,
+  MembershipVerifier,
+  Tree,
+  Poseidon,
+  NIZK
+} from "../src";
+
 describe("membership prove and verify", () => {
   // Init prover
   const treeDepth = 20;
@@ -25,7 +26,6 @@ describe("membership prove and verify", () => {
   // Sign (Use privKeys[0] for proving)
   const proverIndex = 0;
   const proverPrivKey = privKeys[proverIndex];
-  let proverAddress: bigint;
 
   let msg = Buffer.from("harry potter");
   const msgHash = hashPersonalMessage(msg);
@@ -84,11 +84,14 @@ describe("membership prove and verify", () => {
       const index = pubKeyTree.indexOf(proverPubKeyHash as bigint);
       const merkleProof = pubKeyTree.createProof(index);
 
-      nizk = await pubKeyMembershipProver.prove(sig, msgHash, merkleProof);
+      nizk = await pubKeyMembershipProver.prove({ sig, msgHash, merkleProof });
 
       const { proof, publicInput } = nizk;
       expect(
-        await pubKeyMembershipVerifier.verify(proof, publicInput.serialize())
+        await pubKeyMembershipVerifier.verify({
+          proof,
+          publicInputSer: publicInput.serialize()
+        })
       ).toBe(true);
     });
 
@@ -97,17 +100,23 @@ describe("membership prove and verify", () => {
       let proof = nizk.proof;
       proof[0] = proof[0] += 1;
       expect(
-        await pubKeyMembershipVerifier.verify(proof, publicInput.serialize())
+        await pubKeyMembershipVerifier.verify({
+          proof,
+          publicInputSer: publicInput.serialize()
+        })
       ).toBe(false);
     });
 
     it("should assert invalid public input", async () => {
       const { proof } = nizk;
-      let publicInput = nizk.publicInput.serialize();
-      publicInput[0] = publicInput[0] += 1;
-      expect(await pubKeyMembershipVerifier.verify(proof, publicInput)).toBe(
-        false
-      );
+      let publicInputSer = nizk.publicInput.serialize();
+      publicInputSer[0] = publicInputSer[0] += 1;
+      expect(
+        await pubKeyMembershipVerifier.verify({
+          proof,
+          publicInputSer
+        })
+      ).toBe(false);
     });
   });
 
@@ -154,14 +163,14 @@ describe("membership prove and verify", () => {
 
       await addressMembershipProver.initWasm();
 
-      nizk = await addressMembershipProver.prove(sig, msgHash, merkleProof);
+      nizk = await addressMembershipProver.prove({ sig, msgHash, merkleProof });
       await addressMembershipVerifier.initWasm();
 
       expect(
-        await addressMembershipVerifier.verify(
-          nizk.proof,
-          nizk.publicInput.serialize()
-        )
+        await addressMembershipVerifier.verify({
+          proof: nizk.proof,
+          publicInputSer: nizk.publicInput.serialize()
+        })
       ).toBe(true);
     });
 
@@ -170,17 +179,23 @@ describe("membership prove and verify", () => {
       let proof = nizk.proof;
       proof[0] = proof[0] += 1;
       expect(
-        await addressMembershipVerifier.verify(proof, publicInput.serialize())
+        await addressMembershipVerifier.verify({
+          proof,
+          publicInputSer: publicInput.serialize()
+        })
       ).toBe(false);
     });
 
     it("should assert invalid public input", async () => {
       const { proof } = nizk;
-      let publicInput = nizk.publicInput.serialize();
-      publicInput[0] = publicInput[0] += 1;
-      expect(await addressMembershipVerifier.verify(proof, publicInput)).toBe(
-        false
-      );
+      let publicInputSer = nizk.publicInput.serialize();
+      publicInputSer[0] = publicInputSer[0] += 1;
+      expect(
+        await addressMembershipVerifier.verify({
+          proof,
+          publicInputSer
+        })
+      ).toBe(false);
     });
   });
 });

packages/lib/tests/tree.test.ts

@@ -0,0 +1,31 @@
+import { Tree, Poseidon } from "../src";
+
+describe("Merkle tree prove and verify", () => {
+  let poseidon: Poseidon;
+  let tree: Tree;
+  const members = new Array(10).fill(0).map((_, i) => BigInt(i));
+
+  beforeAll(async () => {
+    // Init Poseidon
+    poseidon = new Poseidon();
+    await poseidon.initWasm();
+    const treeDepth = 20;
+
+    tree = new Tree(treeDepth, poseidon);
+    for (const member of members) {
+      tree.insert(member);
+    }
+  });
+
+  it("should prove and verify a valid Merkle proof", async () => {
+    const proof = tree.createProof(0);
+    expect(tree.verifyProof(proof, members[0])).toBe(true);
+  });
+
+  it("should assert an invalid Merkle proof", async () => {
+    const proof = tree.createProof(0);
+    proof.siblings[0][0] = proof.siblings[0][0] += BigInt(1);
+    expect(tree.verifyProof(proof, members[0])).toBe(false);
+    proof.siblings[0][0] = proof.siblings[0][0] -= BigInt(1);
+  });
+});

packages/lib/tsconfig.build.json

@@ -0,0 +1,6 @@
+{
+    "extends": "./tsconfig.json",
+    "exclude": [
+        "./tests/**/*"
+    ],
+}

packages/lib/tsconfig.json

@@ -1,25 +1,31 @@
 {
+  "compilerOptions": {
+    "baseUrl": ".",
+    "rootDir": ".",
+    "outDir": "./dist",
+    "declaration": true,
+    "target": "ES6",
+    "module": "CommonJS",
+    "moduleResolution": "node",
+    "allowJs": true,
+    "esModuleInterop": true,
+    "forceConsistentCasingInFileNames": true,
+    "strict": true,
+    "skipLibCheck": true,
+    "paths": {
+      "@src/*": [
+        "src/*"
+      ]
+    },
+  },
   "include": [
     "./src/**/*",
     "./src/**/*.wasm",
+    "./tests/**/*"
   ],
   "exclude": [
     "./jest.config.js",
     "./node_modules",
-    "./tests",
-      "./build"
+    "./dist"
   ],
-  "compilerOptions": {
-    "declaration": true,
-    "target": "ES6",                           
-    "module": "CommonJS",                               
-    "rootDir": "./src",                                
-    "moduleResolution": "node",                     
-    "allowJs": true,                                 
-    "outDir": "./build",                
-    "esModuleInterop": true,                            
-    "forceConsistentCasingInFileNames": true,      
-    "strict": true,                                  
-    "skipLibCheck": true         
-  }
 }

packages/poseidon/Cargo.toml

@@ -10,6 +10,7 @@ hex = "0.4.3"
 hex-literal = "0.3.4"
 secq256k1 = { path = "../secq256k1" }
 getrandom = { version = "0.2.8", features = ["js"] }
+lazy_static = "1.4.0"
 #typenum = { version = "1.16.0", optional = true }
 #neptune = { version = "8.1.0", optional = true }
 #blstrs = { version = "0.6.0", optional = true }

packages/poseidon/src/k256_consts.rs

@@ -1,215 +1,224 @@
-pub const NUM_FULL_ROUNDS: usize = 8;
-pub const NUM_PARTIAL_ROUNDS: usize = 56;
+use ff::PrimeField;
+use lazy_static::lazy_static;
+pub use secq256k1::field::field_secp::FieldElement;
 
-pub static MDS_MATRIX: &'static [[&str; 3]; 3] = &[
-    [
-        "92469348809186613947252340883344274339611751744959319352506666082431267346705",
-        "100938028378191533449096235266991198229563815869344032449592738345766724371160",
-        "77486311749148948616988559783475694076613010381924638436641318334458515006661",
-    ],
-    [
-        "110352262556914082363749654180080464794716701228558638957603951672835474954408",
-        "27607004873684391669404739690441550149894883072418944161048725383958774443141",
-        "29671705769502357195586268679831947082918094959101307962374709600277676341325",
-    ],
-    [
-        "77762103796341032609398578911486222569419103128091016773380377798879650228751",
-        "1753012011204964731088925227042671869111026487299375073665493007998674391999",
-        "70274477372358662369456035572054501601454406272695978931839980644925236550307",
-    ],
-];
+pub(crate) const NUM_FULL_ROUNDS: usize = 8;
+pub(crate) const NUM_PARTIAL_ROUNDS: usize = 56;
 
-pub static ROUND_CONSTANTS: &'static [&str; 192] = &[
-    "15180568604901803243989155929934437997245952775071395385994322939386074967328",
-    "98155933184944822056372510812105826951789406432246960633912199752807271851218",
-    "32585497418154084368870158853355239726261349829448673320273043226636389078017",
-    "66713968576806622579829258440960693099797917756640662361943757758980796487698",
-    "61296025743283504825054745787375839406507895949474930140819919915792438454216",
-    "64548089412749542282115556935384382035671782881737715696939837764375912217104",
-    "108421562972909537718478936575770973463273651828765393113349044862621092658552",
-    "93957623861448681916560847065407918286434708744548934125771289238599801659600",
-    "31886767595881910145119755249133120645312710313371225820300496900248094187131",
-    "36511615103248888903406040506250394762206798360602726106046630438239169384653",
-    "21193239787133737740669439860809806837993750509086389566475677877580362491125",
-    "15159189447883181997488877417695825734356570617827322308691834229181804753656",
-    "19272373877630561389686073945290625876718814210798194797601715657476609730306",
-    "23132197996397121955527964729507651432518694856862854469217474256539272053037",
-    "9869753235007825662020275771343858285582964429845049469800863115040150206544",
-    "36536341316285671890133896506951910369952562161551585116256678375995315827743",
-    "62582239167707347777855528698896708360409296899261565735324151945083720570858",
-    "96597358901965097853721114962031771931271685249979807653919643952343419105640",
-    "99475971754252188104003224702005940217163363685728394033034788135108600073953",
-    "52080483875928847502018688921126796935417602445765802481027972679966274137987",
-    "101922748752417217354391348649359865075718358385248454632698502400961567227929",
-    "26980595292132221181330746499613907829041623688147011560382352796984836870749",
-    "7059991836806083192408106370472821784612460308866802565871813230060135266390",
-    "19329812920723038526370491239817117039289784665617181727933894076969997926129",
-    "65570620823578601926240439251563587376966657231502120214692324496443514623818",
-    "58403733332589349613112270854204921427257113546270812628317365115158685715742",
-    "45021021211732634759643776743541935700591354899980928498981462362035961745443",
-    "313468157086800401026946312285365733155132234906935411743639256319782592571",
-    "101316949793045093761117346380310841944294663456931203380573537653884068660109",
-    "23683935571424619534194393788101669168630123784066421490798386323411538828592",
-    "45470730427236677197026094498490008082250264942279323465121581539984407294442",
-    "48141067373531800337373447278127981363951468257064369512416205750641258258193",
-    "42554919225040466028330117313396362347164995917041931400909482795914116747618",
-    "11551941832988244108260444347046942236051939264069344013774353630451796870907",
-    "60185799182545404739011626517355854847787627814101363386450657535504094743765",
-    "81823160578900678880708744457872721685515019032370491632046212317701226128393",
-    "7165646831054215773988859638722974820791178194871546344315162343128362695647",
-    "75289707601640398424243937567716657896680380639974371761136292031415717685949",
-    "7150842764562742184396161198129263121409208675362553300851082062734889620953",
-    "24380904705269761063866540342138412601132455197711667167747524315310027386226",
-    "9728986075621437350131504894128984146939551938810073671231633620616345344412",
-    "10579382052089733216628873394134968879891026686695240299956972154694558493896",
-    "8171994519466002143995890536756742287314780571933910736618431096190430536601",
-    "30420144259409274775063072923609924427757612539094840146996944760708902708570",
-    "63962155989812703023698320394024694856871261481871757094333286947755599007133",
-    "25280070391177856032024336895094721131222985610587247589336316615596140400436",
-    "15305872319988027006162258914083163651002306183917888172691618513722838997098",
-    "51545603291342006705870081001071419395633279951502747769141857387796043104608",
-    "91109680756552587805002537489407348773333405839144382221272597323798859182191",
-    "72175452855185658158184807496160149169667221240389196996344579971523681433202",
-    "30361989157454953234766224747536334157139256334148153290771332849307087761025",
-    "38169634499980959088614671703639492517637815232220682121652135514105493936992",
-    "49591153263237620796156788742811547511792615129981565620486914545749079774827",
-    "47403873018260745456113868791119169163627014766514972598212646481717066065016",
-    "93989849689047144228924801010853106857960399638657695410345207191739048300111",
-    "10590240512802509131776989274411792739339398409955259174829387591089799115255",
-    "29183703335869638067547208413224742887766212046438654772943025958628178245227",
-    "4131650227136944095885036960767735080970262672750406866066212532739784907379",
-    "43395510588213653537697670365796375057855260611965666448183946252832290017444",
-    "95246795133940226900907730059125298420936467652619708443128629427116119621152",
-    "6012209003558496814495903476753006089125143165365334812097313083703216071080",
-    "26183233284429251459198269925441295879550203824094631575778521083706115817955",
-    "26058994700533582730528567480051558438548299522338811756875396252016497202713",
-    "107240485663145290290374164860301805857261278222480421976433215167444496066511",
-    "84412820763898503096477800002865877536719992495674955119188074297975154406587",
-    "52386303852182662900790700046090769869460994629239741773176060026198900130384",
-    "95746062835936512160025091603469309809932540674474329021370075533568318932379",
-    "22711334660013961010382652754865456251782349529764119853461446587583972054666",
-    "16959835233095757670013367728627149851239789174357906293937455553277911805495",
-    "15116421110200928832147360650392633091242147433006813656250997138988179879750",
-    "107878787525302837370688492081178689950008165750500003692400517211520334656293",
-    "44210105558575948369921579518078229089923760124167628288943900602376706136436",
-    "90305995748749060889452130219544332384396626628663475498252761213618628372367",
-    "104941997925797907872686462815914481945432760720471803254797908465921520138024",
-    "100036855232527386145662094141100441220151775745916101660987264242446845728894",
-    "103285582836474146806606752170525767341430483568396209591447274936228630298052",
-    "82197692939371228160449741709034077803239992888716859217989995857278406253737",
-    "10040764964044995095453717286623030376397745892179877153575434454090155545240",
-    "27304226040425863042893623786832369758179176309230053449707879364285977952630",
-    "42627232144930751842910170221862679057276668485045156742021958050665662768084",
-    "76972394926916659428228833084621905890924612368412796262119501852346293848159",
-    "39796921406297542196667238133893946368231540421737718098283349901435707131075",
-    "14745047092916651495052563068083093689676472592445845983334785004125684263162",
-    "43421479365783318841667739359312715738029447177150400204380817518608837765863",
-    "107871536756946365977710326147511195471121248998432910212631960353348700694610",
-    "39505942243687894211614489736115535754716239859353578295470352855493707198619",
-    "59676442091621150164811367352362126934419932715789994860508056194143441226580",
-    "94470526851498636320865653968033227263836954414283116133326109455334870036212",
-    "15044796858044094866329855531761112645684343559112419720568996573556805975600",
-    "67157729293641241473980125231288476062565688273917759533572275886277269201651",
-    "72911083146182058225942884942982388217243826839805061121973109250798137784134",
-    "102973386186208530972563015865701244407271836208547629083437627219683649557477",
-    "57485522356347377122696081086816661784954498123948319434326439317393351620564",
-    "23112275556906805064863694321486306070917598599342299357379251070160695202292",
-    "107618884362423342584703700349292347754139538760798319916678240538294838342400",
-    "83961260400031958812820990908241261093246389047082613562825737834833753517337",
-    "42726953951733266282750892844947149703751388034177248277671157488506520215317",
-    "39379570934119946602507737250800178347029772561352879974941214627084076473292",
-    "72203650529122342092280763801468513707870760755235719535090090101623606334441",
-    "13389660788942842724553143053013919883368472759564135119390935439369513690496",
-    "101745263541280877725997503552978999350831489463993178838531539940805924817361",
-    "76849182334465191824607032600721023780793694103840553871800174717760598910761",
-    "53896256317996838683363773836826653859512780625932638736752563553878867538095",
-    "24688792501674999263943657175455335814404948006469220532686392550824320454904",
-    "69132683906595821927803530074656979217668636557563597358799899743174233903941",
-    "2861982085506615225917620192781928414994576134281371548401916333754363567986",
-    "37311353286221616083824584705974993449107063556724405440534160586561042968316",
-    "83718085796857523832195255218519255973031752296424117786202083986118546906913",
-    "103633177691684814414226251117070754499104739002759424774194851613917008856616",
-    "84968411062305024171594435878414659990735518025357685215223731503921265946461",
-    "41865099330909055069143724769818364262362915440371474104937435863183989905059",
-    "46156624920251322979270606388518884047396423747179340919303543598300663968593",
-    "64416327466854458915398302811825971539792429791049027619471115285308743811583",
-    "94942471312481523091911417289540395651121558150571128515230470225155209280585",
-    "109682618775735319282534546194470743032129102295907200313471041846112653687024",
-    "61531999191737540795124202104235799899980935519651613893518293245268304980543",
-    "17797352534596268622733030076742840951214734697361029060619245779495726996632",
-    "2323150752778983462106829021155031678603044899339819935981200101818542000989",
-    "16998018904363448507967526489917057882529252665835717172712095240271574074587",
-    "110634872413902251217040490777568744431854972018399530234679399294372694506842",
-    "31639545145649753705216327198217551838008233610574104460826956396569310697060",
-    "107845103764339268987018917144483935480716224058844669233389185480836000033760",
-    "46240297572174662698030819651333060930818959915797061274854448535534474175039",
-    "53065607123105696930220421963755520777674094852857308823370049733888025985616",
-    "16931881300947470270453776207625163368485560075525342751440832370220475352149",
-    "79254110800481916763656344422402393723573490114487681345184594841431920461089",
-    "42268569642639492314994307446626647824927989776691987788682655102426770655233",
-    "9749633319307409894058984489496091535125232227316143918000642155415596066903",
-    "57606597628648270579042266322415267200058617178318601782866227410456726724976",
-    "56082250485913115488341301630850455009935943641292622301678990296508134206571",
-    "17957245764842844288802777667800779232762688847417238921175068882796163705248",
-    "94356229516444419318132697346021621194464273500135725160277725602263001442644",
-    "52536631226748676066386651084538409050048707922045928887930261833545619358914",
-    "107794922118166328243581272159394479176678094739027519706768813902978100436849",
-    "92984368734102511759118281503078145182557799453616537383408606074187034371208",
-    "59652553897137603386525572460411404882917571255327541516871354737502335133690",
-    "49012645345644326995052653072578673750516379655033952006121214224119466671764",
-    "79025576845143484310735291619293962982804358365838961371044480386743856799994",
-    "5437377540613244374799729812489584777222423091155743557287567155811057717409",
-    "100687592213090267900708728796310211082532607828753010566886681655775031329660",
-    "99074462968857696481475128596339544396152341206708424767062829343406495063192",
-    "67476872698289965626550204192782761730653024363949045140720348870736942130242",
-    "103307125141718054130755829916960708430672826104789971350239945481960770107890",
-    "74087383014714668160537499936376991041273055222568604413015844459913259357334",
-    "40924049099780965904051946083599822761993164889139026432053420731164022206736",
-    "32594924940463736641240515015317856157169105212942308502676422036626316673214",
-    "98990663138035055774586216545398054668349058134877723031747421828753359974443",
-    "55821766022768786066770462759796825978667805772707620106340033118519147871694",
-    "4001942224536365489828915551180230767516454384395893814399938353050969198154",
-    "30136373426492646221252150708518703998248891683881870400906269276900707426865",
-    "34943205764464817266133164313915763122699935186597909347522822673832250079664",
-    "27737330737483170511275902246508559278973986181590368845166383812793468814968",
-    "96292398813565494438359802278723334615526914389306923046282571355958508916558",
-    "97147334956505986101750230325438660094766812949748276042292963837380833668274",
-    "24754519562402723848413674701792328284127274989440581643644298347747941238812",
-    "76111103490248669364580390783887028636436246028943665707064153006971943621186",
-    "33764090322658516047637223655525551979364055499647855895233821795694749902854",
-    "100536990630540359004783976190215234627391515555181073681294901127179838732969",
-    "55991997435987096996680289872758998763908676069536901375395297778729059185671",
-    "32860959903680178324832991459746631238726690317249285658471597044247794502256",
-    "70074816806976994707467706079200635184034023598764203123459335544110485476930",
-    "46213940675829172331116620705134022102338250410334045747023950259088879662946",
-    "77000624259024986585504351395777746568094934279771127334532438603183524642061",
-    "21719649576090832101273013788716623377603297433777804572370785470329817725170",
-    "29209622978540575483991966565508890231057362045066230397327380085945876837821",
-    "2445742484263083651472035320255578071935687960412507452207899496253120999364",
-    "86846812580007547526361109808384103509272544750564766849178767957571523649544",
-    "43025640639926253696325070988523609146060819319830735794100778654425057363895",
-    "108957662689228031021948854644435971168708642184764962508575441689859324862868",
-    "83891545396650121758556392255189778590486277180642660527000882403085396114823",
-    "42527013475786190604202451803064937203698027000671529418992521798122995373551",
-    "115180194520889678365425151865713593680657747284471744934804370945935167043862",
-    "28979598171177052880917135045920701144584888536299261666846302083645491369348",
-    "68351312608110279019109436395199010412431777911149851157132527077210966351650",
-    "61759623963943995967580147094342313397376358019837276043205235302342147116585",
-    "80714625408576660514217469096827255752431164791924432025682445176737446783085",
-    "33048555646676368266608424610100449208381357250300222636992099726804869416731",
-    "50682223610667325089810868083131721901859473966415125289975106060759036109476",
-    "4271213571706787092297985431667190050727614825584809797590204884727103716461",
-    "101314046722405990971733763321368296660561930294000591067108115987088407142646",
-    "55565500177602146197728150332647093173137211885612327122425918553270191254877",
-    "65556764608648687291293889343854786421750589271167654521933267288313526422497",
-    "66877533773422945979143954094644173219583178339199697252673545117318799706373",
-    "30511098623357801425494143655999121699575856091238269679669864984061501512835",
-    "95900192636363991637086954986559552472749485926252879461208179855482821976623",
-    "37879946127489462347049192209554168578320892231852882971030128420645686965013",
-    "80479504274334215471057938992198620419540634144266821121799003865782336406529",
-    "13326262422954139210095783388743602482455840337093117010479445267213907605425",
-    "16047106134611124637925332265703907202779549268127518502853950466090054176776",
-    "71499356105233640605079063493613576024353801558965221134519779175477723594865",
-    "28438981751956157476540225984733791304599172905715743025543841239013139121102",
-    "56066317647068426981453448715118237747130321302262827290362392918472904421147",
-];
+lazy_static! {
+    pub(crate) static ref MDS_MATRIX: [[FieldElement; 3]; 3] = [
+        [
+            "92469348809186613947252340883344274339611751744959319352506666082431267346705",
+            "100938028378191533449096235266991198229563815869344032449592738345766724371160",
+            "77486311749148948616988559783475694076613010381924638436641318334458515006661",
+        ]
+        .map(|y| FieldElement::from_str_vartime(y).unwrap()),
+        [
+            "110352262556914082363749654180080464794716701228558638957603951672835474954408",
+            "27607004873684391669404739690441550149894883072418944161048725383958774443141",
+            "29671705769502357195586268679831947082918094959101307962374709600277676341325",
+        ]
+        .map(|y| FieldElement::from_str_vartime(y).unwrap()),
+        [
+            "77762103796341032609398578911486222569419103128091016773380377798879650228751",
+            "1753012011204964731088925227042671869111026487299375073665493007998674391999",
+            "70274477372358662369456035572054501601454406272695978931839980644925236550307",
+        ]
+        .map(|y| FieldElement::from_str_vartime(y).unwrap()),
+    ];
+    pub(crate) static ref ROUND_CONSTANTS: [FieldElement; 192] = [
+        "15180568604901803243989155929934437997245952775071395385994322939386074967328",
+        "98155933184944822056372510812105826951789406432246960633912199752807271851218",
+        "32585497418154084368870158853355239726261349829448673320273043226636389078017",
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+        "66877533773422945979143954094644173219583178339199697252673545117318799706373",
+        "30511098623357801425494143655999121699575856091238269679669864984061501512835",
+        "95900192636363991637086954986559552472749485926252879461208179855482821976623",
+        "37879946127489462347049192209554168578320892231852882971030128420645686965013",
+        "80479504274334215471057938992198620419540634144266821121799003865782336406529",
+        "13326262422954139210095783388743602482455840337093117010479445267213907605425",
+        "16047106134611124637925332265703907202779549268127518502853950466090054176776",
+        "71499356105233640605079063493613576024353801558965221134519779175477723594865",
+        "28438981751956157476540225984733791304599172905715743025543841239013139121102",
+        "56066317647068426981453448715118237747130321302262827290362392918472904421147",
+    ]
+    .map(|y| FieldElement::from_str_vartime(y).unwrap());
+}

packages/poseidon/src/lib.rs

@@ -27,14 +27,14 @@ impl<F: PrimeField> PoseidonConstants<F> {
 }
 
 pub struct Poseidon<F: PrimeField> {
-    pub state: Vec<F>,
+    pub state: [F; 3],
     pub constants: PoseidonConstants<F>,
     pub pos: usize,
 }
 
 impl<F: PrimeField> Poseidon<F> {
     pub fn new(constants: PoseidonConstants<F>) -> Self {
-        let state = vec![F::zero(); 3];
+        let state = [F::zero(); 3];
         Self {
             state,
             constants,
@@ -42,12 +42,10 @@ impl<F: PrimeField> Poseidon<F> {
         }
     }
 
-    pub fn hash(&mut self, input: Vec<F>) -> F {
-        // add padding
-        let mut input = input.clone();
-
-        let domain_tag = 3; // 2^arity - 1
-        input.insert(0, F::from(domain_tag));
+    pub fn hash(&mut self, input: &[F; 2]) -> F {
+        // add the domain tag
+        let domain_tag = F::from(3); // 2^arity - 1
+        let input = [domain_tag, input[0], input[1]];
 
         self.state = input;
 
@@ -80,14 +78,14 @@ impl<F: PrimeField> Poseidon<F> {
 
     // MDS matrix multiplication
     fn matrix_mul(&mut self) {
-        let mut result = Vec::new();
+        let mut result = [F::zero(); 3];
 
-        for val in self.constants.mds_matrix.iter() {
+        for (i, val) in self.constants.mds_matrix.iter().enumerate() {
             let mut tmp = F::zero();
             for (j, element) in self.state.iter().enumerate() {
                 tmp += val[j] * element
             }
-            result.push(tmp)
+            result[i] = tmp;
         }
 
         self.state = result;
@@ -124,40 +122,30 @@ impl<F: PrimeField> Poseidon<F> {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use k256_consts::*;
     use secq256k1::field::{field_secp, BaseField};
 
     #[test]
     fn test_k256() {
         type Scalar = field_secp::FieldElement;
-        let input = vec![
+        let input = [
             Scalar::from_str_vartime("1234567").unwrap(),
             Scalar::from_str_vartime("109987").unwrap(),
         ];
 
-        let round_constants: Vec<Scalar> = k256_consts::ROUND_CONSTANTS
-            .iter()
-            .map(|x| Scalar::from_str_vartime(x).unwrap())
-            .collect();
-
-        let mds_matrix: Vec<Vec<Scalar>> = k256_consts::MDS_MATRIX
-            .iter()
-            .map(|x| {
-                x.iter()
-                    .map(|y| Scalar::from_str_vartime(y).unwrap())
-                    .collect::<Vec<Scalar>>()
-            })
-            .collect();
-
-        let constants = PoseidonConstants::<Scalar>::new(
-            round_constants,
-            mds_matrix,
-            k256_consts::NUM_FULL_ROUNDS,
-            k256_consts::NUM_PARTIAL_ROUNDS,
+        let constants = PoseidonConstants::<FieldElement>::new(
+            ROUND_CONSTANTS.to_vec(),
+            vec![
+                MDS_MATRIX[0].to_vec(),
+                MDS_MATRIX[1].to_vec(),
+                MDS_MATRIX[2].to_vec(),
+            ],
+            NUM_FULL_ROUNDS,
+            NUM_PARTIAL_ROUNDS,
         );
-
         let mut poseidon = Poseidon::new(constants);
 
-        let digest = poseidon.hash(input);
+        let digest = poseidon.hash(&input);
 
         assert_eq!(
             digest,

packages/poseidon/src/poseidon_k256.rs

@@ -1,28 +1,18 @@
-use crate::{k256_consts, Poseidon, PoseidonConstants};
-use ff::PrimeField;
+use crate::k256_consts::*;
+use crate::{Poseidon, PoseidonConstants};
 pub use secq256k1::field::field_secp::FieldElement;
 
 #[allow(dead_code)]
-pub fn hash(input: Vec<FieldElement>) -> FieldElement {
-    let round_constants: Vec<FieldElement> = k256_consts::ROUND_CONSTANTS
-        .iter()
-        .map(|x| FieldElement::from_str_vartime(x).unwrap())
-        .collect();
-
-    let mds_matrix: Vec<Vec<FieldElement>> = k256_consts::MDS_MATRIX
-        .iter()
-        .map(|x| {
-            x.iter()
-                .map(|y| FieldElement::from_str_vartime(y).unwrap())
-                .collect::<Vec<FieldElement>>()
-        })
-        .collect();
-
+pub fn hash(input: &[FieldElement; 2]) -> FieldElement {
     let constants = PoseidonConstants::<FieldElement>::new(
-        round_constants,
-        mds_matrix,
-        k256_consts::NUM_FULL_ROUNDS,
-        k256_consts::NUM_PARTIAL_ROUNDS,
+        ROUND_CONSTANTS.to_vec(),
+        vec![
+            MDS_MATRIX[0].to_vec(),
+            MDS_MATRIX[1].to_vec(),
+            MDS_MATRIX[2].to_vec(),
+        ],
+        NUM_FULL_ROUNDS,
+        NUM_PARTIAL_ROUNDS,
     );
     let mut poseidon = Poseidon::new(constants);
 

packages/spartan_wasm/Cargo.toml

@@ -11,7 +11,7 @@ crate-type = ["cdylib", "rlib"]
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
-spartan = { git = "https://github.com/DanTehrani/Spartan-secq.git", branch="master" }
+spartan = { path = "../Spartan-secq" }
 wasm-bindgen = { version = "0.2.81", features = ["serde-serialize"]}
 console_error_panic_hook = "0.1.7"
 merlin = "3.0.0"
@@ -32,14 +32,3 @@ poseidon = { path = "../poseidon" }
 itertools = "0.9.0"
 group = "0.12.0"
 
-# Do not compile these dependencies when targeting wasm
-#[target.'cfg(not(target_family = "wasm"))'.dependencies]
-#nova-scotia = { git = "https://github.com/DanTehrani/Nova-Scotia.git" }
-#nova-snark = "0.9.0"
-#ff = "0.12.1"
-#ark-std = { version = "0.3.0", features = ["print-trace"] }
-
-
-[[bin]]
-name = "gen_spartan_inst"
-path = "src/bin/gen_spartan_inst.rs"

packages/spartan_wasm/src/lib.rs

@@ -1,4 +1 @@
 pub mod wasm;
-
-#[cfg(not(target_family = "wasm"))]
-pub mod circom_reader;

packages/spartan_wasm/src/wasm.rs

@@ -84,14 +84,14 @@ pub fn verify(circuit: &[u8], proof: &[u8], public_input: &[u8]) -> Result<bool,
 
 #[wasm_bindgen]
 pub fn poseidon(input_bytes: &[u8]) -> Result<Vec<u8>, JsValue> {
-    let mut input = Vec::new();
-    for i in 0..(input_bytes.len() / 32) {
-        let f: [u8; 32] = input_bytes[(i * 32)..(i + 1) * 32].try_into().unwrap();
-        let val = FieldElement::from_bytes(&f).unwrap();
-        input.push(FieldElement::from(val));
-    }
+    assert_eq!(input_bytes.len(), 64);
 
-    let result = hash(input);
+    let input = [
+        FieldElement::from_bytes(&input_bytes[0..32].try_into().unwrap()).unwrap(),
+        FieldElement::from_bytes(&input_bytes[32..64].try_into().unwrap()).unwrap(),
+    ];
+
+    let result = hash(&input);
 
     Ok(result.to_bytes().to_vec())
 }

scripts/test.sh

@@ -0,0 +1,2 @@
+cargo test --release &&
+yarn lerna run test

yarn.lock

@@ -2057,6 +2057,14 @@
     node-addon-api "^3.2.1"
     node-gyp-build "^4.3.0"
 
+"@personaelabs/spartan-ecdsa@file:./packages/lib":
+  version "2.3.0"
+  dependencies:
+    "@ethereumjs/util" "^8.0.3"
+    "@zk-kit/incremental-merkle-tree" "^1.0.0"
+    elliptic "^6.5.4"
+    snarkjs "^0.7.1"
+
 "@phenomnomnominal/tsquery@4.1.1":
   version "4.1.1"
   resolved "https://registry.npmjs.org/@phenomnomnominal/tsquery/-/tsquery-4.1.1.tgz"
@@ -3136,6 +3144,13 @@ circom_runtime@0.1.21:
   dependencies:
     ffjavascript "0.2.56"
 
+circom_runtime@0.1.24:
+  version "0.1.24"
+  resolved "https://registry.yarnpkg.com/circom_runtime/-/circom_runtime-0.1.24.tgz#60ca8a31c3675802fbab5a0bcdeb02556e510733"
+  integrity sha512-H7/7I2J/cBmRnZm9docOCGhfxzS61BEm4TMCWcrZGsWNBQhePNfQq88Oj2XpUfzmBTCd8pRvRb3Mvazt3TMrJw==
+  dependencies:
+    ffjavascript "0.2.60"
+
 circom_tester@^0.0.19:
   version "0.0.19"
   resolved "https://registry.npmjs.org/circom_tester/-/circom_tester-0.0.19.tgz"
@@ -4300,6 +4315,15 @@ ffjavascript@0.2.56:
     wasmcurves "0.2.0"
     web-worker "^1.2.0"
 
+ffjavascript@0.2.60:
+  version "0.2.60"
+  resolved "https://registry.yarnpkg.com/ffjavascript/-/ffjavascript-0.2.60.tgz#4d8ae613d6bf4e98b3cc29ba10c626f5853854cf"
+  integrity sha512-T/9bnEL5xAZRDbQoEMf+pM9nrhK+C3JyZNmqiWub26EQorW7Jt+jR54gpqDhceA4Nj0YctPQwYnl8xa52/A26A==
+  dependencies:
+    wasmbuilder "0.0.16"
+    wasmcurves "0.2.2"
+    web-worker "^1.2.0"
+
 ffjavascript@^0.2.45, ffjavascript@^0.2.48, ffjavascript@^0.2.56, ffjavascript@^0.2.57:
   version "0.2.57"
   resolved "https://registry.npmjs.org/ffjavascript/-/ffjavascript-0.2.57.tgz"
@@ -7070,6 +7094,16 @@ r1csfile@0.0.41, r1csfile@^0.0.41:
     fastfile "0.0.20"
     ffjavascript "0.2.56"
 
+r1csfile@0.0.47:
+  version "0.0.47"
+  resolved "https://registry.yarnpkg.com/r1csfile/-/r1csfile-0.0.47.tgz#ed95a0dc8e910e9c070253906f7a31bd8c5333c8"
+  integrity sha512-oI4mAwuh1WwuFg95eJDNDDL8hCaZkwnPuNZrQdLBWvDoRU7EG+L/MOHL7SwPW2Y+ZuYcTLpj3rBkgllBQZN/JA==
+  dependencies:
+    "@iden3/bigarray" "0.0.2"
+    "@iden3/binfileutils" "0.0.11"
+    fastfile "0.0.20"
+    ffjavascript "0.2.60"
+
 react-dom@18.2.0:
   version "18.2.0"
   resolved "https://registry.npmjs.org/react-dom/-/react-dom-18.2.0.tgz"
@@ -7446,7 +7480,7 @@ smart-buffer@^4.2.0:
   resolved "https://registry.npmjs.org/smart-buffer/-/smart-buffer-4.2.0.tgz"
   integrity sha512-94hK0Hh8rPqQl2xXc3HsaBoOXKV20MToPkcXvwbISWLEs+64sBq5kFgn2kJDHb1Pry9yrP0dxrCI9RRci7RXKg==
 
-snarkjs@0.5.0, snarkjs@^0.5.0:
+snarkjs@0.5.0:
   version "0.5.0"
   resolved "https://registry.npmjs.org/snarkjs/-/snarkjs-0.5.0.tgz"
   integrity sha512-KWz8mZ2Y+6wvn6GGkQo6/ZlKwETdAGohd40Lzpwp5TUZCn6N6O4Az1SuX1rw/qREGL6Im+ycb19suCFE8/xaKA==
@@ -7462,6 +7496,22 @@ snarkjs@0.5.0, snarkjs@^0.5.0:
     logplease "^1.2.15"
     r1csfile "0.0.41"
 
+snarkjs@^0.7.1:
+  version "0.7.1"
+  resolved "https://registry.yarnpkg.com/snarkjs/-/snarkjs-0.7.1.tgz#c96ecaf4db8c2eb44d60b17ee02f37ed39c821bb"
+  integrity sha512-Qs1oxssa135WZkzfARgEp5SuKHKvKNtcspeJbE5je6MurUpBylD1rzcAzQSTGWA/EH/BV/TmUyTaTD64xScvbA==
+  dependencies:
+    "@iden3/binfileutils" "0.0.11"
+    bfj "^7.0.2"
+    blake2b-wasm "^2.4.0"
+    circom_runtime "0.1.24"
+    ejs "^3.1.6"
+    fastfile "0.0.20"
+    ffjavascript "0.2.60"
+    js-sha3 "^0.8.0"
+    logplease "^1.2.15"
+    r1csfile "0.0.47"
+
 socks-proxy-agent@^7.0.0:
   version "7.0.0"
   resolved "https://registry.npmjs.org/socks-proxy-agent/-/socks-proxy-agent-7.0.0.tgz"
@@ -8133,6 +8183,13 @@ wasmcurves@0.2.0:
   dependencies:
     wasmbuilder "0.0.16"
 
+wasmcurves@0.2.2:
+  version "0.2.2"
+  resolved "https://registry.yarnpkg.com/wasmcurves/-/wasmcurves-0.2.2.tgz#ca444f6a6f6e2a5cbe6629d98ff478a62b4ccb2b"
+  integrity sha512-JRY908NkmKjFl4ytnTu5ED6AwPD+8VJ9oc94kdq7h5bIwbj0L4TDJ69mG+2aLs2SoCmGfqIesMWTEJjtYsoQXQ==
+  dependencies:
+    wasmbuilder "0.0.16"
+
 wcwidth@^1.0.0, wcwidth@^1.0.1:
   version "1.0.1"
   resolved "https://registry.npmjs.org/wcwidth/-/wcwidth-1.0.1.tgz"