re-added zkrsa

2026-01-09 14:48:06 -05:00 · 2023-07-22 14:35:37 +02:00
parent 77490b59b5
commit 29e259be6e
473 changed files with 72958 additions and 0 deletions
--- a/zkrsa/.gitattributes
+++ b/zkrsa/.gitattributes
@@ -0,0 +1,3 @@
+*.vk_proof filter=lfs diff=lfs merge=lfs -text
+*.vk_verifier filter=lfs diff=lfs merge=lfs -text
+circom-rsa-verify/** linguist-vendored
--- a/zkrsa/.gitignore
+++ b/zkrsa/.gitignore
@@ -0,0 +1,14 @@
+node_modules
+*example*
+.DS_Store
+circuit*.json
+adhaar.pdf
+scripts/extract.ts
+*.pem
+.vercel
+bin
+inputs
+vkeys
+witness
+proofs
+publicSignals
--- a/zkrsa/.husky/pre-commit
+++ b/zkrsa/.husky/pre-commit
@@ -0,0 +1,4 @@
+#!/usr/bin/env sh
+. "$(dirname -- "$0")/_/husky.sh"
+
+cd frontend && yarn test && yarn pretty-quick --staged
--- a/zkrsa/README.md
+++ b/zkrsa/README.md
@@ -0,0 +1,48 @@
+### zkRSA
+
+[![code style: prettier](https://img.shields.io/badge/code_style-prettier-ff69b4.svg?style=flat-square)](https://github.com/prettier/prettier)
+
+This repository's goal is to perform zero knowledge (zk) proofs generation and verification of RSA signatures. All from within a web browser, with local computing resources.
+
+The `circom-rsa-verify` folder contains all necessary circuits and tests for generating zk proofs of valid RSA signatures. It has been cloned from [here](https://github.com/zkp-application/circom-rsa-verify). You should check it out!
+
+The `frontend` folder contains the UI for generating or verifying proofs of valid RSA signatures using circom.
+
+### Generating RSA-SHA256 signatures from the CLI
+
+To generate signatures from the CLI - note that your message does not need to be quoted and can be of arbitrary length -, you can clone this repo and run:
+
+```sh
+$ yarn install
+$ yarn sign this is a message to sign
+```
+
+It will log a new signature, generated out of an randomly generated RSA keypair - uses `node:crypto` -. You can copy those values and use them directly within the [zkRSA UI](https://zkrsa.vercel.app/) for generating a new proof.
+
+### Verifying proofs
+
+On the zkRSA UI, you can generate and verify proofs for valid RSA signatures. The verify tab accepts a JSON with the following format:
+
+```js
+{
+    "proof": proof,
+    "publicSignals": publicSignals
+}
+```
+
+This is the output format when downloading a proof from the "generate" tab. You can also pre-format your own proof to verify it from the UI.
+
+### Running a frontend locally
+
+To run the UI locally you can clone the repo and run:
+
+```sh
+$ cd frontend && yarn install
+$ yarn dev
+```
+
+There are a few other commands within `frontend/package.json` file, for testing or building the project.
+
+### Links
+
+- [Grant proposal V2](https://hackmd.io/DoZPolTRRN-WNYheT7MauA)
--- a/zkrsa/circom-rsa-verify/.gitmodules
+++ b/zkrsa/circom-rsa-verify/.gitmodules
@@ -0,0 +1,6 @@
+[submodule "circomlib"]
+	path = circomlib
+	url = https://github.com/iden3/circomlib.git
+[submodule "circom-bigint"]
+	path = circom-bigint
+	url = https://github.com/jacksoom/circom-bigint.git
--- a/zkrsa/circom-rsa-verify/LICENSE
+++ b/zkrsa/circom-rsa-verify/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2021 zkp-application
+
+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.
--- a/zkrsa/circom-rsa-verify/README.md
+++ b/zkrsa/circom-rsa-verify/README.md
@@ -0,0 +1,25 @@
+# circom-rsa-verify
+This repository contains an implementation of a Zero Knowledge Proof for RSA signature verify for the circom language.
+Currently supported pkcs1v15 + sha256 and exponent is 65537
+# Getting started
+Running circuits test cases
+```sh
+git submodule update --init --recursive; npm install; npm test
+```
+
+## Circuits Benchmark
+RSA verify: pkcs1v15/sha256/2048 bits key
+* Env: Mac mini (M1, 2020). 8 cores. 8 threads   
+* Memory consumption: 1.7G   
+* Time consumption: 150s   
+## The circom compiler
+
+This repository uses a modified version of the circom compiler found at
+[alex-ozdemir/circom](https://github.com/alex-ozdemir/circom).
+It includes a few extra features not found in the original:
+
+   * Clearer error printouts
+   * More comprehensive/informative treatment of `log` statements
+   * A new type `int` which enables bigints to be handled during witness
+      computations.
+   * `compute` blocks
--- a/zkrsa/circom-rsa-verify/circom-bigint/.gitignore
+++ b/zkrsa/circom-rsa-verify/circom-bigint/.gitignore
@@ -0,0 +1 @@
+node_modules
--- a/zkrsa/circom-rsa-verify/circom-bigint/.gitmodules
+++ b/zkrsa/circom-rsa-verify/circom-bigint/.gitmodules
@@ -0,0 +1,3 @@
+[submodule "circomlib"]
+	path = circomlib
+	url = https://github.com/iden3/circomlib
--- a/zkrsa/circom-rsa-verify/circom-bigint/README.md
+++ b/zkrsa/circom-rsa-verify/circom-bigint/README.md
@@ -0,0 +1,32 @@
+# circom-bigint
+
+This repository contains an implementation of arbitrary-precision natural
+numbers for the [`circom`](https://github.com/iden3/circom) language.
+
+## Getting Started
+
+First you'll need a copy of `circomlib` within this repository. You can get it
+by running
+
+    git submodule update --init --recursive
+
+Then you'll need to install a local copy of the `circom` compiler and the
+testing frameworks
+
+    npm install
+
+Then you can run the tests
+
+    npm test
+
+## The circom compiler
+
+This repository uses a modified version of the circom compiler found at
+[alex-ozdemir/circom](https://github.com/alex-ozdemir/circom).
+It includes a few extra features not found in the original:
+
+   * Clearer error printouts
+   * More comprehensive/informative treatment of `log` statements
+   * A new type `int` which enables bigints to be handled during witness
+      computations.
+   * `compute` blocks
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/.eslintrc.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/.eslintrc.js
@@ -0,0 +1,33 @@
+module.exports = {
+    "plugins": [
+        "mocha"
+    ],
+    "env": {
+        "es6": true,
+        "node": true,
+        "mocha": true
+    },
+    "parserOptions": {
+        "ecmaVersion": 2017
+    },
+    "extends": "eslint:recommended",
+    "rules": {
+        "indent": [
+            "error",
+            4
+        ],
+        "linebreak-style": [
+            "error",
+            "unix"
+        ],
+        "quotes": [
+            "error",
+            "double"
+        ],
+        "semi": [
+            "error",
+            "always"
+        ],
+        "mocha/no-exclusive-tests": "error"
+    }
+};
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/.gitignore
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/.gitignore
@@ -0,0 +1,65 @@
+# Logs
+logs
+*.log
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*
+
+# Runtime data
+pids
+*.pid
+*.seed
+*.pid.lock
+
+# Directory for instrumented libs generated by jscoverage/JSCover
+lib-cov
+
+# Coverage directory used by tools like istanbul
+coverage
+
+# nyc test coverage
+.nyc_output
+
+# Grunt intermediate storage (http://gruntjs.com/creating-plugins#storing-task-files)
+.grunt
+
+# Bower dependency directory (https://bower.io/)
+bower_components
+
+# node-waf configuration
+.lock-wscript
+
+# Compiled binary addons (https://nodejs.org/api/addons.html)
+build/Release
+
+# Dependency directories
+node_modules/
+jspm_packages/
+
+# Typescript v1 declaration files
+typings/
+
+# Optional npm cache directory
+.npm
+
+# Optional eslint cache
+.eslintcache
+
+# Optional REPL history
+.node_repl_history
+
+# Output of 'npm pack'
+*.tgz
+
+# Yarn Integrity file
+.yarn-integrity
+
+# dotenv environment variables file
+.env
+
+# next.js build output
+.next
+
+tmp
+
+.DS_Store
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/README.md
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/README.md
@@ -0,0 +1,4 @@
+# cirpedersen
+
+Pedersen Hash and Exponentiation circuits using Baby Jub Curve in circom language
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/calcpedersenbases/calcpedersenbases.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/calcpedersenbases/calcpedersenbases.js
@@ -0,0 +1,83 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+const createBlakeHash = require("blake-hash");
+const babyJub = require("../src/babyjub");
+
+function getPoint(S) {
+    const F = bn128.Fr;
+    const h = createBlakeHash("blake256").update(S).digest();
+
+    if (h.length != 32) {
+        throw new Error("Invalid length")
+    }
+
+    let sign = false;
+    if (h[31] & 0x80) {
+        h[31] = h[31] & 0x7F;
+        sign = true;
+    }
+
+    let y = bigInt(0);
+    for (let i=0; i<32; i++) {
+        y = y.shl(8);
+        y = y.add(bigInt(h[i]));
+    }
+
+    const a = bigInt("168700");
+    const d = bigInt("168696");
+
+    const y2 = F.square(y);
+
+    let x = F.sqrt(F.div(
+        F.sub(F.one, y2),
+        F.sub(a, F.mul(d, y2))));
+
+    if (x == null) return null;
+
+    if (sign) x = F.neg(x);
+
+    const p = [bn128.Fr.affine(x), bn128.Fr.affine(y)];
+
+    const p8 = babyJub.mulPointEscalar(p, 8);
+
+    return p8;
+}
+
+
+function generatePoint(S) {
+    let p= null;
+    let idx = 0;
+    while (p==null) {
+        let sidx = "" + idx;
+        while (sidx.length<16) sidx = "0"+sidx;
+        p = getPoint(S+"_"+sidx);
+        idx++;
+    }
+    if (!babyJub.inCurve(p)){
+        throw new Error("Point not in curve");
+    }
+    return p;
+}
+
+
+
+
+
+const g = [
+    bigInt("5299619240641551281634865583518297030282874472190772894086521144482721001553"),
+    bigInt("16950150798460657717958625567821834550301663161624707787222815936182638968203")];
+
+// Sanity check
+if (!babyJub.inCurve(g)) {
+    throw new Error("Generator not In curve -> Some thing goes wrong...");
+}
+
+for (let i=0; i<25; i++) {
+    let S = "" +i;
+    while (S.length<16) S = "0"+S;
+    const P = generatePoint("Iden3_PedersenGenerator_"+S);
+    console.log(`[${P[0].toString()}, ${P[1].toString()}]`);
+}
+
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/README.md
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/README.md
@@ -0,0 +1,14 @@
+* compconstant - Returns 1 if `in` (expanded to binary array) > `ct`
+* aliascheck - check if `in` (expanded to binary array) oveflowed its 254 bits (<= -1)
+* babyjub - twisted Edwards curve 168700.x^2 + y^2 = 1 + 168696.x^2.y^2
+  * BabyAdd - (`xout`,`yout`) = (`x1`,`y1`) + (`x2`,`y2`)
+  * BabyDbl - (`xout`,`yout`) = 2*(`x`,`y`)
+  * BabyCheck - check that (`x`,`y`) is on the curve
+* binsub - binary subtraction
+* gates - logical gates
+* mimc - SNARK-friendly hash Minimal Multiplicative Complexity.
+  * https://eprint.iacr.org/2016/492.pdf
+  * zcash/zcash#2233
+* smt - Sparse Merkle Tree
+  * https://ethresear.ch/t/optimizing-sparse-merkle-trees/3751
+* montgomery https://en.wikipedia.org/wiki/Montgomery_curve
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/aliascheck.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/aliascheck.circom
@@ -0,0 +1,32 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+
+
+template AliasCheck() {
+
+    signal input in[254];
+
+    component  compConstant = CompConstant(-1);
+
+    for (var i=0; i<254; i++) in[i] ==> compConstant.in[i];
+
+    compConstant.out === 0;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/babyjub.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/babyjub.circom
@@ -0,0 +1,106 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "bitify.circom";
+include "escalarmulfix.circom";
+
+template BabyAdd() {
+    signal input x1;
+    signal input y1;
+    signal input x2;
+    signal input y2;
+    signal output xout;
+    signal output yout;
+
+    signal beta;
+    signal gamma;
+    signal delta;
+    signal tau;
+
+    var a = 168700;
+    var d = 168696;
+
+    beta <== x1*y2;
+    gamma <== y1*x2;
+    delta <== (-a*x1+y1)*(x2 + y2);
+    tau <== beta * gamma;
+
+    xout <-- (beta + gamma) / (1+ d*tau);
+    (1+ d*tau) * xout === (beta + gamma);
+
+    yout <-- (delta + a*beta - gamma) / (1-d*tau);
+    (1-d*tau)*yout === (delta + a*beta - gamma);
+}
+
+template BabyDbl() {
+    signal input x;
+    signal input y;
+    signal output xout;
+    signal output yout;
+
+    component adder = BabyAdd();
+    adder.x1 <== x;
+    adder.y1 <== y;
+    adder.x2 <== x;
+    adder.y2 <== y;
+
+    adder.xout ==> xout;
+    adder.yout ==> yout;
+}
+
+
+template BabyCheck() {
+    signal input x;
+    signal input y;
+
+    signal x2;
+    signal y2;
+
+    var a = 168700;
+    var d = 168696;
+
+    x2 <== x*x;
+    y2 <== y*y;
+
+    a*x2 + y2 === 1 + d*x2*y2;
+}
+
+// Extracts the public key from private key
+template BabyPbk() {
+    signal private input  in;
+    signal         output Ax;
+    signal         output Ay;
+
+    var BASE8 = [
+        5299619240641551281634865583518297030282874472190772894086521144482721001553,
+        16950150798460657717958625567821834550301663161624707787222815936182638968203
+    ];
+
+    component pvkBits = Num2Bits(253);
+    pvkBits.in <== in;
+
+    component mulFix = EscalarMulFix(253, BASE8);
+
+    var i;
+    for (i=0; i<253; i++) {
+        mulFix.e[i] <== pvkBits.out[i];
+    }
+    Ax  <== mulFix.out[0];
+    Ay  <== mulFix.out[1];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/binsub.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/binsub.circom
@@ -0,0 +1,71 @@
+ /*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+This component creates a binary substraction.
+
+
+Main Constraint:
+   (in[0][0]     * 2^0  +  in[0][1]     * 2^1  + ..... + in[0][n-1]    * 2^(n-1))  +
+ +  2^n
+ - (in[1][0]     * 2^0  +  in[1][1]     * 2^1  + ..... + in[1][n-1]    * 2^(n-1))
+ ===
+   out[0] * 2^0  + out[1] * 2^1 +   + out[n-1] *2^(n-1) + aux
+
+
+    out[0]     * (out[0] - 1) === 0
+    out[1]     * (out[0] - 1) === 0
+    .
+    .
+    .
+    out[n-1]   * (out[n-1] - 1) === 0
+    aux * (aux-1) == 0
+
+*/
+
+template BinSub(n) {
+    signal input in[2][n];
+    signal output out[n];
+
+    signal aux;
+
+    var lin = 2**n;
+    var lout = 0;
+
+    for (var i=0; i<n; i++) {
+        lin = lin + in[0][i]*(2**i);
+        lin = lin - in[1][i]*(2**i);
+    }
+
+    for (var i=0; i<n; i++) {
+        out[i] <-- (lin >> i) & 1;
+
+        // Ensure out is binary
+        out[i] * (out[i] - 1) === 0;
+
+        lout = lout + out[i]*(2**i);
+    }
+
+    aux <-- (lin >> n) & 1;
+    aux*(aux-1) === 0;
+    lout = lout + aux*(2**n);
+
+    // Ensure the sum;
+    lin === lout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/binsum.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/binsum.circom
@@ -0,0 +1,93 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+
+Binary Sum
+==========
+
+This component creates a binary sum componet of ops operands and n bits each operand.
+
+e is Number of carries: Depends on the number of operands in the input.
+
+Main Constraint:
+   in[0][0]     * 2^0  +  in[0][1]     * 2^1  + ..... + in[0][n-1]    * 2^(n-1)  +
+ + in[1][0]     * 2^0  +  in[1][1]     * 2^1  + ..... + in[1][n-1]    * 2^(n-1)  +
+ + ..
+ + in[ops-1][0] * 2^0  +  in[ops-1][1] * 2^1  + ..... + in[ops-1][n-1] * 2^(n-1)  +
+ ===
+   out[0] * 2^0  + out[1] * 2^1 +   + out[n+e-1] *2(n+e-1)
+
+To waranty binary outputs:
+
+    out[0]     * (out[0] - 1) === 0
+    out[1]     * (out[0] - 1) === 0
+    .
+    .
+    .
+    out[n+e-1] * (out[n+e-1] - 1) == 0
+
+ */
+
+
+/*
+    This function calculates the number of extra bits in the output to do the full sum.
+ */
+
+function nbits(a) {
+    var n = 1;
+    var r = 0;
+    while (n-1<a) {
+        r++;
+        n *= 2;
+    }
+    return r;
+}
+
+
+template BinSum(n, ops) {
+    var nout = nbits((2**n -1)*ops);
+    signal input in[ops][n];
+    signal output out[nout];
+
+    var lin = 0;
+    var lout = 0;
+
+    var k;
+    var j;
+
+    for (k=0; k<n; k++) {
+        for (j=0; j<ops; j++) {
+            lin += in[j][k] * 2**k;
+        }
+    }
+
+    for (k=0; k<nout; k++) {
+        out[k] <-- (lin >> k) & 1;
+
+        // Ensure out is binary
+        out[k] * (out[k] - 1) === 0;
+
+        lout += out[k] * 2**k;
+    }
+
+    // Ensure the sum;
+
+    lin === lout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/bitify.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/bitify.circom
@@ -0,0 +1,101 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "comparators.circom";
+include "aliascheck.circom";
+
+
+template Num2Bits(n) {
+    signal input in;
+    signal output out[n];
+    var lc1=0;
+
+    for (var i = 0; i<n; i++) {
+        out[i] <-- (in >> i) & 1;
+        out[i] * (out[i] -1 ) === 0;
+        lc1 += out[i] * 2**i;
+    }
+
+    lc1 === in;
+}
+
+template Num2Bits_strict() {
+    signal input in;
+    signal output out[254];
+
+    component aliasCheck = AliasCheck();
+    component n2b = Num2Bits(254);
+    in ==> n2b.in;
+
+    for (var i=0; i<254; i++) {
+        n2b.out[i] ==> out[i];
+        n2b.out[i] ==> aliasCheck.in[i];
+    }
+}
+
+template Bits2Num(n) {
+    signal input in[n];
+    signal output out;
+    var lc1=0;
+
+    for (var i = 0; i<n; i++) {
+        lc1 += in[i] * 2**i;
+    }
+
+    lc1 ==> out;
+}
+
+template Bits2Num_strict() {
+    signal input in[n];
+    signal output out;
+
+    component aliasCheck = AliasCheck();
+    component b2n = Bits2Num(254);
+
+    for (var i=0; i<254; i++) {
+        in[i] ==> b2n.in[i];
+        in[i] ==> aliasCheck.in[i];
+    }
+
+    b2n.out ==> out;
+}
+
+template Num2BitsNeg(n) {
+    signal input in;
+    signal output out[n];
+    var lc1=0;
+
+    component isZero;
+
+    isZero = IsZero();
+
+    var neg = n == 0 ? 0 : 2**n - in;
+
+    for (var i = 0; i<n; i++) {
+        out[i] <-- (neg >> i) & 1;
+        out[i] * (out[i] -1 ) === 0;
+        lc1 += out[i] * 2**i;
+    }
+
+    in ==> isZero.in;
+
+
+
+    lc1 + isZero.out * 2**n === 2**n - in;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/comparators.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/comparators.circom
@@ -0,0 +1,139 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "bitify.circom";
+include "binsum.circom";
+
+template IsZero() {
+    signal input in;
+    signal output out;
+
+    signal inv;
+
+    inv <-- in!=0 ? 1/in : 0;
+
+    out <== -in*inv +1;
+    in*out === 0;
+}
+
+
+template IsEqual() {
+    signal input in[2];
+    signal output out;
+
+    component isz = IsZero();
+
+    in[1] - in[0] ==> isz.in;
+
+    isz.out ==> out;
+}
+
+template ForceEqualIfEnabled() {
+    signal input enabled;
+    signal input in[2];
+
+    component isz = IsZero();
+
+    in[1] - in[0] ==> isz.in;
+
+    (1 - isz.out)*enabled === 0;
+}
+
+/*
+// N is the number of bits the input  have.
+// The MSF is the sign bit.
+template LessThan(n) {
+    signal input in[2];
+    signal output out;
+
+    component num2Bits0;
+    component num2Bits1;
+
+    component adder;
+
+    adder = BinSum(n, 2);
+
+    num2Bits0 = Num2Bits(n);
+    num2Bits1 = Num2BitsNeg(n);
+
+    in[0] ==> num2Bits0.in;
+    in[1] ==> num2Bits1.in;
+
+    var i;
+    for (i=0;i<n;i++) {
+        num2Bits0.out[i] ==> adder.in[0][i];
+        num2Bits1.out[i] ==> adder.in[1][i];
+    }
+
+    adder.out[n-1] ==> out;
+}
+*/
+
+template LessThan(n) {
+    signal input in[2];
+    signal output out;
+
+    component n2b = Num2Bits(n*2+1);
+
+    n2b.in <== in[0]+ (1<<n) - in[1];
+
+    out <== 1-n2b.out[n];
+}
+
+
+
+// N is the number of bits the input  have.
+// The MSF is the sign bit.
+template LessEqThan(n) {
+    signal input in[2];
+    signal output out;
+
+    component lt = LessThan(n);
+
+    lt.in[0] <== in[0];
+    lt.in[1] <== in[1]+1;
+    lt.out ==> out;
+}
+
+// N is the number of bits the input  have.
+// The MSF is the sign bit.
+template GreaterThan(n) {
+    signal input in[2];
+    signal output out;
+
+    component lt = LessThan(n);
+
+    lt.in[0] <== in[1];
+    lt.in[1] <== in[0];
+    lt.out ==> out;
+}
+
+// N is the number of bits the input  have.
+// The MSF is the sign bit.
+template GreaterEqThan(n) {
+    signal input in[2];
+    signal output out;
+
+    component lt = LessThan(n);
+
+    lt.in[0] <== in[1];
+    lt.in[1] <== in[0]+1;
+    lt.out ==> out;
+}
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/compconstant.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/compconstant.circom
@@ -0,0 +1,74 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "bitify.circom";
+
+// Returns 1 if in (in binary) > ct
+
+template CompConstant(ct) {
+    signal input in[254];
+    signal output out;
+
+    signal parts[127];
+    signal sout;
+
+    var clsb;
+    var cmsb;
+    var slsb;
+    var smsb;
+
+    var sum=0;
+
+    var b = (1 << 128) -1;
+    var a = 1;
+    var e = 1;
+    var i;
+
+    for (i=0;i<127; i++) {
+        clsb = (ct >> (i*2)) & 1;
+        cmsb = (ct >> (i*2+1)) & 1;
+        slsb = in[i*2];
+        smsb = in[i*2+1];
+
+
+        if ((cmsb==0)&(clsb==0)) {
+            parts[i] <== -b*smsb*slsb + b*smsb + b*slsb;
+        } else if ((cmsb==0)&(clsb==1)) {
+            parts[i] <== a*smsb*slsb - a*slsb + b*smsb - a*smsb + a;
+        } else if ((cmsb==1)&(clsb==0)) {
+            parts[i] <== b*smsb*slsb - a*smsb + a;
+        } else {
+            parts[i] <== -a*smsb*slsb + a;
+        }
+
+        sum = sum + parts[i];
+
+        b = b -e;
+        a = a +e;
+        e = e*2;
+    }
+
+    sout <== sum;
+
+    component num2bits = Num2Bits(135);
+
+    num2bits.in <== sout;
+
+    out <== num2bits.out[127];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsa.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsa.circom
@@ -0,0 +1,138 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+include "pointbits.circom";
+include "pedersen.circom";
+include "escalarmulany.circom";
+include "escalarmulfix.circom";
+
+template EdDSAVerifier(n) {
+    signal input msg[n];
+
+    signal input A[256];
+    signal input R8[256];
+    signal input S[256];
+
+    signal Ax;
+    signal Ay;
+
+    signal R8x;
+    signal R8y;
+
+    var i;
+
+// Ensure S<Subgroup Order
+
+    component  compConstant = CompConstant(2736030358979909402780800718157159386076813972158567259200215660948447373040);
+
+    for (i=0; i<254; i++) {
+        S[i] ==> compConstant.in[i];
+    }
+    compConstant.out === 0;
+    S[254] === 0;
+    S[255] === 0;
+
+// Convert A to Field elements (And verify A)
+
+    component bits2pointA = Bits2Point_Strict();
+
+    for (i=0; i<256; i++) {
+        bits2pointA.in[i] <== A[i];
+    }
+    Ax <== bits2pointA.out[0];
+    Ay <== bits2pointA.out[1];
+
+// Convert R8 to Field elements (And verify R8)
+
+    component bits2pointR8 = Bits2Point_Strict();
+
+    for (i=0; i<256; i++) {
+        bits2pointR8.in[i] <== R8[i];
+    }
+    R8x <== bits2pointR8.out[0];
+    R8y <== bits2pointR8.out[1];
+
+// Calculate the h = H(R,A, msg)
+
+    component hash = Pedersen(512+n);
+
+    for (i=0; i<256; i++) {
+        hash.in[i] <== R8[i];
+        hash.in[256+i] <== A[i];
+    }
+    for (i=0; i<n; i++) {
+        hash.in[512+i] <== msg[i];
+    }
+
+    component point2bitsH = Point2Bits_Strict();
+    point2bitsH.in[0] <== hash.out[0];
+    point2bitsH.in[1] <== hash.out[1];
+
+// Calculate second part of the right side:  right2 = h*8*A
+
+    // Multiply by 8 by adding it 3 times.  This also ensure that the result is in
+    // the subgroup.
+    component dbl1 = BabyDbl();
+    dbl1.x <== Ax;
+    dbl1.y <== Ay;
+    component dbl2 = BabyDbl();
+    dbl2.x <== dbl1.xout;
+    dbl2.y <== dbl1.yout;
+    component dbl3 = BabyDbl();
+    dbl3.x <== dbl2.xout;
+    dbl3.y <== dbl2.yout;
+
+    // We check that A is not zero.
+    component isZero = IsZero();
+    isZero.in <== dbl3.x;
+    isZero.out === 0;
+
+    component mulAny = EscalarMulAny(256);
+    for (i=0; i<256; i++) {
+        mulAny.e[i] <== point2bitsH.out[i];
+    }
+    mulAny.p[0] <== dbl3.xout;
+    mulAny.p[1] <== dbl3.yout;
+
+
+// Compute the right side: right =  R8 + right2
+
+    component addRight = BabyAdd();
+    addRight.x1 <== R8x;
+    addRight.y1 <== R8y;
+    addRight.x2 <== mulAny.out[0];
+    addRight.y2 <== mulAny.out[1];
+
+// Calculate left side of equation left = S*B8
+
+    var BASE8 = [
+        5299619240641551281634865583518297030282874472190772894086521144482721001553,
+        16950150798460657717958625567821834550301663161624707787222815936182638968203
+    ];
+    component mulFix = EscalarMulFix(256, BASE8);
+    for (i=0; i<256; i++) {
+        mulFix.e[i] <== S[i];
+    }
+
+// Do the comparation left == right
+
+    mulFix.out[0] === addRight.xout;
+    mulFix.out[1] === addRight.yout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsamimc.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsamimc.circom
@@ -0,0 +1,123 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+include "pointbits.circom";
+include "mimc.circom";
+include "bitify.circom";
+include "escalarmulany.circom";
+include "escalarmulfix.circom";
+
+template EdDSAMiMCVerifier() {
+    signal input enabled;
+    signal input Ax;
+    signal input Ay;
+
+    signal input S;
+    signal input R8x;
+    signal input R8y;
+
+    signal input M;
+
+    var i;
+
+// Ensure S<Subgroup Order
+
+    component snum2bits = Num2Bits(253);
+    snum2bits.in <== S;
+
+    component  compConstant = CompConstant(2736030358979909402780800718157159386076813972158567259200215660948447373040);
+
+    for (i=0; i<253; i++) {
+        snum2bits.out[i] ==> compConstant.in[i];
+    }
+    compConstant.in[253] <== 0;
+    compConstant.out === 0;
+
+// Calculate the h = H(R,A, msg)
+
+    component hash = MultiMiMC7(5, 91);
+    hash.in[0] <== R8x;
+    hash.in[1] <== R8y;
+    hash.in[2] <== Ax;
+    hash.in[3] <== Ay;
+    hash.in[4] <== M;
+    hash.k <== 0;
+
+    component h2bits = Num2Bits_strict();
+    h2bits.in <== hash.out;
+
+// Calculate second part of the right side:  right2 = h*8*A
+
+    // Multiply by 8 by adding it 3 times.  This also ensure that the result is in
+    // the subgroup.
+    component dbl1 = BabyDbl();
+    dbl1.x <== Ax;
+    dbl1.y <== Ay;
+    component dbl2 = BabyDbl();
+    dbl2.x <== dbl1.xout;
+    dbl2.y <== dbl1.yout;
+    component dbl3 = BabyDbl();
+    dbl3.x <== dbl2.xout;
+    dbl3.y <== dbl2.yout;
+
+    // We check that A is not zero.
+    component isZero = IsZero();
+    isZero.in <== dbl3.x;
+    isZero.out === 0;
+
+    component mulAny = EscalarMulAny(254);
+    for (i=0; i<254; i++) {
+        mulAny.e[i] <== h2bits.out[i];
+    }
+    mulAny.p[0] <== dbl3.xout;
+    mulAny.p[1] <== dbl3.yout;
+
+
+// Compute the right side: right =  R8 + right2
+
+    component addRight = BabyAdd();
+    addRight.x1 <== R8x;
+    addRight.y1 <== R8y;
+    addRight.x2 <== mulAny.out[0];
+    addRight.y2 <== mulAny.out[1];
+
+// Calculate left side of equation left = S*B8
+
+    var BASE8 = [
+        5299619240641551281634865583518297030282874472190772894086521144482721001553,
+        16950150798460657717958625567821834550301663161624707787222815936182638968203
+    ];
+    component mulFix = EscalarMulFix(253, BASE8);
+    for (i=0; i<253; i++) {
+        mulFix.e[i] <== snum2bits.out[i];
+    }
+
+// Do the comparation left == right if enabled;
+
+    component eqCheckX = ForceEqualIfEnabled();
+    eqCheckX.enabled <== enabled;
+    eqCheckX.in[0] <== mulFix.out[0];
+    eqCheckX.in[1] <== addRight.xout;
+
+    component eqCheckY = ForceEqualIfEnabled();
+    eqCheckY.enabled <== enabled;
+    eqCheckY.in[0] <== mulFix.out[1];
+    eqCheckY.in[1] <== addRight.yout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsamimcsponge.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsamimcsponge.circom
@@ -0,0 +1,123 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+include "pointbits.circom";
+include "mimcsponge.circom";
+include "bitify.circom";
+include "escalarmulany.circom";
+include "escalarmulfix.circom";
+
+template EdDSAMiMCSpongeVerifier() {
+    signal input enabled;
+    signal input Ax;
+    signal input Ay;
+
+    signal input S;
+    signal input R8x;
+    signal input R8y;
+
+    signal input M;
+
+    var i;
+
+// Ensure S<Subgroup Order
+
+    component snum2bits = Num2Bits(253);
+    snum2bits.in <== S;
+
+    component  compConstant = CompConstant(2736030358979909402780800718157159386076813972158567259200215660948447373040);
+
+    for (i=0; i<253; i++) {
+        snum2bits.out[i] ==> compConstant.in[i];
+    }
+    compConstant.in[253] <== 0;
+    compConstant.out === 0;
+
+// Calculate the h = H(R,A, msg)
+
+    component hash = MiMCSponge(5, 220, 1);
+    hash.ins[0] <== R8x;
+    hash.ins[1] <== R8y;
+    hash.ins[2] <== Ax;
+    hash.ins[3] <== Ay;
+    hash.ins[4] <== M;
+    hash.k <== 0;
+
+    component h2bits = Num2Bits_strict();
+    h2bits.in <== hash.outs[0];
+
+// Calculate second part of the right side:  right2 = h*8*A
+
+    // Multiply by 8 by adding it 3 times.  This also ensure that the result is in
+    // the subgroup.
+    component dbl1 = BabyDbl();
+    dbl1.x <== Ax;
+    dbl1.y <== Ay;
+    component dbl2 = BabyDbl();
+    dbl2.x <== dbl1.xout;
+    dbl2.y <== dbl1.yout;
+    component dbl3 = BabyDbl();
+    dbl3.x <== dbl2.xout;
+    dbl3.y <== dbl2.yout;
+
+    // We check that A is not zero.
+    component isZero = IsZero();
+    isZero.in <== dbl3.x;
+    isZero.out === 0;
+
+    component mulAny = EscalarMulAny(254);
+    for (i=0; i<254; i++) {
+        mulAny.e[i] <== h2bits.out[i];
+    }
+    mulAny.p[0] <== dbl3.xout;
+    mulAny.p[1] <== dbl3.yout;
+
+
+// Compute the right side: right =  R8 + right2
+
+    component addRight = BabyAdd();
+    addRight.x1 <== R8x;
+    addRight.y1 <== R8y;
+    addRight.x2 <== mulAny.out[0];
+    addRight.y2 <== mulAny.out[1];
+
+// Calculate left side of equation left = S*B8
+
+    var BASE8 = [
+        5299619240641551281634865583518297030282874472190772894086521144482721001553,
+        16950150798460657717958625567821834550301663161624707787222815936182638968203
+    ];
+    component mulFix = EscalarMulFix(253, BASE8);
+    for (i=0; i<253; i++) {
+        mulFix.e[i] <== snum2bits.out[i];
+    }
+
+// Do the comparation left == right if enabled;
+
+    component eqCheckX = ForceEqualIfEnabled();
+    eqCheckX.enabled <== enabled;
+    eqCheckX.in[0] <== mulFix.out[0];
+    eqCheckX.in[1] <== addRight.xout;
+
+    component eqCheckY = ForceEqualIfEnabled();
+    eqCheckY.enabled <== enabled;
+    eqCheckY.in[0] <== mulFix.out[1];
+    eqCheckY.in[1] <== addRight.yout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsaposeidon.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/eddsaposeidon.circom
@@ -0,0 +1,122 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+include "poseidon.circom";
+include "bitify.circom";
+include "escalarmulany.circom";
+include "escalarmulfix.circom";
+
+template EdDSAPoseidonVerifier() {
+    signal input enabled;
+    signal input Ax;
+    signal input Ay;
+
+    signal input S;
+    signal input R8x;
+    signal input R8y;
+
+    signal input M;
+
+    var i;
+
+// Ensure S<Subgroup Order
+
+    component snum2bits = Num2Bits(253);
+    snum2bits.in <== S;
+
+    component  compConstant = CompConstant(2736030358979909402780800718157159386076813972158567259200215660948447373040);
+
+    for (i=0; i<253; i++) {
+        snum2bits.out[i] ==> compConstant.in[i];
+    }
+    compConstant.in[253] <== 0;
+    compConstant.out === 0;
+
+// Calculate the h = H(R,A, msg)
+
+    component hash = Poseidon(5, 6, 8, 57);
+
+    hash.inputs[0] <== R8x;
+    hash.inputs[1] <== R8y;
+    hash.inputs[2] <== Ax;
+    hash.inputs[3] <== Ay;
+    hash.inputs[4] <== M;
+
+    component h2bits = Num2Bits_strict();
+    h2bits.in <== hash.out;
+
+// Calculate second part of the right side:  right2 = h*8*A
+
+    // Multiply by 8 by adding it 3 times.  This also ensure that the result is in
+    // the subgroup.
+    component dbl1 = BabyDbl();
+    dbl1.x <== Ax;
+    dbl1.y <== Ay;
+    component dbl2 = BabyDbl();
+    dbl2.x <== dbl1.xout;
+    dbl2.y <== dbl1.yout;
+    component dbl3 = BabyDbl();
+    dbl3.x <== dbl2.xout;
+    dbl3.y <== dbl2.yout;
+
+    // We check that A is not zero.
+    component isZero = IsZero();
+    isZero.in <== dbl3.x;
+    isZero.out === 0;
+
+    component mulAny = EscalarMulAny(254);
+    for (i=0; i<254; i++) {
+        mulAny.e[i] <== h2bits.out[i];
+    }
+    mulAny.p[0] <== dbl3.xout;
+    mulAny.p[1] <== dbl3.yout;
+
+
+// Compute the right side: right =  R8 + right2
+
+    component addRight = BabyAdd();
+    addRight.x1 <== R8x;
+    addRight.y1 <== R8y;
+    addRight.x2 <== mulAny.out[0];
+    addRight.y2 <== mulAny.out[1];
+
+// Calculate left side of equation left = S*B8
+
+    var BASE8 = [
+        5299619240641551281634865583518297030282874472190772894086521144482721001553,
+        16950150798460657717958625567821834550301663161624707787222815936182638968203
+    ];
+    component mulFix = EscalarMulFix(253, BASE8);
+    for (i=0; i<253; i++) {
+        mulFix.e[i] <== snum2bits.out[i];
+    }
+
+// Do the comparation left == right if enabled;
+
+    component eqCheckX = ForceEqualIfEnabled();
+    eqCheckX.enabled <== enabled;
+    eqCheckX.in[0] <== mulFix.out[0];
+    eqCheckX.in[1] <== addRight.xout;
+
+    component eqCheckY = ForceEqualIfEnabled();
+    eqCheckY.enabled <== enabled;
+    eqCheckY.in[0] <== mulFix.out[1];
+    eqCheckY.in[1] <== addRight.yout;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmul.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmul.circom
@@ -0,0 +1,165 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+
+                                                        ┏━━━━━━━━━━━┓
+                                                        ┃           ┃
+                                                        ┃           ┃
+  (inx, iny) ══════════════════════════════════════════▶┃ EC Point  ┃
+                                                        ┃           ╠═▶ (outx, outy)
+                                                    ╔══▶┃   Adder   ┃
+                                                    ║   ┃           ┃
+                                                    ║   ┃           ┃
+                                                    ║   ┃           ┃
+       ┏━━━━━━━━━━━┓                ┏━━━━━━━━━━━━┓  ║   ┗━━━━━━━━━━━┛
+       ┃           ┃                ┃            ┃  ║
+       ┃           ┃                ┃            ┃  ║
+       ┃           ╠═══(p0x,p0y)═══▶┃            ┃  ║
+       ┃           ╠═══(p1x,p1y)═══▶┃            ┃  ║
+       ┃           ╠═══(p2x,p2y)═══▶┃            ┃  ║
+       ┃           ╠═══(p3x,p3y)═══▶┃            ┃  ║
+       ┃           ╠═══(p4x,p4y)═══▶┃            ┃  ║
+       ┃           ╠═══(p5x,p5y)═══▶┃            ┃  ║
+       ┃           ╠═══(p6x,p6y)═══▶┃            ┃  ║
+       ┃ Constant  ╠═══(p7x,p7y)═══▶┃            ┃  ║
+       ┃  Points   ┃                ┃    Mux4    ╠══╝
+       ┃           ╠═══(p8x,p8y)═══▶┃            ┃
+       ┃           ╠═══(p9x,p9y)═══▶┃            ┃
+       ┃           ╠══(p10x,p10y)══▶┃            ┃
+       ┃           ╠══(p11x,p11y)══▶┃            ┃
+       ┃           ╠══(p12x,p12y)══▶┃            ┃
+       ┃           ╠══(p13x,p13y)══▶┃            ┃
+       ┃           ╠══(p14x,p14y)══▶┃            ┃
+       ┃           ╠══(p15x,p15y)══▶┃            ┃
+       ┃           ┃                ┃            ┃
+       ┃           ┃                ┃            ┃
+       ┗━━━━━━━━━━━┛                ┗━━━━━━━━━━━━┛
+                                      ▲  ▲  ▲  ▲
+                                      │  │  │  │
+  s0 ─────────────────────────────────┘  │  │  │
+  s1 ────────────────────────────────────┘  │  │
+  s2 ───────────────────────────────────────┘  │
+  s3 ──────────────────────────────────────────┘
+
+
+ */
+
+include "mux4.circom";
+include "escalarmulw4table.circom";
+include "babyjub.circom";
+
+template EscalarMulWindow(base, k) {
+
+    signal input in[2];
+    signal input sel[4];
+    signal output out[2];
+
+    component table;
+    component mux;
+    component adder;
+
+    var i;
+
+    table = EscalarMulW4Table(base, k);
+    mux = MultiMux4(2);
+    adder = BabyAdd();
+
+    for (i=0; i<4; i++) {
+        sel[i] ==> mux.s[i];
+    }
+
+    for (i=0; i<16; i++) {
+        table.out[i][0] ==> mux.c[0][i];
+        table.out[i][1] ==> mux.c[1][i];
+    }
+
+    in[0] ==> adder.x1;
+    in[1] ==> adder.y1;
+
+    mux.out[0] ==> adder.x2;
+    mux.out[1] ==> adder.y2;
+
+    adder.xout ==> out[0];
+    adder.yout ==> out[1];
+}
+
+/*
+
+
+                ┏━━━━━━━━━┓      ┏━━━━━━━━━┓                            ┏━━━━━━━━━━━━━━━━━━━┓
+                ┃         ┃      ┃         ┃                            ┃                   ┃
+      inp  ════▶┃Window(0)┃═════▶┃Window(1)┃════════  . . . . ═════════▶┃ Window(nBlocks-1) ┃═════▶ out
+                ┃         ┃      ┃         ┃                            ┃                   ┃
+                ┗━━━━━━━━━┛      ┗━━━━━━━━━┛                            ┗━━━━━━━━━━━━━━━━━━━┛
+                  ▲ ▲ ▲ ▲          ▲ ▲ ▲ ▲                                    ▲ ▲ ▲ ▲
+    in[0]─────────┘ │ │ │          │ │ │ │                                    │ │ │ │
+    in[1]───────────┘ │ │          │ │ │ │                                    │ │ │ │
+    in[2]─────────────┘ │          │ │ │ │                                    │ │ 0 0
+    in[3]───────────────┘          │ │ │ │                                    │ │
+    in[4]──────────────────────────┘ │ │ │                                    │ │
+    in[5]────────────────────────────┘ │ │                                    │ │
+    in[6]──────────────────────────────┘ │                                    │ │
+    in[7]────────────────────────────────┘                                    │ │
+        .                                                                     │ │
+        .                                                                     │ │
+  in[n-2]─────────────────────────────────────────────────────────────────────┘ │
+  in[n-1]───────────────────────────────────────────────────────────────────────┘
+
+ */
+
+template EscalarMul(n, base) {
+    signal input in[n];
+    signal input inp[2];   // Point input to be added
+    signal output out[2];
+
+    var nBlocks = ((n-1)>>2)+1;
+    var i;
+    var j;
+
+    component windows[nBlocks];
+
+    // Construct the windows
+    for (i=0; i<nBlocks; i++) {
+      windows[i] = EscalarMulWindow(base, i);
+    }
+
+    // Connect the selectors
+    for (i=0; i<nBlocks; i++) {
+        for (j=0; j<4; j++) {
+            if (i*4+j >= n) {
+                windows[i].sel[j] <== 0;
+            } else {
+                windows[i].sel[j] <== in[i*4+j];
+            }
+        }
+    }
+
+    // Start with generator
+    windows[0].in[0] <== inp[0];
+    windows[0].in[1] <== inp[1];
+
+    for(i=0; i<nBlocks-1; i++) {
+        windows[i].out[0] ==> windows[i+1].in[0];
+        windows[i].out[1] ==> windows[i+1].in[1];
+    }
+
+    windows[nBlocks-1].out[0] ==> out[0];
+    windows[nBlocks-1].out[1] ==> out[1];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulany.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulany.circom
@@ -0,0 +1,192 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "montgomery.circom";
+include "babyjub.circom";
+
+template Multiplexor2() {
+    signal input sel;
+    signal input in[2][2];
+    signal output out[2];
+
+    out[0] <== (in[1][0] - in[0][0])*sel + in[0][0];
+    out[1] <== (in[1][1] - in[0][1])*sel + in[0][1];
+}
+
+template BitElementMulAny() {
+    signal input sel;
+    signal input dblIn[2];
+    signal input addIn[2];
+    signal output dblOut[2];
+    signal output addOut[2];
+
+    component doubler = MontgomeryDouble();
+    component adder = MontgomeryAdd();
+    component selector = Multiplexor2();
+
+
+    sel ==> selector.sel;
+
+    dblIn[0] ==> doubler.in[0];
+    dblIn[1] ==> doubler.in[1];
+    doubler.out[0] ==> adder.in1[0];
+    doubler.out[1] ==> adder.in1[1];
+    addIn[0] ==> adder.in2[0];
+    addIn[1] ==> adder.in2[1];
+    addIn[0] ==> selector.in[0][0];
+    addIn[1] ==> selector.in[0][1];
+    adder.out[0] ==> selector.in[1][0];
+    adder.out[1] ==> selector.in[1][1];
+
+    doubler.out[0] ==> dblOut[0];
+    doubler.out[1] ==> dblOut[1];
+    selector.out[0] ==> addOut[0];
+    selector.out[1] ==> addOut[1];
+}
+
+// p is montgomery point
+// n must be <= 248
+// returns out in twisted edwards
+// Double is in montgomery to be linked;
+
+template SegmentMulAny(n) {
+    signal input e[n];
+    signal input p[2];
+    signal output out[2];
+    signal output dbl[2];
+
+    component bits[n-1];
+
+    component e2m = Edwards2Montgomery();
+
+    p[0] ==> e2m.in[0];
+    p[1] ==> e2m.in[1];
+
+    var i;
+
+    bits[0] = BitElementMulAny();
+    e2m.out[0] ==> bits[0].dblIn[0]
+    e2m.out[1] ==> bits[0].dblIn[1]
+    e2m.out[0] ==> bits[0].addIn[0]
+    e2m.out[1] ==> bits[0].addIn[1]
+    e[1] ==> bits[0].sel;
+
+    for (i=1; i<n-1; i++) {
+        bits[i] = BitElementMulAny();
+
+        bits[i-1].dblOut[0] ==> bits[i].dblIn[0]
+        bits[i-1].dblOut[1] ==> bits[i].dblIn[1]
+        bits[i-1].addOut[0] ==> bits[i].addIn[0]
+        bits[i-1].addOut[1] ==> bits[i].addIn[1]
+        e[i+1] ==> bits[i].sel;
+    }
+
+    bits[n-2].dblOut[0] ==> dbl[0];
+    bits[n-2].dblOut[1] ==> dbl[1];
+
+    component m2e = Montgomery2Edwards();
+
+    bits[n-2].addOut[0] ==> m2e.in[0];
+    bits[n-2].addOut[1] ==> m2e.in[1];
+
+    component eadder = BabyAdd();
+
+    m2e.out[0] ==> eadder.x1;
+    m2e.out[1] ==> eadder.y1;
+    -p[0] ==> eadder.x2;
+    p[1] ==> eadder.y2;
+
+    component lastSel = Multiplexor2();
+
+    e[0] ==> lastSel.sel;
+    eadder.xout ==> lastSel.in[0][0];
+    eadder.yout ==> lastSel.in[0][1];
+    m2e.out[0] ==> lastSel.in[1][0];
+    m2e.out[1] ==> lastSel.in[1][1];
+
+    lastSel.out[0] ==> out[0];
+    lastSel.out[1] ==> out[1];
+}
+
+// This function assumes that p is in the subgroup and it is different to 0
+
+template EscalarMulAny(n) {
+    signal input e[n];              // Input in binary format
+    signal input p[2];              // Point (Twisted format)
+    signal output out[2];           // Point (Twisted format)
+
+    var nsegments = (n-1)\148 +1;
+    var nlastsegment = n - (nsegments-1)*148;
+
+    component segments[nsegments];
+    component doublers[nsegments-1];
+    component m2e[nsegments-1];
+    component adders[nsegments-1];
+
+    var s;
+    var i;
+    var nseg;
+
+    for (s=0; s<nsegments; s++) {
+
+        nseg = (s < nsegments-1) ? 148 : nlastsegment;
+
+        segments[s] = SegmentMulAny(nseg);
+
+        for (i=0; i<nseg; i++) {
+            e[s*148+i] ==> segments[s].e[i];
+        }
+
+        if (s==0) {
+            p[0] ==> segments[s].p[0];
+            p[1] ==> segments[s].p[1];
+        } else {
+            doublers[s-1] = MontgomeryDouble();
+            m2e[s-1] = Montgomery2Edwards();
+            adders[s-1] = BabyAdd();
+
+            segments[s-1].dbl[0] ==> doublers[s-1].in[0];
+            segments[s-1].dbl[1] ==> doublers[s-1].in[1];
+
+            doublers[s-1].out[0] ==> m2e[s-1].in[0];
+            doublers[s-1].out[1] ==> m2e[s-1].in[1];
+
+            m2e[s-1].out[0] ==> segments[s].p[0];
+            m2e[s-1].out[1] ==> segments[s].p[1];
+
+            if (s==1) {
+                segments[s-1].out[0] ==> adders[s-1].x1;
+                segments[s-1].out[1] ==> adders[s-1].y1;
+            } else {
+                adders[s-2].xout ==> adders[s-1].x1;
+                adders[s-2].yout ==> adders[s-1].y1;
+            }
+            segments[s].out[0] ==> adders[s-1].x2;
+            segments[s].out[1] ==> adders[s-1].y2;
+        }
+    }
+
+    if (nsegments == 1) {
+        segments[0].out[0] ==> out[0];
+        segments[0].out[1] ==> out[1];
+    } else {
+        adders[nsegments-2].xout ==> out[0];
+        adders[nsegments-2].yout ==> out[1];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulfix.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulfix.circom
@@ -0,0 +1,298 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "mux3.circom";
+include "montgomery.circom";
+include "babyjub.circom";
+
+/*
+    Window of 3 elements, it calculates
+        out = base + base*in[0] + 2*base*in[1] + 4*base*in[2]
+        out4 = 4*base
+
+    The result should be compensated.
+ */
+
+/*
+
+    The scalar is s = a0 + a1*2^3 + a2*2^6 + ...... + a81*2^243
+    First We calculate Q = B + 2^3*B + 2^6*B + ......... + 2^246*B
+
+    Then we calculate S1 = 2*2^246*B + (1 + a0)*B + (2^3 + a1)*B + .....+ (2^243 + a81)*B
+
+    And Finaly we compute the result: RES = SQ - Q
+
+    As you can see the input of the adders cannot be equal nor zero, except for the last
+    substraction that it's done in montgomery.
+
+    A good way to see it is that the accumulator input of the adder >= 2^247*B and the other input
+    is the output of the windows that it's going to be <= 2^246*B
+ */
+template WindowMulFix() {
+    signal input in[3];
+    signal input base[2];
+    signal output out[2];
+    signal output out8[2];   // Returns 8*Base (To be linked)
+
+    component mux = MultiMux3(2);
+
+    mux.s[0] <== in[0];
+    mux.s[1] <== in[1];
+    mux.s[2] <== in[2];
+
+    component dbl2 = MontgomeryDouble();
+    component adr3 = MontgomeryAdd();
+    component adr4 = MontgomeryAdd();
+    component adr5 = MontgomeryAdd();
+    component adr6 = MontgomeryAdd();
+    component adr7 = MontgomeryAdd();
+    component adr8 = MontgomeryAdd();
+
+// in[0]  -> 1*BASE
+
+    mux.c[0][0] <== base[0];
+    mux.c[1][0] <== base[1];
+
+// in[1] -> 2*BASE
+    dbl2.in[0] <== base[0];
+    dbl2.in[1] <== base[1];
+    mux.c[0][1] <== dbl2.out[0];
+    mux.c[1][1] <== dbl2.out[1];
+
+// in[2] -> 3*BASE
+    adr3.in1[0] <== base[0];
+    adr3.in1[1] <== base[1];
+    adr3.in2[0] <== dbl2.out[0];
+    adr3.in2[1] <== dbl2.out[1];
+    mux.c[0][2] <== adr3.out[0];
+    mux.c[1][2] <== adr3.out[1];
+
+// in[3] -> 4*BASE
+    adr4.in1[0] <== base[0];
+    adr4.in1[1] <== base[1];
+    adr4.in2[0] <== adr3.out[0];
+    adr4.in2[1] <== adr3.out[1];
+    mux.c[0][3] <== adr4.out[0];
+    mux.c[1][3] <== adr4.out[1];
+
+// in[4] -> 5*BASE
+    adr5.in1[0] <== base[0];
+    adr5.in1[1] <== base[1];
+    adr5.in2[0] <== adr4.out[0];
+    adr5.in2[1] <== adr4.out[1];
+    mux.c[0][4] <== adr5.out[0];
+    mux.c[1][4] <== adr5.out[1];
+
+// in[5] -> 6*BASE
+    adr6.in1[0] <== base[0];
+    adr6.in1[1] <== base[1];
+    adr6.in2[0] <== adr5.out[0];
+    adr6.in2[1] <== adr5.out[1];
+    mux.c[0][5] <== adr6.out[0];
+    mux.c[1][5] <== adr6.out[1];
+
+// in[6] -> 7*BASE
+    adr7.in1[0] <== base[0];
+    adr7.in1[1] <== base[1];
+    adr7.in2[0] <== adr6.out[0];
+    adr7.in2[1] <== adr6.out[1];
+    mux.c[0][6] <== adr7.out[0];
+    mux.c[1][6] <== adr7.out[1];
+
+// in[7] -> 8*BASE
+    adr8.in1[0] <== base[0];
+    adr8.in1[1] <== base[1];
+    adr8.in2[0] <== adr7.out[0];
+    adr8.in2[1] <== adr7.out[1];
+    mux.c[0][7] <== adr8.out[0];
+    mux.c[1][7] <== adr8.out[1];
+
+    out8[0] <== adr8.out[0];
+    out8[1] <== adr8.out[1];
+
+    out[0] <== mux.out[0];
+    out[1] <== mux.out[1];
+}
+
+
+/*
+    This component does a multiplication of a escalar times a fix base
+    Signals:
+        e: The scalar in bits
+        base: the base point in edwards format
+        out:  The result
+        dbl: Point in Edwards to be linked to the next segment.
+ */
+
+template SegmentMulFix(nWindows) {
+    signal input e[nWindows*3];
+    signal input base[2];
+    signal output out[2];
+    signal output dbl[2];
+
+    var i;
+    var j;
+
+    // Convert the base to montgomery
+
+    component e2m = Edwards2Montgomery();
+    e2m.in[0] <== base[0];
+    e2m.in[1] <== base[1];
+
+    component windows[nWindows];
+    component adders[nWindows];
+    component cadders[nWindows];
+
+    // In the last step we add an extra doubler so that numbers do not match.
+    component dblLast = MontgomeryDouble();
+
+    for (i=0; i<nWindows; i++) {
+        windows[i] = WindowMulFix();
+        cadders[i] = MontgomeryAdd();
+        if (i==0) {
+            windows[i].base[0] <== e2m.out[0];
+            windows[i].base[1] <== e2m.out[1];
+            cadders[i].in1[0] <== e2m.out[0];
+            cadders[i].in1[1] <== e2m.out[1];
+        } else {
+            windows[i].base[0] <== windows[i-1].out8[0];
+            windows[i].base[1] <== windows[i-1].out8[1];
+            cadders[i].in1[0] <== cadders[i-1].out[0];
+            cadders[i].in1[1] <== cadders[i-1].out[1];
+        }
+        if (i<nWindows-1) {
+            cadders[i].in2[0] <== windows[i].out8[0];
+            cadders[i].in2[1] <== windows[i].out8[1];
+        } else {
+            dblLast.in[0] <== windows[i].out8[0];
+            dblLast.in[1] <== windows[i].out8[1];
+            cadders[i].in2[0] <== dblLast.out[0];
+            cadders[i].in2[1] <== dblLast.out[1];
+        }
+        for (j=0; j<3; j++) {
+            windows[i].in[j] <== e[3*i+j];
+        }
+    }
+
+    for (i=0; i<nWindows; i++) {
+        adders[i] = MontgomeryAdd();
+        if (i==0) {
+            adders[i].in1[0] <== dblLast.out[0];
+            adders[i].in1[1] <== dblLast.out[1];
+        } else {
+            adders[i].in1[0] <== adders[i-1].out[0];
+            adders[i].in1[1] <== adders[i-1].out[1];
+        }
+        adders[i].in2[0] <== windows[i].out[0];
+        adders[i].in2[1] <== windows[i].out[1];
+    }
+
+    component m2e = Montgomery2Edwards();
+    component cm2e = Montgomery2Edwards();
+
+    m2e.in[0] <== adders[nWindows-1].out[0];
+    m2e.in[1] <== adders[nWindows-1].out[1];
+    cm2e.in[0] <== cadders[nWindows-1].out[0];
+    cm2e.in[1] <== cadders[nWindows-1].out[1];
+
+    component cAdd = BabyAdd();
+    cAdd.x1 <== m2e.out[0];
+    cAdd.y1 <== m2e.out[1];
+    cAdd.x2 <== -cm2e.out[0];
+    cAdd.y2 <== cm2e.out[1];
+
+    cAdd.xout ==> out[0];
+    cAdd.yout ==> out[1];
+
+    windows[nWindows-1].out8[0] ==> dbl[0];
+    windows[nWindows-1].out8[1] ==> dbl[1];
+}
+
+
+/*
+This component multiplies a escalar times a fixed point BASE (twisted edwards format)
+    Signals
+        e: The escalar in binary format
+        out: The output point in twisted edwards
+ */
+template EscalarMulFix(n, BASE) {
+    signal input e[n];              // Input in binary format
+    signal output out[2];           // Point (Twisted format)
+
+    var nsegments = (n-1)\246 +1;       // 249 probably would work. But I'm not sure and for security I keep 246
+    var nlastsegment = n - (nsegments-1)*249;
+
+    component segments[nsegments];
+
+    component m2e[nsegments-1];
+    component adders[nsegments-1];
+
+    var s;
+    var i;
+    var nseg;
+    var nWindows
+
+    for (s=0; s<nsegments; s++) {
+
+        nseg = (s < nsegments-1) ? 249 : nlastsegment;
+        nWindows = ((nseg - 1)\3)+1;
+
+        segments[s] = SegmentMulFix(nWindows);
+
+        for (i=0; i<nseg; i++) {
+            segments[s].e[i] <== e[s*249+i];
+        }
+
+        for (i = nseg; i<nWindows*3; i++) {
+            segments[s].e[i] <== 0;
+        }
+
+        if (s==0) {
+            segments[s].base[0] <== BASE[0];
+            segments[s].base[1] <== BASE[1];
+        } else {
+            m2e[s-1] = Montgomery2Edwards();
+            adders[s-1] = BabyAdd();
+
+            segments[s-1].dbl[0] ==> m2e[s-1].in[0];
+            segments[s-1].dbl[1] ==> m2e[s-1].in[1];
+
+            m2e[s-1].out[0] ==> segments[s].base[0];
+            m2e[s-1].out[1] ==> segments[s].base[1];
+
+            if (s==1) {
+                segments[s-1].out[0] ==> adders[s-1].x1;
+                segments[s-1].out[1] ==> adders[s-1].y1;
+            } else {
+                adders[s-2].xout ==> adders[s-1].x1;
+                adders[s-2].yout ==> adders[s-1].y1;
+            }
+            segments[s].out[0] ==> adders[s-1].x2;
+            segments[s].out[1] ==> adders[s-1].y2;
+        }
+    }
+
+    if (nsegments == 1) {
+        segments[0].out[0] ==> out[0];
+        segments[0].out[1] ==> out[1];
+    } else {
+        adders[nsegments-2].xout ==> out[0];
+        adders[nsegments-2].yout ==> out[1];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulw4table.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/escalarmulw4table.circom
@@ -0,0 +1,49 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+function pointAdd(x1,y1,x2,y2) {
+    var a = 168700;
+    var d = 168696;
+
+    var res[2];
+    res[0] = (x1*y2 + y1*x2) / (1 + d*x1*x2*y1*y2);
+    res[1] = (y1*y2 - a*x1*x2) / (1 - d*x1*x2*y1*y2);
+    return res;
+}
+
+template EscalarMulW4Table(base, k) {
+    signal output out[16][2];
+
+    var i;
+    var p[2];
+
+    var dbl = base;
+
+    for (i=0; i<k*4; i++) {
+        dbl = pointAdd(dbl[0], dbl[1], dbl[0], dbl[1]);
+    }
+
+    out[0][0] <== 0;
+    out[0][1] <== 1;
+    for (i=1; i<16; i++) {
+        p = pointAdd(out[i-1][0], out[i-1][1], dbl[0], dbl[1]);
+        out[i][0] <== p[0];
+        out[i][1] <== p[1];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/gates.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/gates.circom
@@ -0,0 +1,92 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template XOR() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    out <== a + b - 2*a*b;
+}
+
+template AND() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    out <== a*b;
+}
+
+template OR() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    out <== a + b - a*b;
+}
+
+template NOT() {
+    signal input in;
+    signal output out;
+
+    out <== 1 + in - 2*in;
+}
+
+template NAND() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    out <== 1 - a*b;
+}
+
+template NOR() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    out <== a*b + 1 - a - b;
+}
+
+template MultiAND(n) {
+    signal input in[n];
+    signal output out;
+    if (n==1) {
+        out <== in[0];
+    } else if (n==2) {
+        component and1 = AND();
+        and1.a <== in[0];
+        and1.b <== in[1];
+        out <== and1.out;
+    } else {
+        component and2 = AND();
+        component ands[2];
+        var n1 = n\2;
+        var n2 = n-n\2;
+        ands[0] = MultiAND(n1);
+        ands[1] = MultiAND(n2);
+        for (var i=0; i<n1; i++) ands[0].in[i] <== in[i];
+        for (var i=0; i<n2; i++) ands[1].in[i] <== in[n1+i];
+        and2.a <== ands[0].out;
+        and2.b <== ands[1].out;
+        out <== and2.out;
+    }
+}
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mimc.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mimc.circom
@@ -0,0 +1,155 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template MiMC7(nrounds) {
+    signal input x_in;
+    signal input k;
+    signal output out;
+
+    var c = [
+        0,
+        20888961410941983456478427210666206549300505294776164667214940546594746570981,
+        15265126113435022738560151911929040668591755459209400716467504685752745317193,
+        8334177627492981984476504167502758309043212251641796197711684499645635709656,
+        1374324219480165500871639364801692115397519265181803854177629327624133579404,
+        11442588683664344394633565859260176446561886575962616332903193988751292992472,
+        2558901189096558760448896669327086721003508630712968559048179091037845349145,
+        11189978595292752354820141775598510151189959177917284797737745690127318076389,
+        3262966573163560839685415914157855077211340576201936620532175028036746741754,
+        17029914891543225301403832095880481731551830725367286980611178737703889171730,
+        4614037031668406927330683909387957156531244689520944789503628527855167665518,
+        19647356996769918391113967168615123299113119185942498194367262335168397100658,
+        5040699236106090655289931820723926657076483236860546282406111821875672148900,
+        2632385916954580941368956176626336146806721642583847728103570779270161510514,
+        17691411851977575435597871505860208507285462834710151833948561098560743654671,
+        11482807709115676646560379017491661435505951727793345550942389701970904563183,
+        8360838254132998143349158726141014535383109403565779450210746881879715734773,
+        12663821244032248511491386323242575231591777785787269938928497649288048289525,
+        3067001377342968891237590775929219083706800062321980129409398033259904188058,
+        8536471869378957766675292398190944925664113548202769136103887479787957959589,
+        19825444354178182240559170937204690272111734703605805530888940813160705385792,
+        16703465144013840124940690347975638755097486902749048533167980887413919317592,
+        13061236261277650370863439564453267964462486225679643020432589226741411380501,
+        10864774797625152707517901967943775867717907803542223029967000416969007792571,
+        10035653564014594269791753415727486340557376923045841607746250017541686319774,
+        3446968588058668564420958894889124905706353937375068998436129414772610003289,
+        4653317306466493184743870159523234588955994456998076243468148492375236846006,
+        8486711143589723036499933521576871883500223198263343024003617825616410932026,
+        250710584458582618659378487568129931785810765264752039738223488321597070280,
+        2104159799604932521291371026105311735948154964200596636974609406977292675173,
+        16313562605837709339799839901240652934758303521543693857533755376563489378839,
+        6032365105133504724925793806318578936233045029919447519826248813478479197288,
+        14025118133847866722315446277964222215118620050302054655768867040006542798474,
+        7400123822125662712777833064081316757896757785777291653271747396958201309118,
+        1744432620323851751204287974553233986555641872755053103823939564833813704825,
+        8316378125659383262515151597439205374263247719876250938893842106722210729522,
+        6739722627047123650704294650168547689199576889424317598327664349670094847386,
+        21211457866117465531949733809706514799713333930924902519246949506964470524162,
+        13718112532745211817410303291774369209520657938741992779396229864894885156527,
+        5264534817993325015357427094323255342713527811596856940387954546330728068658,
+        18884137497114307927425084003812022333609937761793387700010402412840002189451,
+        5148596049900083984813839872929010525572543381981952060869301611018636120248,
+        19799686398774806587970184652860783461860993790013219899147141137827718662674,
+        19240878651604412704364448729659032944342952609050243268894572835672205984837,
+        10546185249390392695582524554167530669949955276893453512788278945742408153192,
+        5507959600969845538113649209272736011390582494851145043668969080335346810411,
+        18177751737739153338153217698774510185696788019377850245260475034576050820091,
+        19603444733183990109492724100282114612026332366576932662794133334264283907557,
+        10548274686824425401349248282213580046351514091431715597441736281987273193140,
+        1823201861560942974198127384034483127920205835821334101215923769688644479957,
+        11867589662193422187545516240823411225342068709600734253659804646934346124945,
+        18718569356736340558616379408444812528964066420519677106145092918482774343613,
+        10530777752259630125564678480897857853807637120039176813174150229243735996839,
+        20486583726592018813337145844457018474256372770211860618687961310422228379031,
+        12690713110714036569415168795200156516217175005650145422920562694422306200486,
+        17386427286863519095301372413760745749282643730629659997153085139065756667205,
+        2216432659854733047132347621569505613620980842043977268828076165669557467682,
+        6309765381643925252238633914530877025934201680691496500372265330505506717193,
+        20806323192073945401862788605803131761175139076694468214027227878952047793390,
+        4037040458505567977365391535756875199663510397600316887746139396052445718861,
+        19948974083684238245321361840704327952464170097132407924861169241740046562673,
+        845322671528508199439318170916419179535949348988022948153107378280175750024,
+        16222384601744433420585982239113457177459602187868460608565289920306145389382,
+        10232118865851112229330353999139005145127746617219324244541194256766741433339,
+        6699067738555349409504843460654299019000594109597429103342076743347235369120,
+        6220784880752427143725783746407285094967584864656399181815603544365010379208,
+        6129250029437675212264306655559561251995722990149771051304736001195288083309,
+        10773245783118750721454994239248013870822765715268323522295722350908043393604,
+        4490242021765793917495398271905043433053432245571325177153467194570741607167,
+        19596995117319480189066041930051006586888908165330319666010398892494684778526,
+        837850695495734270707668553360118467905109360511302468085569220634750561083,
+        11803922811376367215191737026157445294481406304781326649717082177394185903907,
+        10201298324909697255105265958780781450978049256931478989759448189112393506592,
+        13564695482314888817576351063608519127702411536552857463682060761575100923924,
+        9262808208636973454201420823766139682381973240743541030659775288508921362724,
+        173271062536305557219323722062711383294158572562695717740068656098441040230,
+        18120430890549410286417591505529104700901943324772175772035648111937818237369,
+        20484495168135072493552514219686101965206843697794133766912991150184337935627,
+        19155651295705203459475805213866664350848604323501251939850063308319753686505,
+        11971299749478202793661982361798418342615500543489781306376058267926437157297,
+        18285310723116790056148596536349375622245669010373674803854111592441823052978,
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+        13602139229813231349386885113156901793661719180900395818909719758150455500533
+    ];
+
+    var t;
+    signal t2[nrounds];
+    signal t4[nrounds];
+    signal t6[nrounds];
+    signal t7[nrounds-1];
+
+    for (var i=0; i<nrounds; i++) {
+        t = (i==0) ? k+x_in : k + t7[i-1] + c[i];
+        t2[i] <== t*t;
+        t4[i] <== t2[i]*t2[i];
+        t6[i] <== t4[i]*t2[i];
+        if (i<nrounds-1) {
+            t7[i] <== t6[i]*t;
+        } else {
+            out <== t6[i]*t + k;
+        }
+    }
+}
+
+template MultiMiMC7(nInputs, nRounds) {
+    signal input in[nInputs];
+    signal input k;
+    signal output out;
+    signal r[nInputs +1];
+
+    component mims[nInputs];
+
+    r[0] <== k;
+    for (var i=0; i<nInputs; i++) {
+        mims[i] = MiMC7(nRounds);
+        mims[i].x_in <== in[i];
+        mims[i].k <== r[i];
+        r[i+1] <== r[i] + in[i] + mims[i].out;
+    }
+
+    out <== r[nInputs];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mimcsponge.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mimcsponge.circom
@@ -0,0 +1,283 @@
+// implements MiMC-2n/n as hash using a sponge construction.
+// log_5(21888242871839275222246405745257275088548364400416034343698204186575808495617) ~= 110
+// => nRounds should be 220
+template MiMCSponge(nInputs, nRounds, nOutputs) {
+  signal input ins[nInputs];
+  signal input k;
+  signal output outs[nOutputs];
+
+  // S = R||C
+  component S[nInputs + nOutputs - 1];
+
+  for (var i = 0; i < nInputs; i++) {
+    S[i] = MiMCFeistel(nRounds);
+    S[i].k <== k;
+    if (i == 0) {
+      S[i].xL_in <== ins[0];
+      S[i].xR_in <== 0;
+    } else {
+      S[i].xL_in <== S[i-1].xL_out + ins[i];
+      S[i].xR_in <== S[i-1].xR_out;
+    }
+  }
+
+  outs[0] = S[nInputs - 1].xL_out;
+
+  for (var i = 0; i < nOutputs - 1; i++) {
+    S[nInputs + i] = MiMCFeistel(nRounds);
+    S[nInputs + i].k <== k;
+    S[nInputs + i].xL_in <== S[nInputs + i - 1].xL_out;
+    S[nInputs + i].xR_in <== S[nInputs + i - 1].xR_out;
+    outs[i + 1] <== S[nInputs + i].xL_out;
+  }
+}
+
+template MiMCFeistel(nrounds) {
+    signal input xL_in;
+    signal input xR_in;
+    signal input k;
+    signal output xL_out;
+    signal output xR_out;
+
+    var c = [
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+      5100105771517691442278432864090229416166996183792075307747582375962855820797,
+      8777887112076272395250620301071581171386440850451972412060638225741125310886,
+      5300440870136391278944213332144327695659161151625757537632832724102670898756,
+      1205448543652932944633962232545707633928124666868453915721030884663332604536,
+      5542499997310181530432302492142574333860449305424174466698068685590909336771,
+      11028094245762332275225364962905938096659249161369092798505554939952525894293,
+      19187314764836593118404597958543112407224947638377479622725713735224279297009,
+      17047263688548829001253658727764731047114098556534482052135734487985276987385,
+      19914849528178967155534624144358541535306360577227460456855821557421213606310,
+      2929658084700714257515872921366736697080475676508114973627124569375444665664,
+      15092262360719700162343163278648422751610766427236295023221516498310468956361,
+      21578580340755653236050830649990190843552802306886938815497471545814130084980,
+      1258781501221760320019859066036073675029057285507345332959539295621677296991,
+      3819598418157732134449049289585680301176983019643974929528867686268702720163,
+      8653175945487997845203439345797943132543211416447757110963967501177317426221,
+      6614652990340435611114076169697104582524566019034036680161902142028967568142,
+      19212515502973904821995111796203064175854996071497099383090983975618035391558,
+      18664315914479294273286016871365663486061896605232511201418576829062292269769,
+      11498264615058604317482574216318586415670903094838791165247179252175768794889,
+      10814026414212439999107945133852431304483604215416531759535467355316227331774,
+      17566185590731088197064706533119299946752127014428399631467913813769853431107,
+      14016139747289624978792446847000951708158212463304817001882956166752906714332,
+      8242601581342441750402731523736202888792436665415852106196418942315563860366,
+      9244680976345080074252591214216060854998619670381671198295645618515047080988,
+      12216779172735125538689875667307129262237123728082657485828359100719208190116,
+      10702811721859145441471328511968332847175733707711670171718794132331147396634,
+      6479667912792222539919362076122453947926362746906450079329453150607427372979,
+      15117544653571553820496948522381772148324367479772362833334593000535648316185,
+      6842203153996907264167856337497139692895299874139131328642472698663046726780,
+      12732823292801537626009139514048596316076834307941224506504666470961250728055,
+      6936272626871035740815028148058841877090860312517423346335878088297448888663,
+      17297554111853491139852678417579991271009602631577069694853813331124433680030,
+      16641596134749940573104316021365063031319260205559553673368334842484345864859,
+      7400481189785154329569470986896455371037813715804007747228648863919991399081,
+      2273205422216987330510475127669563545720586464429614439716564154166712854048,
+      15162538063742142685306302282127534305212832649282186184583465569986719234456,
+      5628039096440332922248578319648483863204530861778160259559031331287721255522,
+      16085392195894691829567913404182676871326863890140775376809129785155092531260,
+      14227467863135365427954093998621993651369686288941275436795622973781503444257,
+      18224457394066545825553407391290108485121649197258948320896164404518684305122,
+      274945154732293792784580363548970818611304339008964723447672490026510689427,
+      11050822248291117548220126630860474473945266276626263036056336623671308219529,
+      2119542016932434047340813757208803962484943912710204325088879681995922344971,
+      0
+    ];
+
+    var t;
+    signal t2[nrounds];
+    signal t4[nrounds];
+    signal xL[nrounds-1];
+    signal xR[nrounds-1];
+
+    for (var i=0; i<nrounds; i++) {
+        t = (i==0) ? k+xL_in : k + xL[i-1] + c[i];
+        t2[i] <== t*t;
+        t4[i] <== t2[i]*t2[i];
+        if (i<nrounds-1) {
+          xL[i] <== ((i==0) ? xR_in : xR[i-1]) + t4[i]*t;
+          xR[i] = (i==0) ? xL_in : xL[i-1];
+        } else {
+          xR_out <== xR[i-1] + t4[i]*t;
+          xL_out <== xL[i-1];
+        }
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/montgomery.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/montgomery.circom
@@ -0,0 +1,141 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+    Source: https://en.wikipedia.org/wiki/Montgomery_curve
+
+                1 + y       1 + y
+    [u, v] = [ -------  , ---------- ]
+                1 - y      (1 - y)x
+
+ */
+
+template Edwards2Montgomery() {
+    signal input in[2];
+    signal output out[2];
+
+    out[0] <-- (1 + in[1]) / (1 - in[1]);
+    out[1] <-- out[0] / in[0];
+
+
+    out[0] * (1-in[1]) === (1 + in[1]);
+    out[1] * in[0] === out[0];
+}
+
+/*
+
+                u    u - 1
+    [x, y] = [ ---, ------- ]
+                v    u + 1
+
+ */
+template Montgomery2Edwards() {
+    signal input in[2];
+    signal output out[2];
+
+    out[0] <-- in[0] / in[1];
+    out[1] <-- (in[0] - 1) / (in[0] + 1);
+
+    out[0] * in[1] === in[0];
+    out[1] * (in[0] + 1) === in[0] - 1;
+}
+
+
+/*
+             x2 - x1
+    lamda = ---------
+             y2 - y1
+
+                                                    x3 + A + x1 + x2
+    x3 = B * lamda^2 - A - x1 -x2    =>  lamda^2 = ------------------
+                                                         B
+
+    y3 = (2*x1 + x2 + A)*lamda - B*lamda^3 - y1  =>
+
+
+    =>  y3 = lamda * ( 2*x1 + x2 + A  - x3 - A - x1 - x2)  - y1 =>
+
+    =>  y3 = lamda * ( x1 - x3 ) - y1
+
+----------
+
+             y2 - y1
+    lamda = ---------
+             x2 - x1
+
+    x3 = B * lamda^2 - A - x1 -x2
+
+    y3 = lamda * ( x1 - x3 ) - y1
+
+ */
+
+template MontgomeryAdd() {
+    signal input in1[2];
+    signal input in2[2];
+    signal output out[2];
+
+    var a = 168700;
+    var d = 168696;
+
+    var A = (2 * (a + d)) / (a - d);
+    var B = 4 / (a - d);
+
+    signal lamda;
+
+    lamda <-- (in2[1] - in1[1]) / (in2[0] - in1[0]);
+    lamda * (in2[0] - in1[0]) === (in2[1] - in1[1]);
+
+    out[0] <== B*lamda*lamda - A - in1[0] -in2[0];
+    out[1] <== lamda * (in1[0] - out[0]) - in1[1];
+}
+
+/*
+
+    x1_2 = x1*x1
+
+             3*x1_2 + 2*A*x1 + 1
+    lamda = ---------------------
+                   2*B*y1
+
+    x3 = B * lamda^2 - A - x1 -x1
+
+    y3 = lamda * ( x1 - x3 ) - y1
+
+ */
+template MontgomeryDouble() {
+    signal input in[2];
+    signal output out[2];
+
+    var a = 168700;
+    var d = 168696;
+
+    var A = (2 * (a + d)) / (a - d);
+    var B = 4 / (a - d);
+
+    signal lamda;
+    signal x1_2;
+
+    x1_2 <== in[0] * in[0];
+
+    lamda <-- (3*x1_2 + 2*A*in[0] + 1 ) / (2*B*in[1]);
+    lamda * (2*B*in[1]) === (3*x1_2 + 2*A*in[0] + 1 );
+
+    out[0] <== B*lamda*lamda - A - 2*in[0];
+    out[1] <== lamda * (in[0] - out[0]) - in[1];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/multiplexer.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/multiplexer.circom
@@ -0,0 +1,113 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+// --> Assignation without constraint
+// <-- Assignation without constraint
+// === Constraint
+// <== Assignation with constraint
+// ==> Assignation with constraint
+// All variables are members of the field F[p]
+// https://github.com/zcash-hackworks/sapling-crypto
+// https://github.com/ebfull/bellman
+
+/*
+function log2(a) {
+    if (a==0) {
+        return 0;
+    }
+    let n = 1;
+    let r = 1;
+    while (n<a) {
+        r++;
+        n *= 2;
+    }
+    return r;
+}
+*/
+
+template EscalarProduct(w) {
+    signal input in1[w];
+    signal input in2[w];
+    signal output out;
+    signal aux[w];
+    var lc = 0;
+    for (var i=0; i<w; i++) {
+        aux[i] <== in1[i]*in2[i];
+        lc = lc + aux[i];
+    }
+    out <== lc;
+}
+
+template Decoder(w) {
+    signal input inp;
+    signal output out[w];
+    signal output success;
+    var lc=0;
+
+    for (var i=0; i<w; i++) {
+        out[i] <-- (inp == i) ? 1 : 0;
+        out[i] * (inp-i) === 0;
+        lc = lc + out[i];
+    }
+
+    lc ==> success;
+    success * (success -1) === 0;
+}
+
+
+template Multiplexer(wIn, nIn) {
+    signal input inp[nIn][wIn];
+    signal input sel;
+    signal output out[wIn];
+    component dec = Decoder(nIn);
+    component ep[wIn];
+
+    for (var k=0; k<wIn; k++) {
+        ep[k] = EscalarProduct(nIn);
+    }
+
+    sel ==> dec.inp;
+    for (var j=0; j<wIn; j++) {
+        for (var k=0; k<nIn; k++) {
+            inp[k][j] ==> ep[j].in1[k];
+            dec.out[k] ==> ep[j].in2[k];
+        }
+        ep[j].out ==> out[j];
+    }
+    dec.success === 1;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux1.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux1.circom
@@ -0,0 +1,47 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template MultiMux1(n) {
+    signal input c[n][2];  // Constants
+    signal input s;   // Selector
+    signal output out[n];
+
+    for (var i=0; i<n; i++) {
+
+        out[i] <== (c[i][1] - c[i][0])*s + c[i][0];
+
+    }
+}
+
+template Mux1() {
+    var i;
+    signal input c[2];  // Constants
+    signal input s;   // Selector
+    signal output out;
+
+    component mux = MultiMux1(1);
+
+    for (i=0; i<2; i++) {
+        mux.c[0][i] <== c[i];
+    }
+
+    s ==> mux.s;
+
+    mux.out[0] ==> out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux2.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux2.circom
@@ -0,0 +1,62 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template MultiMux2(n) {
+    signal input c[n][4];  // Constants
+    signal input s[2];   // Selector
+    signal output out[n];
+
+    signal a10[n];
+    signal a1[n];
+    signal a0[n];
+    signal a[n];
+
+    signal  s10;
+    s10 <== s[1] * s[0];
+
+    for (var i=0; i<n; i++) {
+
+          a10[i] <==  ( c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) * s10;
+           a1[i] <==  ( c[i][ 2]-c[i][ 0] ) * s[1];
+           a0[i] <==  ( c[i][ 1]-c[i][ 0] ) * s[0];
+            a[i] <==  ( c[i][ 0] )
+
+          out[i] <==  (  a10[i] +  a1[i] +  a0[i] +  a[i] );
+
+    }
+}
+
+template Mux2() {
+    var i;
+    signal input c[4];  // Constants
+    signal input s[2];   // Selector
+    signal output out;
+
+    component mux = MultiMux2(1);
+
+    for (i=0; i<4; i++) {
+        mux.c[0][i] <== c[i];
+    }
+
+    for (i=0; i<2; i++) {
+      s[i] ==> mux.s[i];
+    }
+
+    mux.out[0] ==> out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux3.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux3.circom
@@ -0,0 +1,74 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template MultiMux3(n) {
+    signal input c[n][8];  // Constants
+    signal input s[3];   // Selector
+    signal output out[n];
+
+    signal a210[n];
+    signal a21[n];
+    signal a20[n];
+    signal a2[n];
+
+    signal a10[n];
+    signal a1[n];
+    signal a0[n];
+    signal a[n];
+
+    // 4 constrains for the intermediary variables
+    signal  s10;
+    s10 <== s[1] * s[0];
+
+    for (var i=0; i<n; i++) {
+
+         a210[i] <==  ( c[i][ 7]-c[i][ 6]-c[i][ 5]+c[i][ 4] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) * s10;
+          a21[i] <==  ( c[i][ 6]-c[i][ 4]-c[i][ 2]+c[i][ 0] ) * s[1];
+          a20[i] <==  ( c[i][ 5]-c[i][ 4]-c[i][ 1]+c[i][ 0] ) * s[0];
+           a2[i] <==  ( c[i][ 4]-c[i][ 0] );
+
+          a10[i] <==  ( c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) * s10;
+           a1[i] <==  ( c[i][ 2]-c[i][ 0] ) * s[1];
+           a0[i] <==  ( c[i][ 1]-c[i][ 0] ) * s[0];
+            a[i] <==  ( c[i][ 0] )
+
+          out[i] <== ( a210[i] + a21[i] + a20[i] + a2[i] ) * s[2] +
+                     (  a10[i] +  a1[i] +  a0[i] +  a[i] );
+
+    }
+}
+
+template Mux3() {
+    var i;
+    signal input c[8];  // Constants
+    signal input s[3];   // Selector
+    signal output out;
+
+    component mux = MultiMux3(1);
+
+    for (i=0; i<8; i++) {
+        mux.c[0][i] <== c[i];
+    }
+
+    for (i=0; i<3; i++) {
+      s[i] ==> mux.s[i];
+    }
+
+    mux.out[0] ==> out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux4.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/mux4.circom
@@ -0,0 +1,118 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template MultiMux4(n) {
+    signal input c[n][16];  // Constants
+    signal input s[4];   // Selector
+    signal output out[n];
+
+    signal a3210[n];
+    signal a321[n];
+    signal a320[n];
+    signal a310[n];
+    signal a32[n];
+    signal a31[n];
+    signal a30[n];
+    signal a3[n];
+
+    signal a210[n];
+    signal a21[n];
+    signal a20[n];
+    signal a10[n];
+    signal a2[n];
+    signal a1[n];
+    signal a0[n];
+    signal a[n];
+
+    // 4 constrains for the intermediary variables
+    signal  s10;
+    s10 <== s[1] * s[0];
+    signal  s20;
+    s20 <== s[2] * s[0];
+    signal  s21;
+    s21 <== s[2] * s[1];
+    signal s210;
+    s210 <==  s21 * s[0];
+
+
+    for (var i=0; i<n; i++) {
+
+        a3210[i] <==  ( c[i][15]-c[i][14]-c[i][13]+c[i][12] - c[i][11]+c[i][10]+c[i][ 9]-c[i][ 8]
+                       -c[i][ 7]+c[i][ 6]+c[i][ 5]-c[i][ 4] + c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) * s210;
+         a321[i] <==  ( c[i][14]-c[i][12]-c[i][10]+c[i][ 8] - c[i][ 6]+c[i][ 4]+c[i][ 2]-c[i][ 0] ) * s21;
+         a320[i] <==  ( c[i][13]-c[i][12]-c[i][ 9]+c[i][ 8] - c[i][ 5]+c[i][ 4]+c[i][ 1]-c[i][ 0] ) * s20;
+         a310[i] <==  ( c[i][11]-c[i][10]-c[i][ 9]+c[i][ 8] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) * s10;
+          a32[i] <==  ( c[i][12]-c[i][ 8]-c[i][ 4]+c[i][ 0] ) * s[2];
+          a31[i] <==  ( c[i][10]-c[i][ 8]-c[i][ 2]+c[i][ 0] ) * s[1];
+          a30[i] <==  ( c[i][ 9]-c[i][ 8]-c[i][ 1]+c[i][ 0] ) * s[0];
+           a3[i] <==  ( c[i][ 8]-c[i][ 0] );
+
+         a210[i] <==  ( c[i][ 7]-c[i][ 6]-c[i][ 5]+c[i][ 4] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) * s210;
+          a21[i] <==  ( c[i][ 6]-c[i][ 4]-c[i][ 2]+c[i][ 0] ) * s21;
+          a20[i] <==  ( c[i][ 5]-c[i][ 4]-c[i][ 1]+c[i][ 0] ) * s20;
+          a10[i] <==  ( c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) * s10;
+           a2[i] <==  ( c[i][ 4]-c[i][ 0] ) * s[2];
+           a1[i] <==  ( c[i][ 2]-c[i][ 0] ) * s[1];
+           a0[i] <==  ( c[i][ 1]-c[i][ 0] ) * s[0];
+            a[i] <==  ( c[i][ 0] )
+
+          out[i] <== ( a3210[i] + a321[i] + a320[i] + a310[i] + a32[i] + a31[i] + a30[i] + a3[i] ) * s[3] +
+                     (  a210[i] +  a21[i] +  a20[i] +  a10[i] +  a2[i] +  a1[i] +  a0[i] +  a[i] );
+
+/*
+        out[i] <== (  s210 * ( c[i][15]-c[i][14]-c[i][13]+c[i][12] - c[i][11]+c[i][10]+c[i][ 9]-c[i][ 8]
+                              -c[i][ 7]+c[i][ 6]+c[i][ 5]-c[i][ 4] + c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) +
+                       s21 * ( c[i][14]-c[i][12]-c[i][10]+c[i][ 8] - c[i][ 6]+c[i][ 4]+c[i][ 2]-c[i][ 0] ) +
+                       s20 * ( c[i][13]-c[i][12]-c[i][ 9]+c[i][ 8] - c[i][ 5]+c[i][ 4]+c[i][ 1]-c[i][ 0] ) +
+                       s10 * ( c[i][11]-c[i][10]-c[i][ 9]+c[i][ 8] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) +
+                      s[2] * ( c[i][12]-c[i][ 8]-c[i][ 4]+c[i][ 0] ) +
+                      s[1] * ( c[i][10]-c[i][ 8]-c[i][ 2]+c[i][ 0] ) +
+                      s[0] * ( c[i][ 9]-c[i][ 8]-c[i][ 1]+c[i][ 0] ) +
+                             ( c[i][ 8]-c[i][ 0] ) ) * s[3]  +
+                (     s210 * ( c[i][ 7]-c[i][ 6]-c[i][ 5]+c[i][ 4] - c[i][ 3]+c[i][ 2]+c[i][ 1]-c[i][ 0] ) +
+                       s21 * ( c[i][ 6]-c[i][ 4]-c[i][ 2]+c[i][ 0] ) +
+                       s20 * ( c[i][ 5]-c[i][ 4]-c[i][ 1]+c[i][ 0] ) +
+                       s10 * ( c[i][ 3]-c[i][ 2]-c[i][ 1]+c[i][ 0] ) +
+                      s[2] * ( c[i][ 4]-c[i][ 0] ) +
+                      s[1] * ( c[i][ 2]-c[i][ 0] ) +
+                      s[0] * ( c[i][ 1]-c[i][ 0] ) +
+                             ( c[i][ 0] ));
+
+*/
+    }
+}
+
+template Mux4() {
+    var i;
+    signal input c[16];  // Constants
+    signal input s[4];   // Selector
+    signal output out;
+
+    component mux = MultiMux4(1);
+
+    for (i=0; i<16; i++) {
+        mux.c[0][i] <== c[i];
+    }
+
+    for (i=0; i<4; i++) {
+      s[i] ==> mux.s[i];
+    }
+
+    mux.out[0] ==> out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pedersen.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pedersen.circom
@@ -0,0 +1,255 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "montgomery.circom";
+include "mux3.circom";
+include "babyjub.circom";
+
+template Window4() {
+    signal input in[4];
+    signal input base[2];
+    signal output out[2];
+    signal output out8[2];   // Returns 8*Base (To be linked)
+
+    component mux = MultiMux3(2);
+
+    mux.s[0] <== in[0];
+    mux.s[1] <== in[1];
+    mux.s[2] <== in[2];
+
+    component dbl2 = MontgomeryDouble();
+    component adr3 = MontgomeryAdd();
+    component adr4 = MontgomeryAdd();
+    component adr5 = MontgomeryAdd();
+    component adr6 = MontgomeryAdd();
+    component adr7 = MontgomeryAdd();
+    component adr8 = MontgomeryAdd();
+
+// in[0]  -> 1*BASE
+
+    mux.c[0][0] <== base[0];
+    mux.c[1][0] <== base[1];
+
+// in[1] -> 2*BASE
+    dbl2.in[0] <== base[0];
+    dbl2.in[1] <== base[1];
+    mux.c[0][1] <== dbl2.out[0];
+    mux.c[1][1] <== dbl2.out[1];
+
+// in[2] -> 3*BASE
+    adr3.in1[0] <== base[0];
+    adr3.in1[1] <== base[1];
+    adr3.in2[0] <== dbl2.out[0];
+    adr3.in2[1] <== dbl2.out[1];
+    mux.c[0][2] <== adr3.out[0];
+    mux.c[1][2] <== adr3.out[1];
+
+// in[3] -> 4*BASE
+    adr4.in1[0] <== base[0];
+    adr4.in1[1] <== base[1];
+    adr4.in2[0] <== adr3.out[0];
+    adr4.in2[1] <== adr3.out[1];
+    mux.c[0][3] <== adr4.out[0];
+    mux.c[1][3] <== adr4.out[1];
+
+// in[4] -> 5*BASE
+    adr5.in1[0] <== base[0];
+    adr5.in1[1] <== base[1];
+    adr5.in2[0] <== adr4.out[0];
+    adr5.in2[1] <== adr4.out[1];
+    mux.c[0][4] <== adr5.out[0];
+    mux.c[1][4] <== adr5.out[1];
+
+// in[5] -> 6*BASE
+    adr6.in1[0] <== base[0];
+    adr6.in1[1] <== base[1];
+    adr6.in2[0] <== adr5.out[0];
+    adr6.in2[1] <== adr5.out[1];
+    mux.c[0][5] <== adr6.out[0];
+    mux.c[1][5] <== adr6.out[1];
+
+// in[6] -> 7*BASE
+    adr7.in1[0] <== base[0];
+    adr7.in1[1] <== base[1];
+    adr7.in2[0] <== adr6.out[0];
+    adr7.in2[1] <== adr6.out[1];
+    mux.c[0][6] <== adr7.out[0];
+    mux.c[1][6] <== adr7.out[1];
+
+// in[7] -> 8*BASE
+    adr8.in1[0] <== base[0];
+    adr8.in1[1] <== base[1];
+    adr8.in2[0] <== adr7.out[0];
+    adr8.in2[1] <== adr7.out[1];
+    mux.c[0][7] <== adr8.out[0];
+    mux.c[1][7] <== adr8.out[1];
+
+    out8[0] <== adr8.out[0];
+    out8[1] <== adr8.out[1];
+
+    out[0] <== mux.out[0];
+    out[1] <== - mux.out[1]*2*in[3] + mux.out[1];  // Negate y if in[3] is one
+}
+
+
+template Segment(nWindows) {
+    signal input in[nWindows*4];
+    signal input base[2];
+    signal output out[2];
+
+    var i;
+    var j;
+
+    // Convert the base to montgomery
+
+    component e2m = Edwards2Montgomery();
+    e2m.in[0] <== base[0];
+    e2m.in[1] <== base[1];
+
+    component windows[nWindows];
+    component doublers1[nWindows-1];
+    component doublers2[nWindows-1];
+    component adders[nWindows-1];
+    for (i=0; i<nWindows; i++) {
+        windows[i] = Window4();
+        if (i==0) {
+            windows[i].base[0] <== e2m.out[0];
+            windows[i].base[1] <== e2m.out[1];
+        } else {
+            doublers1[i-1] = MontgomeryDouble();
+            doublers2[i-1] = MontgomeryDouble();
+            doublers1[i-1].in[0] <== windows[i-1].out8[0];
+            doublers1[i-1].in[1] <== windows[i-1].out8[1];
+            doublers2[i-1].in[0] <== doublers1[i-1].out[0];
+            doublers2[i-1].in[1] <== doublers1[i-1].out[1];
+
+            windows[i].base[0] <== doublers2[i-1].out[0];
+            windows[i].base[1] <== doublers2[i-1].out[1];
+
+            adders[i-1] = MontgomeryAdd();
+            if (i==1) {
+                adders[i-1].in1[0] <== windows[0].out[0];
+                adders[i-1].in1[1] <== windows[0].out[1];
+            } else {
+                adders[i-1].in1[0] <== adders[i-2].out[0];
+                adders[i-1].in1[1] <== adders[i-2].out[1];
+            }
+            adders[i-1].in2[0] <== windows[i].out[0];
+            adders[i-1].in2[1] <== windows[i].out[1];
+        }
+        for (j=0; j<4; j++) {
+            windows[i].in[j] <== in[4*i+j];
+        }
+    }
+
+    component m2e = Montgomery2Edwards();
+
+    if (nWindows > 1) {
+        m2e.in[0] <== adders[nWindows-2].out[0];
+        m2e.in[1] <== adders[nWindows-2].out[1];
+    } else {
+        m2e.in[0] <== windows[0].out[0];
+        m2e.in[1] <== windows[0].out[1];
+    }
+
+    out[0] <== m2e.out[0];
+    out[1] <== m2e.out[1];
+}
+
+template Pedersen(n) {
+    signal input in[n];
+    signal output out[2];
+
+    var BASE = [
+        [10457101036533406547632367118273992217979173478358440826365724437999023779287,19824078218392094440610104313265183977899662750282163392862422243483260492317],
+        [2671756056509184035029146175565761955751135805354291559563293617232983272177,2663205510731142763556352975002641716101654201788071096152948830924149045094],
+        [5802099305472655231388284418920769829666717045250560929368476121199858275951,5980429700218124965372158798884772646841287887664001482443826541541529227896],
+        [7107336197374528537877327281242680114152313102022415488494307685842428166594,2857869773864086953506483169737724679646433914307247183624878062391496185654],
+        [20265828622013100949498132415626198973119240347465898028410217039057588424236,1160461593266035632937973507065134938065359936056410650153315956301179689506],
+        [1487999857809287756929114517587739322941449154962237464737694709326309567994,14017256862867289575056460215526364897734808720610101650676790868051368668003],
+        [14618644331049802168996997831720384953259095788558646464435263343433563860015,13115243279999696210147231297848654998887864576952244320558158620692603342236],
+        [6814338563135591367010655964669793483652536871717891893032616415581401894627,13660303521961041205824633772157003587453809761793065294055279768121314853695],
+        [3571615583211663069428808372184817973703476260057504149923239576077102575715,11981351099832644138306422070127357074117642951423551606012551622164230222506],
+        [18597552580465440374022635246985743886550544261632147935254624835147509493269,6753322320275422086923032033899357299485124665258735666995435957890214041481]
+    ]
+
+    var nSegments = ((n-1)\200)+1;
+
+    component segments[nSegments];
+
+    var i;
+    var j;
+    var nBits;
+    var nWindows;
+    for (i=0; i<nSegments; i++) {
+        nBits = (i == (nSegments-1)) ? n - (nSegments-1)*200 : 200;
+        nWindows = ((nBits - 1)\4)+1;
+        segments[i] = Segment(nWindows);
+        segments[i].base[0] <== BASE[i][0];
+        segments[i].base[1] <== BASE[i][1];
+        for (j = 0; j<nBits; j++) {
+            segments[i].in[j] <== in[i*200+j];
+        }
+        // Fill padding bits
+        for (j = nBits; j < nWindows*4; j++) {
+            segments[i].in[j] <== 0;
+        }
+    }
+
+    component adders[nSegments-1];
+
+    for (i=0; i<nSegments-1; i++) {
+        adders[i] = BabyAdd();
+        if (i==0) {
+            adders[i].x1 <== segments[0].out[0];
+            adders[i].y1 <== segments[0].out[1];
+            adders[i].x2 <== segments[1].out[0];
+            adders[i].y2 <== segments[1].out[1];
+        } else {
+            adders[i].x1 <== adders[i-1].xout;
+            adders[i].y1 <== adders[i-1].yout;
+            adders[i].x2 <== segments[i+1].out[0];
+            adders[i].y2 <== segments[i+1].out[1];
+        }
+    }
+
+/*
+    coponent packPoint = PackPoint();
+
+    if (nSegments>1) {
+        packPoint.in[0] <== adders[nSegments-2].xout;
+        packPoint.in[1] <== adders[nSegments-2].yout;
+    } else {
+        packPoint.in[0] <== segments[0].out[0];
+        packPoint.in[1] <== segments[0].out[1];
+    }
+
+    out[0] <== packPoint.out[0];
+    out[1] <== packPoint.out[1];
+*/
+
+    if (nSegments>1) {
+        out[0] <== adders[nSegments-2].xout;
+        out[1] <== adders[nSegments-2].yout;
+    } else {
+        out[0] <== segments[0].out[0];
+        out[1] <== segments[0].out[1];
+    }
+}
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pedersen_old.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pedersen_old.circom
@@ -0,0 +1,66 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "escalarmul.circom";
+
+template Pedersen(n) {
+    signal input in[n];
+    signal output out[2];
+
+    var nexps = ((n-1) \ 250) + 1;
+    var nlastbits = n - (nexps-1)*250;
+
+    component escalarMuls[nexps];
+
+    var PBASE = [
+        [10457101036533406547632367118273992217979173478358440826365724437999023779287,19824078218392094440610104313265183977899662750282163392862422243483260492317],
+        [2671756056509184035029146175565761955751135805354291559563293617232983272177,2663205510731142763556352975002641716101654201788071096152948830924149045094],
+        [5802099305472655231388284418920769829666717045250560929368476121199858275951,5980429700218124965372158798884772646841287887664001482443826541541529227896],
+        [7107336197374528537877327281242680114152313102022415488494307685842428166594,2857869773864086953506483169737724679646433914307247183624878062391496185654],
+        [20265828622013100949498132415626198973119240347465898028410217039057588424236,1160461593266035632937973507065134938065359936056410650153315956301179689506],
+        [1487999857809287756929114517587739322941449154962237464737694709326309567994,14017256862867289575056460215526364897734808720610101650676790868051368668003],
+        [14618644331049802168996997831720384953259095788558646464435263343433563860015,13115243279999696210147231297848654998887864576952244320558158620692603342236],
+        [6814338563135591367010655964669793483652536871717891893032616415581401894627,13660303521961041205824633772157003587453809761793065294055279768121314853695],
+        [3571615583211663069428808372184817973703476260057504149923239576077102575715,11981351099832644138306422070127357074117642951423551606012551622164230222506],
+        [18597552580465440374022635246985743886550544261632147935254624835147509493269,6753322320275422086923032033899357299485124665258735666995435957890214041481]
+    ];
+
+    var i;
+    var j;
+    var nexpbits;
+    for (i=0; i<nexps; i++) {
+        nexpbits = (i == nexps-1) ? nlastbits : 250;
+        escalarMuls[i] = EscalarMul(nexpbits, PBASE[i]);
+
+        for (j=0; j<nexpbits; j++) {
+            escalarMuls[i].in[j] <== in[250*i + j];
+        }
+
+        if (i==0) {
+            escalarMuls[i].inp[0] <== 0;
+            escalarMuls[i].inp[1] <== 1;
+        } else {
+            escalarMuls[i].inp[0] <== escalarMuls[i-1].out[0];
+            escalarMuls[i].inp[1] <== escalarMuls[i-1].out[1];
+        }
+    }
+
+    escalarMuls[nexps-1].out[0] ==> out[0];
+    escalarMuls[nexps-1].out[1] ==> out[1];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pointbits.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/pointbits.circom
@@ -0,0 +1,163 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "bitify.circom";
+include "aliascheck.circom";
+include "compconstant.circom";
+include "babyjub.circom";
+
+
+function sqrt(n) {
+
+    if (n == 0) {
+        return 0;
+    }
+
+    // Test that have solution
+    var res = n ** ((-1) >> 1);
+//        if (res!=1) assert(false, "SQRT does not exists");
+    if (res!=1) return 0;
+
+    var m = 28;
+    var c = 19103219067921713944291392827692070036145651957329286315305642004821462161904;
+    var t = n ** 81540058820840996586704275553141814055101440848469862132140264610111;
+    var r = n ** ((81540058820840996586704275553141814055101440848469862132140264610111+1)>>1);
+    var sq;
+    var i;
+    var b;
+    var j;
+
+    while ((r != 0)&&(t != 1)) {
+        sq = t*t;
+        i = 1;
+        while (sq!=1) {
+            i++;
+            sq = sq*sq;
+        }
+
+        // b = c ^ m-i-1
+        b = c;
+        for (j=0; j< m-i-1; j ++) b = b*b;
+
+        m = i;
+        c = b*b;
+        t = t*c;
+        r = r*b;
+    }
+
+    if (r > ((-1) >> 1)) {
+        r = -r;
+    }
+
+    return r;
+}
+
+
+template Bits2Point() {
+    signal input in[256];
+    signal output out[2];
+}
+
+template Bits2Point_Strict() {
+    signal input in[256];
+    signal output out[2];
+
+    var i;
+
+    // Check aliasing
+    component aliasCheckY = AliasCheck();
+    for (i=0; i<254; i++) {
+        aliasCheckY.in[i] <== in[i];
+    }
+    in[254] === 0;
+
+    component b2nY = Bits2Num(254);
+    for (i=0; i<254; i++) {
+        b2nY.in[i] <== in[i];
+    }
+
+    out[1] <== b2nY.out;
+
+    var a = 168700;
+    var d = 168696;
+
+    var y2 = out[1] * out[1];
+
+    var x = sqrt(   (1-y2)/(a - d*y2)  );
+
+    if (in[255] == 1) x = -x;
+
+    out[0] <-- x;
+
+    component babyCheck = BabyCheck();
+    babyCheck.x <== out[0];
+    babyCheck.y <== out[1];
+
+    component n2bX = Num2Bits(254);
+    n2bX.in <== out[0];
+    component aliasCheckX = AliasCheck();
+    for (i=0; i<254; i++) {
+        aliasCheckX.in[i] <== n2bX.out[i];
+    }
+
+    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
+    for (i=0; i<254; i++) {
+        signCalc.in[i] <== n2bX.out[i];
+    }
+
+    signCalc.out === in[255];
+}
+
+
+template Point2Bits() {
+    signal input in[2];
+    signal output out[256];
+
+
+}
+
+template Point2Bits_Strict() {
+    signal input in[2];
+    signal output out[256];
+
+    var i;
+
+    component n2bX = Num2Bits(254);
+    n2bX.in <== in[0];
+    component n2bY = Num2Bits(254);
+    n2bY.in <== in[1];
+
+    component aliasCheckX = AliasCheck();
+    component aliasCheckY = AliasCheck();
+    for (i=0; i<254; i++) {
+        aliasCheckX.in[i] <== n2bX.out[i];
+        aliasCheckY.in[i] <== n2bY.out[i];
+    }
+
+    component signCalc = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
+    for (i=0; i<254; i++) {
+        signCalc.in[i] <== n2bX.out[i];
+    }
+
+    for (i=0; i<254; i++) {
+        out[i] <== n2bY.out[i];
+    }
+    out[254] <== 0;
+    out[255] <== signCalc.out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/poseidon.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/poseidon.circom
@@ -0,0 +1,203 @@
+
+template Sigma() {
+    signal input in;
+    signal output out;
+
+    signal in2;
+    signal in4;
+
+    in2 <== in*in;
+    in4 <== in2*in2;
+
+    out <== in4*in;
+}
+
+template Ark(t, C) {
+    signal input in[t];
+    signal output out[t];
+    for (var i=0; i<t; i++) {
+        out[i] <== in[i] + C;
+    }
+}
+
+template Mix(t, M) {
+    signal input in[t];
+    signal output out[t];
+    var lc;
+
+    for (var i=0; i<t; i++) {
+        lc = 0;
+        for (var j=0; j<t; j++) {
+            lc = lc + M[i][j]*in[j];
+        }
+        out[i] <== lc;
+    }
+}
+
+//    var nRoundsF = 8;
+//    var nRoundsP = 57;
+//    var t = 6;
+
+template Poseidon(nInputs, t, nRoundsF, nRoundsP) {
+
+    var C = [
+        14397397413755236225575615486459253198602422701513067526754101844196324375522,
+        10405129301473404666785234951972711717481302463898292859783056520670200613128,
+        5179144822360023508491245509308555580251733042407187134628755730783052214509,
+        9132640374240188374542843306219594180154739721841249568925550236430986592615,
+        20360807315276763881209958738450444293273549928693737723235350358403012458514,
+        17933600965499023212689924809448543050840131883187652471064418452962948061619,
+        3636213416533737411392076250708419981662897009810345015164671602334517041153,
+        2008540005368330234524962342006691994500273283000229509835662097352946198608,
+        16018407964853379535338740313053768402596521780991140819786560130595652651567,
+        20653139667070586705378398435856186172195806027708437373983929336015162186471,
+        17887713874711369695406927657694993484804203950786446055999405564652412116765,
+        4852706232225925756777361208698488277369799648067343227630786518486608711772,
+        8969172011633935669771678412400911310465619639756845342775631896478908389850,
+        20570199545627577691240476121888846460936245025392381957866134167601058684375,
+        16442329894745639881165035015179028112772410105963688121820543219662832524136,
+        20060625627350485876280451423010593928172611031611836167979515653463693899374,
+        16637282689940520290130302519163090147511023430395200895953984829546679599107,
+        15599196921909732993082127725908821049411366914683565306060493533569088698214,
+        16894591341213863947423904025624185991098788054337051624251730868231322135455,
+        1197934381747032348421303489683932612752526046745577259575778515005162320212,
+        6172482022646932735745595886795230725225293469762393889050804649558459236626,
+        21004037394166516054140386756510609698837211370585899203851827276330669555417,
+        15262034989144652068456967541137853724140836132717012646544737680069032573006,
+        15017690682054366744270630371095785995296470601172793770224691982518041139766,
+        15159744167842240513848638419303545693472533086570469712794583342699782519832,
+        11178069035565459212220861899558526502477231302924961773582350246646450941231,
+        21154888769130549957415912997229564077486639529994598560737238811887296922114,
+        20162517328110570500010831422938033120419484532231241180224283481905744633719,
+        2777362604871784250419758188173029886707024739806641263170345377816177052018,
+        15732290486829619144634131656503993123618032247178179298922551820261215487562,
+        6024433414579583476444635447152826813568595303270846875177844482142230009826,
+        17677827682004946431939402157761289497221048154630238117709539216286149983245,
+        10716307389353583413755237303156291454109852751296156900963208377067748518748,
+        14925386988604173087143546225719076187055229908444910452781922028996524347508,
+        8940878636401797005293482068100797531020505636124892198091491586778667442523,
+        18911747154199663060505302806894425160044925686870165583944475880789706164410,
+        8821532432394939099312235292271438180996556457308429936910969094255825456935,
+        20632576502437623790366878538516326728436616723089049415538037018093616927643,
+        71447649211767888770311304010816315780740050029903404046389165015534756512,
+        2781996465394730190470582631099299305677291329609718650018200531245670229393,
+        12441376330954323535872906380510501637773629931719508864016287320488688345525,
+        2558302139544901035700544058046419714227464650146159803703499681139469546006,
+        10087036781939179132584550273563255199577525914374285705149349445480649057058,
+        4267692623754666261749551533667592242661271409704769363166965280715887854739,
+        4945579503584457514844595640661884835097077318604083061152997449742124905548,
+        17742335354489274412669987990603079185096280484072783973732137326144230832311,
+        6266270088302506215402996795500854910256503071464802875821837403486057988208,
+        2716062168542520412498610856550519519760063668165561277991771577403400784706,
+        19118392018538203167410421493487769944462015419023083813301166096764262134232,
+        9386595745626044000666050847309903206827901310677406022353307960932745699524,
+        9121640807890366356465620448383131419933298563527245687958865317869840082266,
+        3078975275808111706229899605611544294904276390490742680006005661017864583210,
+        7157404299437167354719786626667769956233708887934477609633504801472827442743,
+        14056248655941725362944552761799461694550787028230120190862133165195793034373,
+        14124396743304355958915937804966111851843703158171757752158388556919187839849,
+        11851254356749068692552943732920045260402277343008629727465773766468466181076,
+        9799099446406796696742256539758943483211846559715874347178722060519817626047,
+        10156146186214948683880719664738535455146137901666656566575307300522957959544,
+        19908645952733301583346063785055921934459499091029406575311417879963332475861,
+        11766105336238068471342414351862472329437473380853789942065610694000443387471,
+        11002137593249972174092192767251572171769044073555430468487809799220351297047,
+        284136377911685911941431040940403846843630064858778505937392780738953624163,
+        19448733709802908339787967270452055364068697565906862913410983275341804035680,
+        14423660424692802524250720264041003098290275890428483723270346403986712981505,
+        10635360132728137321700090133109897687122647659471659996419791842933639708516
+    ];
+
+    var M = [
+        [
+            19167410339349846567561662441069598364702008768579734801591448511131028229281,
+            14183033936038168803360723133013092560869148726790180682363054735190196956789,
+            9067734253445064890734144122526450279189023719890032859456830213166173619761,
+            16378664841697311562845443097199265623838619398287411428110917414833007677155,
+            12968540216479938138647596899147650021419273189336843725176422194136033835172,
+            3636162562566338420490575570584278737093584021456168183289112789616069756675
+        ],[
+            17034139127218860091985397764514160131253018178110701196935786874261236172431,
+            2799255644797227968811798608332314218966179365168250111693473252876996230317,
+            2482058150180648511543788012634934806465808146786082148795902594096349483974,
+            16563522740626180338295201738437974404892092704059676533096069531044355099628,
+            10468644849657689537028565510142839489302836569811003546969773105463051947124,
+            3328913364598498171733622353010907641674136720305714432354138807013088636408
+        ],[
+            18985203040268814769637347880759846911264240088034262814847924884273017355969,
+            8652975463545710606098548415650457376967119951977109072274595329619335974180,
+            970943815872417895015626519859542525373809485973005165410533315057253476903,
+            19406667490568134101658669326517700199745817783746545889094238643063688871948,
+            17049854690034965250221386317058877242629221002521630573756355118745574274967,
+            4964394613021008685803675656098849539153699842663541444414978877928878266244
+        ],[
+            19025623051770008118343718096455821045904242602531062247152770448380880817517,
+            9077319817220936628089890431129759976815127354480867310384708941479362824016,
+            4770370314098695913091200576539533727214143013236894216582648993741910829490,
+            4298564056297802123194408918029088169104276109138370115401819933600955259473,
+            6905514380186323693285869145872115273350947784558995755916362330070690839131,
+            4783343257810358393326889022942241108539824540285247795235499223017138301952
+        ],[
+            16205238342129310687768799056463408647672389183328001070715567975181364448609,
+            8303849270045876854140023508764676765932043944545416856530551331270859502246,
+            20218246699596954048529384569730026273241102596326201163062133863539137060414,
+            1712845821388089905746651754894206522004527237615042226559791118162382909269,
+            13001155522144542028910638547179410124467185319212645031214919884423841839406,
+            16037892369576300958623292723740289861626299352695838577330319504984091062115
+        ],[
+            15162889384227198851506890526431746552868519326873025085114621698588781611738,
+            13272957914179340594010910867091459756043436017766464331915862093201960540910,
+            9416416589114508529880440146952102328470363729880726115521103179442988482948,
+            8035240799672199706102747147502951589635001418759394863664434079699838251138,
+            21642389080762222565487157652540372010968704000567605990102641816691459811717,
+            20261355950827657195644012399234591122288573679402601053407151083849785332516
+        ]
+    ];
+
+
+    signal input inputs[nInputs];
+    signal output out;
+
+    component ark[nRoundsF + nRoundsP];
+    component sigmaF[nRoundsF][t];
+    component sigmaP[nRoundsP];
+    component mix[nRoundsF + nRoundsP];
+
+    var k;
+
+    for (var i=0; i<(nRoundsF + nRoundsP); i++) {
+        ark[i] = Ark(t, C[i]);
+        mix[i] = Mix(t, M);
+
+        for (var j=0; j<t; j++) {
+            if (i==0) {
+                if (j<nInputs) {
+                    ark[i].in[j] <== inputs[j];
+                } else {
+                    ark[i].in[j] <== 0;
+                }
+            } else {
+                ark[i].in[j] <== mix[i-1].out[j];
+            }
+        }
+
+        if ((i<(nRoundsF/2)) || (i>= (nRoundsP + nRoundsF/2))) {
+            k= i<nRoundsF/2 ? i : (i-nRoundsP);
+            for (var j=0; j<t; j++) {
+                sigmaF[k][j] = Sigma();
+                sigmaF[k][j].in <== ark[i].out[j];
+                mix[i].in[j] <== sigmaF[k][j].out;
+            }
+        } else {
+            k= i-nRoundsF/2;
+            sigmaP[k] = Sigma();
+            sigmaP[k].in <== ark[i].out[0];
+            mix[i].in[0] <== sigmaP[k].out;
+            for (var j=1; j<t; j++) {
+                mix[i].in[j] <== ark[i].out[j];
+            }
+        }
+    }
+
+    out <== mix[nRoundsF + nRoundsP -1].out[0];
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/ch.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/ch.circom
@@ -0,0 +1,46 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Ch
+
+000 0
+001 1
+010 0
+011 1
+100 0
+101 0
+110 1
+111 1
+
+out = a&b ^ (!a)&c =>
+
+out = a*(b-c) + c
+
+*/
+
+template Ch(n) {
+    signal input a[n];
+    signal input b[n];
+    signal input c[n];
+    signal output out[n];
+
+    for (var k=0; k<n; k++) {
+        out[k] <== a[k] * (b[k]-c[k]) + c[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/constants.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/constants.circom
@@ -0,0 +1,52 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template H(x) {
+    signal output out[32];
+    var c = [0x6a09e667,
+             0xbb67ae85,
+             0x3c6ef372,
+             0xa54ff53a,
+             0x510e527f,
+             0x9b05688c,
+             0x1f83d9ab,
+             0x5be0cd19];
+
+    for (var i=0; i<32; i++) {
+        out[i] <== (c[x] >> i) & 1;
+    }
+}
+
+template K(x) {
+    signal output out[32];
+    var c = [
+        0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
+        0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
+        0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
+        0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
+        0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
+        0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
+        0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
+        0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
+    ];
+
+    for (var i=0; i<32; i++) {
+        out[i] <== (c[x] >> i) & 1;
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/main.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/main.circom
@@ -0,0 +1,34 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "sha256_2.jaz";
+
+template Main() {
+    signal private input a;
+    signal private input b;
+    signal output out;
+
+    component sha256_2 = SHA256_2();
+
+    sha256_2.a <== a;
+    sha256_2.b <== a;
+    out <== sha256_2.out;
+}
+
+component main = Main();
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/maj.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/maj.circom
@@ -0,0 +1,44 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Maj function for sha256
+
+out = a&b ^ a&c ^ b&c  =>
+
+out = a*b   +  a*c  +  b*c  -  2*a*b*c  =>
+
+out = a*( b + c - 2*b*c ) + b*c =>
+
+mid = b*c
+out = a*( b + c - 2*mid ) + mid
+
+*/
+
+template Maj(n) {
+    signal input a[n];
+    signal input b[n];
+    signal input c[n];
+    signal output out[n];
+    signal mid[n];
+
+    for (var k=0; k<n; k++) {
+        mid[k] <== b[k]*c[k];
+        out[k] <== a[k] * (b[k]+c[k]-2*mid[k]) + mid[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/rotate.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/rotate.circom
@@ -0,0 +1,27 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template RotR(n, r) {
+    signal input in[n];
+    signal output out[n];
+
+    for (var i=0; i<n; i++) {
+        out[i] <== in[ (i+r)%n ];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sha256_2.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sha256_2.circom
@@ -0,0 +1,67 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "sha256compression.circom";
+include "../bitify.circom"
+
+template Sha256_2() {
+    signal input a;
+    signal input b;
+    signal output out;
+
+    component bits2num = Bits2Num(216);
+    component num2bits[2];
+
+    num2bits[0] = Num2Bits(216);
+    num2bits[1] = Num2Bits(216);
+
+    num2bits[0].in <== a;
+    num2bits[1].in <== b;
+
+    component sha256compression = Sha256compression() ;
+
+    var i;
+
+    for (i=0; i<216; i++) {
+        sha256compression.inp[i] <== num2bits[0].out[215-i];
+        sha256compression.inp[i+216] <== num2bits[1].out[215-i];
+    }
+
+    sha256compression.inp[432] <== 1;
+
+    for (i=433; i<503; i++) {
+        sha256compression.inp[i] <== 0;
+    }
+
+    sha256compression.inp[503] <== 1;
+    sha256compression.inp[504] <== 1;
+    sha256compression.inp[505] <== 0;
+    sha256compression.inp[506] <== 1;
+    sha256compression.inp[507] <== 1;
+    sha256compression.inp[508] <== 0;
+    sha256compression.inp[509] <== 0;
+    sha256compression.inp[510] <== 0;
+    sha256compression.inp[511] <== 0;
+
+    for (i=0; i<216; i++) {
+        bits2num.in[i] <== sha256compression.out[255-i];
+    }
+
+    out <== bits2num.out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sha256compression.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sha256compression.circom
@@ -0,0 +1,164 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "constants.circom";
+include "t1.circom";
+include "t2.circom";
+include "../binsum.circom";
+include "sigmaplus.circom";
+
+template Sha256compression() {
+    signal input inp[512];
+    signal output out[256];
+    signal a[65][32];
+    signal b[65][32];
+    signal c[65][32];
+    signal d[65][32];
+    signal e[65][32];
+    signal f[65][32];
+    signal g[65][32];
+    signal h[65][32];
+    signal w[64][32];
+
+    var i;
+
+    component sigmaPlus[48];
+    for (i=0; i<48; i++) sigmaPlus[i] = SigmaPlus();
+
+    component ct_k[64];
+    for (i=0; i<64; i++) ct_k[i] = K(i);
+
+    component ha0 = H(0);
+    component hb0 = H(1);
+    component hc0 = H(2);
+    component hd0 = H(3);
+    component he0 = H(4);
+    component hf0 = H(5);
+    component hg0 = H(6);
+    component hh0 = H(7);
+
+    component t1[64];
+    for (i=0; i<64; i++) t1[i] = T1();
+
+    component t2[64];
+    for (i=0; i<64; i++) t2[i] = T2();
+
+    component suma[64];
+    for (i=0; i<64; i++) suma[i] = BinSum(32, 2);
+
+    component sume[64];
+    for (i=0; i<64; i++) sume[i] = BinSum(32, 2);
+
+    component fsum[8];
+    for (i=0; i<8; i++) fsum[i] = BinSum(32, 2);
+
+    var k;
+    var t;
+
+    for (t=0; t<64; t++) {
+        if (t<16) {
+            for (k=0; k<32; k++) {
+                w[t][k] <== inp[t*32+31-k];
+            }
+        } else {
+            for (k=0; k<32; k++) {
+                sigmaPlus[t-16].in2[k] <== w[t-2][k];
+                sigmaPlus[t-16].in7[k] <== w[t-7][k];
+                sigmaPlus[t-16].in15[k] <== w[t-15][k];
+                sigmaPlus[t-16].in16[k] <== w[t-16][k];
+                w[t][k] <== sigmaPlus[t-16].out[k];
+            }
+        }
+    }
+
+    for (k=0; k<32; k++ ) {
+        a[0][k] <== ha0.out[k]
+        b[0][k] <== hb0.out[k]
+        c[0][k] <== hc0.out[k]
+        d[0][k] <== hd0.out[k]
+        e[0][k] <== he0.out[k]
+        f[0][k] <== hf0.out[k]
+        g[0][k] <== hg0.out[k]
+        h[0][k] <== hh0.out[k]
+    }
+
+    for (t = 0; t<64; t++) {
+        for (k=0; k<32; k++) {
+            t1[t].h[k] <== h[t][k];
+            t1[t].e[k] <== e[t][k];
+            t1[t].f[k] <== f[t][k];
+            t1[t].g[k] <== g[t][k];
+            t1[t].k[k] <== ct_k[t].out[k];
+            t1[t].w[k] <== w[t][k];
+
+            t2[t].a[k] <== a[t][k];
+            t2[t].b[k] <== b[t][k];
+            t2[t].c[k] <== c[t][k];
+        }
+
+        for (k=0; k<32; k++) {
+            sume[t].in[0][k] <== d[t][k];
+            sume[t].in[1][k] <== t1[t].out[k];
+
+            suma[t].in[0][k] <== t1[t].out[k];
+            suma[t].in[1][k] <== t2[t].out[k];
+        }
+
+        for (k=0; k<32; k++) {
+            h[t+1][k] <== g[t][k];
+            g[t+1][k] <== f[t][k];
+            f[t+1][k] <== e[t][k];
+            e[t+1][k] <== sume[t].out[k];
+            d[t+1][k] <== c[t][k];
+            c[t+1][k] <== b[t][k];
+            b[t+1][k] <== a[t][k];
+            a[t+1][k] <== suma[t].out[k];
+        }
+    }
+
+    for (k=0; k<32; k++) {
+        fsum[0].in[0][k] <==  ha0.out[k];
+        fsum[0].in[1][k] <==  a[64][k];
+        fsum[1].in[0][k] <==  hb0.out[k];
+        fsum[1].in[1][k] <==  b[64][k];
+        fsum[2].in[0][k] <==  hc0.out[k];
+        fsum[2].in[1][k] <==  c[64][k];
+        fsum[3].in[0][k] <==  hd0.out[k];
+        fsum[3].in[1][k] <==  d[64][k];
+        fsum[4].in[0][k] <==  he0.out[k];
+        fsum[4].in[1][k] <==  e[64][k];
+        fsum[5].in[0][k] <==  hf0.out[k];
+        fsum[5].in[1][k] <==  f[64][k];
+        fsum[6].in[0][k] <==  hg0.out[k];
+        fsum[6].in[1][k] <==  g[64][k];
+        fsum[7].in[0][k] <==  hh0.out[k];
+        fsum[7].in[1][k] <==  h[64][k];
+    }
+
+    for (k=0; k<32; k++) {
+        out[31-k]     <== fsum[0].out[k];
+        out[32+31-k]  <== fsum[1].out[k];
+        out[64+31-k]  <== fsum[2].out[k];
+        out[96+31-k]  <== fsum[3].out[k];
+        out[128+31-k] <== fsum[4].out[k];
+        out[160+31-k] <== fsum[5].out[k];
+        out[192+31-k] <== fsum[6].out[k];
+        out[224+31-k] <== fsum[7].out[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/shift.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/shift.circom
@@ -0,0 +1,32 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+template ShR(n, r) {
+    signal input in[n];
+    signal output out[n];
+
+    for (var i=0; i<n; i++) {
+        if (i+r >= n) {
+            out[i] <== 0;
+        } else {
+            out[i] <== in[ i+r ];
+        }
+    }
+}
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sigma.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sigma.circom
@@ -0,0 +1,68 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "xor3.circom";
+include "rotate.circom";
+include "shift.circom";
+
+template SmallSigma(ra, rb, rc) {
+    signal input in[32];
+    signal output out[32];
+
+    component xor3 = Xor3(32);
+
+    component rota = RotR(32, ra);
+    component rotb = RotR(32, rb);
+    component shrc = ShR(32, rc);
+
+    for (var k=0; k<32; k++) {
+        rota.in[k] <== in[k];
+        rotb.in[k] <== in[k];
+        shrc.in[k] <== in[k];
+
+        xor3.a[k] <== rota.out[k];
+        xor3.b[k] <== rotb.out[k];
+        xor3.c[k] <== shrc.out[k];
+
+        out[k] <== xor3.out[k];
+    }
+}
+
+template BigSigma(ra, rb, rc) {
+    signal input in[32];
+    signal output out[32];
+
+    component xor3 = Xor3(32);
+
+    component rota = RotR(32, ra);
+    component rotb = RotR(32, rb);
+    component rotc = RotR(32, rc);
+
+    for (var k=0; k<32; k++) {
+        rota.in[k] <== in[k];
+        rotb.in[k] <== in[k];
+        rotc.in[k] <== in[k];
+
+        xor3.a[k] <== rota.out[k];
+        xor3.b[k] <== rotb.out[k];
+        xor3.c[k] <== rotc.out[k];
+
+        out[k] <== xor3.out[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sigmaplus.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/sigmaplus.circom
@@ -0,0 +1,45 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "../binsum.circom"
+include "sigma.circom"
+
+template SigmaPlus() {
+    signal input in2[32];
+    signal input in7[32];
+    signal input in15[32];
+    signal input in16[32];
+    signal output out[32];
+
+    component sum = BinSum(32, 4);
+    component sigma1 = SmallSigma(17,19,10);
+    component sigma0 = SmallSigma(7, 18, 3);
+
+    for (var k=0; k<32; k++) {
+        sigma1.in[k] <== in2[k];
+        sigma0.in[k] <== in15[k];
+
+        sum.in[0][k] <== sigma1.out[k];
+        sum.in[1][k] <== in7[k];
+        sum.in[2][k] <== sigma0.out[k];
+        sum.in[3][k] <== in16[k];
+
+        out[k] <== sum.out[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/t1.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/t1.circom
@@ -0,0 +1,52 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "../binsum.circom";
+include "sigma.circom";
+include "ch.circom";
+
+template T1() {
+    signal input h[32];
+    signal input e[32];
+    signal input f[32];
+    signal input g[32];
+    signal input k[32];
+    signal input w[32];
+    signal output out[32];
+
+    component sum = BinSum(32, 5);
+    component ch = Ch(32);
+
+    component bigsigma1 = BigSigma(6, 11, 25);
+
+    for (var ki=0; ki<32; ki++) {
+        bigsigma1.in[ki] <== e[ki];
+        ch.a[ki] <== e[ki];
+        ch.b[ki] <== f[ki];
+        ch.c[ki] <== g[ki]
+
+        sum.in[0][ki] <== h[ki];
+        sum.in[1][ki] <== bigsigma1.out[ki];
+        sum.in[2][ki] <== ch.out[ki];
+        sum.in[3][ki] <== k[ki];
+        sum.in[4][ki] <== w[ki];
+
+        out[ki] <== sum.out[ki];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/t2.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/t2.circom
@@ -0,0 +1,47 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "../binsum.circom";
+include "sigma.circom";
+include "maj.circom"
+
+template T2() {
+    signal input a[32];
+    signal input b[32];
+    signal input c[32];
+    signal output out[32];
+
+    component sum = BinSum(32, 2);
+
+    component bigsigma0 = BigSigma(2, 13, 22);
+    component maj = Maj(32);
+
+    for (var k=0; k<32; k++) {
+
+        bigsigma0.in[k] <== a[k];
+        maj.a[k] <== a[k];
+        maj.b[k] <== b[k];
+        maj.c[k] <== c[k];
+
+        sum.in[0][k] <== bigsigma0.out[k];
+        sum.in[1][k] <== maj.out[k];
+
+        out[k] <== sum.out[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/xor3.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sha256/xor3.circom
@@ -0,0 +1,44 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Xor3 function for sha256
+
+out = a ^ b ^ c  =>
+
+out = a+b+c - 2*a*b - 2*a*c - 2*b*c + 4*a*b*c   =>
+
+out = a*( 1 - 2*b - 2*c + 4*b*c ) + b + c - 2*b*c =>
+
+mid = b*c
+out = a*( 1 - 2*b -2*c + 4*mid ) + b + c - 2 * mid
+
+*/
+
+template Xor3(n) {
+    signal input a[n];
+    signal input b[n];
+    signal input c[n];
+    signal output out[n];
+    signal mid[n];
+
+    for (var k=0; k<n; k++) {
+        mid[k] <== b[k]*c[k];
+        out[k] <== a[k] * (1 -2*b[k]  -2*c[k] +4*mid[k]) + b[k] + c[k] -2*mid[k];
+    }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sign.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/sign.circom
@@ -0,0 +1,35 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "compconstant.circom";
+
+template Sign() {
+    signal input in[254];
+    signal output sign;
+
+    component comp = CompConstant(10944121435919637611123202872628637544274182200208017171849102093287904247808);
+
+    var i;
+
+    for (i=0; i<254; i++) {
+        comp.in[i] <== in[i];
+    }
+
+    sign <== comp.out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smthash_mimc.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smthash_mimc.circom
@@ -0,0 +1,57 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "../mimc.circom";
+
+
+/*
+    Hash1 = H(1 | key | value)
+ */
+
+template SMTHash1() {
+    signal input key;
+    signal input value;
+    signal output out;
+
+    component h = MultiMiMC7(2, 91);   // Constant
+    h.in[0] <== key;
+    h.in[1] <== value;
+    h.k <== 1;
+
+    out <== h.out;
+}
+
+/*
+    This component is used to create the 2 nodes.
+
+    Hash2 = H(Hl | Hr)
+ */
+
+template SMTHash2() {
+    signal input L;
+    signal input R;
+    signal output out;
+
+    component h = MultiMiMC7(2, 91);   // Constant
+    h.in[0] <== L;
+    h.in[1] <== R;
+    h.k <== 0;
+
+    out <== h.out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smthash_poseidon.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smthash_poseidon.circom
@@ -0,0 +1,56 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+include "../poseidon.circom";
+
+
+/*
+    Hash1 = H(1 | key | value)
+ */
+
+template SMTHash1() {
+    signal input key;
+    signal input value;
+    signal output out;
+
+    component h = Poseidon(3, 6, 8, 57);   // Constant
+    h.inputs[0] <== key;
+    h.inputs[1] <== value;
+    h.inputs[2] <== 1;
+
+    out <== h.out;
+}
+
+/*
+    This component is used to create the 2 nodes.
+
+    Hash2 = H(Hl | Hr)
+ */
+
+template SMTHash2() {
+    signal input L;
+    signal input R;
+    signal output out;
+
+    component h = Poseidon(2, 6, 8, 57);   // Constant
+    h.inputs[0] <== L;
+    h.inputs[1] <== R;
+
+    out <== h.out;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtlevins.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtlevins.circom
@@ -0,0 +1,100 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+
+This component finds the level where the oldInsert is done.
+The rules are:
+
+levIns[i] == 1 if its level and all the child levels have a sibling of 0 and
+the parent level has a sibling != 0.  Considere that the root level always has
+a parent with a sibling != 0.
+
+
+                                  ┌──────────────┐
+                                  │              │
+                                  │              │───▶ levIns[0] <== (1-done[i])
+                                  │              │
+                                  └──────────────┘
+                                          ▲
+                                          │
+                                          │
+                                       done[0]
+
+
+
+                                      done[i-1] <== levIns[i] + done[i]
+                                          ▲
+                                          │
+                                          │
+                   ┌───────────┐  ┌──────────────┐
+                   │           │  │              │
+   sibling[i-1]───▶│IsZero[i-1]│─▶│              │───▶ levIns[i] <== (1-done[i])*(1-isZero[i-1].out)
+                   │           │  │              │
+                   └───────────┘  └──────────────┘
+                                          ▲
+                                          │
+                                          │
+                                       done[i]
+
+
+
+                                     done[n-2] <== levIns[n-1]
+                                         ▲
+                                         │
+                                         │
+                  ┌───────────┐  ┌──────────────┐
+                  │           │  │              │
+  sibling[n-2]───▶│IsZero[n-2]│─▶│              │────▶ levIns[n-1] <== (1-isZero[n-2].out)
+                  │           │  │              │
+                  └───────────┘  └──────────────┘
+
+                  ┌───────────┐
+                  │           │
+  sibling[n-1]───▶│IsZero[n-1]│────▶ === 0
+                  │           │
+                  └───────────┘
+
+ */
+
+template SMTLevIns(nLevels) {
+    signal input enabled;
+    signal input siblings[nLevels];
+    signal output levIns[nLevels];
+    signal done[nLevels-1];        // Indicates if the insLevel has aready been detected.
+
+    component isZero[nLevels];
+
+    for (var i=0; i<nLevels; i++) {
+        isZero[i] = IsZero();
+        isZero[i].in <== siblings[i];
+    }
+
+    // The last level must always have a sibling of 0. If not, then it cannot be inserted.
+    (isZero[nLevels-1].out - 1) * enabled === 0;
+
+    levIns[nLevels-1] <== (1-isZero[nLevels-2].out);
+    done[nLevels-2] <== levIns[nLevels-1];
+    for (var i=nLevels-2; i>0; i--) {
+        levIns[i] <== (1-done[i])*(1-isZero[i-1].out)
+        done[i-1] <== levIns[i] + done[i];
+    }
+
+    levIns[0] <== (1-done[0]);
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessor.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessor.circom
@@ -0,0 +1,258 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/***************************************************************************************************
+
+SMTProcessor: Sparse Merkle Tree processor is a component to verify an insert/update/delete elements
+into the Sparse Merkle tree.
+
+
+Insert to an empty leaf
+=======================
+
+  STATE                 OLD STATE                                       NEW STATE
+  =====                 =========                                       =========
+
+                         oldRoot                                          newRoot
+                            ▲                                               ▲
+                            │                                               │
+          ┌───────┐     ┏━━━┻━━━┓                         ┌───────┐     ┏━━━┻━━━┓
+   top    │Sibling├────▶┃ Hash  ┃◀─┐                      │Sibling├────▶┃ Hash  ┃◀─┐
+          └───────┘     ┗━━━━━━━┛  │                      └───────┘     ┗━━━━━━━┛  │
+                                   │                                               │
+                                   │                                               │
+                               ┏━━━┻━━━┓   ┌───────┐                           ┏━━━┻━━━┓   ┌───────┐
+   top                  ┌─────▶┃ Hash  ┃◀──┤Sibling│                    ┌─────▶┃ Hash  ┃◀──┤Sibling│
+                        │      ┗━━━━━━━┛   └───────┘                    │      ┗━━━━━━━┛   └───────┘
+                        │                                               │
+                        │                                               │
+        ┌───────┐   ┏━━━┻━━━┓                           ┌───────┐   ┏━━━┻━━━┓
+   top  │Sibling├──▶┃ Hash  ┃◀─────┐                    │Sibling├──▶┃ Hash  ┃◀─────┐
+        └───────┘   ┗━━━━━━━┛      │                    └───────┘   ┗━━━━━━━┛      │
+                                   │                                               │
+                                   │                                               │
+                              ┌────┴────┐                                     ┌────┴────┐
+  old0                        │    0    │                                     │New1Leaf │
+                              └─────────┘                                     └─────────┘
+
+
+                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
+   na                ┃ Hash  ┃                                      ┃ Hash  ┃
+                     ┗━━━━━━━┛                                      ┗━━━━━━━┛
+
+
+                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
+   na                ┃ Hash  ┃                                      ┃ Hash  ┃
+                     ┗━━━━━━━┛                                      ┗━━━━━━━┛
+
+
+
+Insert to a used leaf.
+=====================
+
+  STATE                 OLD STATE                                       NEW STATE
+  =====                 =========                                       =========
+
+
+                         oldRoot                                          newRoot
+                            ▲                                               ▲
+                            │                                               │
+          ┌───────┐     ┏━━━┻━━━┓                         ┌───────┐     ┏━━━┻━━━┓
+   top    │Sibling├────▶┃ Hash  ┃◀─┐                      │Sibling├────▶┃ Hash  ┃◀─┐
+          └───────┘     ┗━━━━━━━┛  │                      └───────┘     ┗━━━━━━━┛  │
+                                   │                                               │
+                                   │                                               │
+                               ┏━━━┻━━━┓   ┌───────┐                           ┏━━━┻━━━┓   ┌───────┐
+   top                  ┌─────▶┃ Hash  ┃◀──┤Sibling│                    ┌─────▶┃ Hash  ┃◀──┤Sibling│
+                        │      ┗━━━━━━━┛   └───────┘                    │      ┗━━━━━━━┛   └───────┘
+                        │                                               │
+                        │                                               │
+        ┌───────┐   ┏━━━┻━━━┓                           ┌───────┐   ┏━━━┻━━━┓
+   top  │Sibling├──▶┃ Hash  ┃◀─────┐                    │Sibling├──▶┃ Hash  ┃◀─────┐
+        └───────┘   ┗━━━━━━━┛      │                    └───────┘   ┗━━━━━━━┛      │
+                                   │                                               │
+                                   │                                               │
+                              ┌────┴────┐                                      ┏━━━┻━━━┓   ┌───────┐
+   bot                        │Old1Leaf │                               ┌─────▶┃ Hash  ┃◀──┼─  0   │
+                              └─────────┘                               │      ┗━━━━━━━┛   └───────┘
+                                                                        │
+                                                                        │
+                     ┏━━━━━━━┓                          ┌───────┐   ┏━━━┻━━━┓
+   bot               ┃ Hash  ┃                          │   0  ─┼──▶┃ Hash  ┃◀─────┐
+                     ┗━━━━━━━┛                          └───────┘   ┗━━━━━━━┛      │
+                                                                                   │
+                                                                                   │
+                     ┏━━━━━━━┓                                                 ┏━━━┻━━━┓   ┌───────┐
+   bot               ┃ Hash  ┃                                          ┌─────▶┃ Hash  ┃◀──│   0   │
+                     ┗━━━━━━━┛                                          │      ┗━━━━━━━┛   └───────┘
+                                                                        │
+                                                                        │
+                     ┏━━━━━━━┓                        ┌─────────┐   ┏━━━┻━━━┓   ┌─────────┐
+  new1               ┃ Hash  ┃                        │Old1Leaf ├──▶┃ Hash  ┃◀──│New1Leaf │
+                     ┗━━━━━━━┛                        └─────────┘   ┗━━━━━━━┛   └─────────┘
+
+
+                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
+   na                ┃ Hash  ┃                                      ┃ Hash  ┃
+                     ┗━━━━━━━┛                                      ┗━━━━━━━┛
+
+
+                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
+   na                ┃ Hash  ┃                                      ┃ Hash  ┃
+                     ┗━━━━━━━┛                                      ┗━━━━━━━┛
+
+
+Fnction
+fnc[0]  fnc[1]
+0       0             NOP
+0       1             UPDATE
+1       0             INSERT
+1       1             DELETE
+
+
+***************************************************************************************************/
+
+include "../gates.circom";
+include "../bitify.circom";
+include "../comparators.circom";
+include "../switcher.circom";
+include "smtlevins.circom";
+include "smtprocessorlevel.circom";
+include "smtprocessorsm.circom";
+include "smthash_poseidon.circom";
+
+template SMTProcessor(nLevels) {
+    signal input oldRoot;
+    signal output newRoot;
+    signal input siblings[nLevels];
+    signal input oldKey;
+    signal input oldValue;
+    signal input isOld0;
+    signal input newKey;
+    signal input newValue;
+    signal input fnc[2];
+
+    signal enabled;
+
+    enabled <== fnc[0] + fnc[1] - fnc[0]*fnc[1]
+
+    component hash1Old = SMTHash1();
+    hash1Old.key <== oldKey;
+    hash1Old.value <== oldValue;
+
+    component hash1New = SMTHash1();
+    hash1New.key <== newKey;
+    hash1New.value <== newValue;
+
+    component n2bOld = Num2Bits_strict();
+    component n2bNew = Num2Bits_strict();
+
+    n2bOld.in <== oldKey;
+    n2bNew.in <== newKey;
+
+    component smtLevIns = SMTLevIns(nLevels);
+    for (var i=0; i<nLevels; i++) smtLevIns.siblings[i] <== siblings[i];
+    smtLevIns.enabled <== enabled;
+
+    component xors[nLevels];
+    for (var i=0; i<nLevels; i++) {
+        xors[i] = XOR();
+        xors[i].a <== n2bOld.out[i];
+        xors[i].b <== n2bNew.out[i];
+    }
+
+    component sm[nLevels];
+    for (var i=0; i<nLevels; i++) {
+        sm[i] = SMTProcessorSM();
+        if (i==0) {
+            sm[i].prev_top <== enabled;
+            sm[i].prev_old0 <== 0;
+            sm[i].prev_bot <== 0;
+            sm[i].prev_new1 <== 0;
+            sm[i].prev_na <== 1-enabled;
+            sm[i].prev_upd <== 0;
+        } else {
+            sm[i].prev_top <== sm[i-1].st_top;
+            sm[i].prev_old0 <== sm[i-1].st_old0;
+            sm[i].prev_bot <== sm[i-1].st_bot;
+            sm[i].prev_new1 <== sm[i-1].st_new1;
+            sm[i].prev_na <== sm[i-1].st_na;
+            sm[i].prev_upd <== sm[i-1].st_upd;
+        }
+        sm[i].is0 <== isOld0;
+        sm[i].xor <== xors[i].out;
+        sm[i].fnc[0] <== fnc[0];
+        sm[i].fnc[1] <== fnc[1];
+        sm[i].levIns <== smtLevIns.levIns[i];
+    }
+    sm[nLevels-1].st_na + sm[nLevels-1].st_new1 + sm[nLevels-1].st_old0 +sm[nLevels-1].st_upd === 1;
+
+    component levels[nLevels];
+    for (var i=nLevels-1; i != -1; i--) {
+        levels[i] = SMTProcessorLevel();
+
+        levels[i].st_top <== sm[i].st_top;
+        levels[i].st_old0 <== sm[i].st_old0;
+        levels[i].st_bot <== sm[i].st_bot;
+        levels[i].st_new1 <== sm[i].st_new1;
+        levels[i].st_na <== sm[i].st_na;
+        levels[i].st_upd <== sm[i].st_upd;
+
+        levels[i].sibling <== siblings[i];
+        levels[i].old1leaf <== hash1Old.out;
+        levels[i].new1leaf <== hash1New.out;
+
+        levels[i].newlrbit <== n2bNew.out[i];
+        if (i==nLevels-1) {
+            levels[i].oldChild <== 0;
+            levels[i].newChild <== 0;
+        } else {
+            levels[i].oldChild <== levels[i+1].oldRoot;
+            levels[i].newChild <== levels[i+1].newRoot;
+        }
+    }
+
+    component topSwitcher = Switcher();
+
+    topSwitcher.sel <== fnc[0]*fnc[1];
+    topSwitcher.L <== levels[0].oldRoot;
+    topSwitcher.R <== levels[0].newRoot;
+
+    component checkOldInput = ForceEqualIfEnabled();
+    checkOldInput.enabled <== enabled;
+    checkOldInput.in[0] <== oldRoot;
+    checkOldInput.in[1] <== topSwitcher.outL;
+
+    newRoot <== enabled * (topSwitcher.outR - oldRoot) + oldRoot;
+
+//    topSwitcher.outL === oldRoot*enabled;
+//    topSwitcher.outR === newRoot*enabled;
+
+    // Ckeck keys are equal if updating
+    component areKeyEquals = IsEqual();
+    areKeyEquals.in[0] <== oldKey;
+    areKeyEquals.in[1] <== newKey;
+
+    component keysOk = MultiAND(3);
+    keysOk.in[0] <== 1-fnc[0];
+    keysOk.in[1] <== fnc[1];
+    keysOk.in[2] <== 1-areKeyEquals.out;
+
+    keysOk.out === 0;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessorlevel.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessorlevel.circom
@@ -0,0 +1,94 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/******
+
+SMTProcessorLevel
+
+This circuit has 2 hash
+
+Outputs according to the state.
+
+State        oldRoot                    newRoot
+=====        =======                    =======
+top          H'(oldChild, sibling)       H'(newChild, sibling)
+old0         0                           new1leaf
+bot          old1leaf                    H'(newChild, 0)
+new1         old1leaf                    H'(new1leaf, old1leaf)
+na           0                           0
+
+upd          old1leaf                    new1leaf
+
+H' is the Hash function with the inputs shifted acordingly.
+
+*****/
+
+
+template SMTProcessorLevel() {
+    signal input st_top;
+    signal input st_old0;
+    signal input st_bot;
+    signal input st_new1;
+    signal input st_na;
+    signal input st_upd;
+
+    signal output oldRoot;
+    signal output newRoot;
+    signal input sibling;
+    signal input old1leaf;
+    signal input new1leaf;
+    signal input newlrbit;
+    signal input oldChild;
+    signal input newChild;
+
+    signal aux[4];
+
+    component oldProofHash = SMTHash2();
+    component newProofHash = SMTHash2();
+
+    component oldSwitcher = Switcher();
+    component newSwitcher = Switcher();
+
+    // Old side
+
+    oldSwitcher.L <== oldChild;
+    oldSwitcher.R <== sibling;
+
+    oldSwitcher.sel <== newlrbit;
+    oldProofHash.L <== oldSwitcher.outL;
+    oldProofHash.R <== oldSwitcher.outR;
+
+    aux[0] <== old1leaf * (st_bot + st_new1 + st_upd);
+    oldRoot <== aux[0] +  oldProofHash.out * st_top;
+
+    // New side
+
+    aux[1] <== newChild * ( st_top + st_bot);
+    newSwitcher.L <== aux[1] + new1leaf*st_new1;
+
+    aux[2] <== sibling*st_top;
+    newSwitcher.R <== aux[2] + old1leaf*st_new1;
+
+    newSwitcher.sel <== newlrbit;
+    newProofHash.L <== newSwitcher.outL;
+    newProofHash.R <== newSwitcher.outR;
+
+    aux[3] <== newProofHash.out * (st_top + st_bot + st_new1);
+    newRoot <==  aux[3] + new1leaf * (st_old0 + st_upd);
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessorsm.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtprocessorsm.circom
@@ -0,0 +1,164 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/***************************************************************************************************
+Each level on a SMTProcessor has a state.
+
+The state of the level depends on the state of te botom level and on `xor` and
+`is0` signals.
+
+`isOldLev` 1 when is the level where oldLeaf is.
+
+`xor` signal is 0 if the index bit at the current level is the same in the old
+and the new index, and 1 if it is different.
+
+`is0` signal, is 1 if we are inserting/deleting in an empty leaf and 0 if we
+are inserting/deleting in a leaf that contains an element.
+
+The states are:
+
+top: While the index bits of the old and new insex in the top level is the same, whe are in the top state.
+old0: When the we reach insert level,  we go to old0 state
+if `is0`=1.
+btn: Once in insert level and `is0` =0 we go to btn or new1 level if xor=1
+new1: This level is reached when xor=1. Here is where we insert/delete the hash of the
+old and the new trees with just one element.
+na: Not appliable.  After processing it, we go to the na level.
+
+
+Fnction
+fnc[0]  fnc[1]
+0       0             NOP
+0       1             UPDATE
+1       0             INSERT
+1       1             DELETE
+
+
+                                                ###########
+                                               #           #
+                ┌────────────────────────────▶#    upd      #─────────────────────┐
+                │                              ##         ##                      │
+                │                                #########                        │
+      levIns=1  │                                                                 │
+      fnc[0]=0  │                                                                 │  any
+                │                                                                 │
+                │                                                                 │
+                │                                                                 │
+                │                                ###########                      │
+                │        levIns=1               #           #                     │
+   levIns=0     │         is0=1  ┌────────────▶#    old0     #────────┐           │     any
+   ┌─────┐      │        fnc[0]=1│              ##         ##         │           │   ┌──────┐
+   │     │      │                │                #########           │ any       │   │      │
+   │     ▼      │                │                                    │           ▼   ▼      │
+   │    ###########              │                                    │          ########### │
+   │   #           # ────────────┘                                    └────────▶#           #│
+   └──#    top      #                                                          #    na       #
+       ##         ## ───────────────────┐ levIns=1                          ┌──▶##         ##
+         #########                      │  is0=0                            │     #########
+             │                          │ fnc[0]=1                          │
+             │                          │  xor=1             ###########    │ any
+             │                          └──────────────────▶#           #   │
+             │                                             #    new1     #──┘
+             │                                              ##         ##
+             └────────────────────────────────┐               #########
+                  levIns=1                    │                   ▲
+                   is0=0                      │             ┌─────┘
+                  fnc[0]=1                    │  ###########│  xor=1
+                   xor=0                      │ #           #
+                                              ▼#    btn      #
+                                                ##         ##
+                                                  #########◀───────┐
+                                                      │            │
+                                                      │            │
+                                                      └────────────┘
+                                                          xor=0
+
+***************************************************************************************************/
+
+template SMTProcessorSM() {
+  signal input xor;
+  signal input is0;
+  signal input levIns;
+  signal input fnc[2];
+
+  signal input prev_top;
+  signal input prev_old0;
+  signal input prev_bot;
+  signal input prev_new1;
+  signal input prev_na;
+  signal input prev_upd;
+
+  signal output st_top;
+  signal output st_old0;
+  signal output st_bot;
+  signal output st_new1;
+  signal output st_na;
+  signal output st_upd;
+
+  signal aux1;
+  signal aux2;
+
+  aux1 <==                  prev_top * levIns;
+  aux2 <== aux1*fnc[0];  // prev_top * levIns * fnc[0]
+
+  // st_top = prev_top*(1-levIns)
+  //    = + prev_top
+  //      - prev_top * levIns            = aux1
+
+  st_top <== prev_top - aux1;
+
+  // st_old0 = prev_top * levIns * is0 * fnc[0]
+  //      = + prev_top * levIns * is0 * fnc[0]            = aux2 * is0
+
+  st_old0 <== aux2 * is0;  // prev_top * levIns * is0 * fnc[0]
+
+  // st_new1 = prev_top * levIns * (1-is0)*fnc[0] * xor   +  prev_bot*xor =
+  //    = + prev_top * levIns *       fnc[0] * xor     = aux2     * xor
+  //      - prev_top * levIns * is0 * fnc[0] * xor     = st_old0  * xor
+  //      + prev_bot *                         xor     = prev_bot * xor
+
+  st_new1 <== (aux2 - st_old0 + prev_bot)*xor;
+
+
+  // st_bot = prev_top * levIns * (1-is0)*fnc[0] * (1-xor) + prev_bot*(1-xor);
+  //    = + prev_top * levIns *       fnc[0]
+  //      - prev_top * levIns * is0 * fnc[0]
+  //      - prev_top * levIns *       fnc[0] * xor
+  //      + prev_top * levIns * is0 * fnc[0] * xor
+  //      + prev_bot
+  //      - prev_bot *                         xor
+
+  st_bot <== (1-xor) * (aux2 - st_old0 + prev_bot)
+
+
+  // st_upd = prev_top * (1-fnc[0]) *levIns;
+  //    = + prev_top * levIns
+  //      - prev_top * levIns * fnc[0]
+
+  st_upd <== aux1 - aux2
+
+  // st_na = prev_new1 + prev_old0 + prev_na + prev_upd;
+  //    = + prev_new1
+  //      + prev_old0
+  //      + prev_na
+  //      + prev_upd
+
+  st_na <== prev_new1 + prev_old0 + prev_na + prev_upd;
+
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifier.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifier.circom
@@ -0,0 +1,135 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+
+SMTVerifier is a component to verify inclusion/exclusion of an element in the tree
+
+
+fnc:  0 -> VERIFY INCLUSION
+      1 -> VERIFY NOT INCLUSION
+
+ */
+
+
+include "../gates.circom";
+include "../bitify.circom";
+include "../comparators.circom";
+include "../switcher.circom";
+include "smtlevins.circom";
+include "smtverifierlevel.circom";
+include "smtverifiersm.circom";
+include "smthash_poseidon.circom";
+
+template SMTVerifier(nLevels) {
+    signal input enabled;
+    signal input root;
+    signal input siblings[nLevels];
+    signal input oldKey;
+    signal input oldValue;
+    signal input isOld0;
+    signal input key;
+    signal input value;
+    signal input fnc;
+
+    component hash1Old = SMTHash1();
+    hash1Old.key <== oldKey;
+    hash1Old.value <== oldValue;
+
+    component hash1New = SMTHash1();
+    hash1New.key <== key;
+    hash1New.value <== value;
+
+    component n2bOld = Num2Bits_strict();
+    component n2bNew = Num2Bits_strict();
+
+    n2bOld.in <== oldKey;
+    n2bNew.in <== key;
+
+    component smtLevIns = SMTLevIns(nLevels);
+    for (var i=0; i<nLevels; i++) smtLevIns.siblings[i] <== siblings[i];
+    smtLevIns.enabled <== enabled;
+
+    component sm[nLevels];
+    for (var i=0; i<nLevels; i++) {
+        sm[i] = SMTVerifierSM();
+        if (i==0) {
+            sm[i].prev_top <== enabled;
+            sm[i].prev_i0 <== 0;
+            sm[i].prev_inew <== 0;
+            sm[i].prev_iold <== 0;
+            sm[i].prev_na <== 1-enabled;
+        } else {
+            sm[i].prev_top <== sm[i-1].st_top;
+            sm[i].prev_i0 <== sm[i-1].st_i0;
+            sm[i].prev_inew <== sm[i-1].st_inew;
+            sm[i].prev_iold <== sm[i-1].st_iold;
+            sm[i].prev_na <== sm[i-1].st_na;
+        }
+        sm[i].is0 <== isOld0;
+        sm[i].fnc <== fnc;
+        sm[i].levIns <== smtLevIns.levIns[i];
+    }
+    sm[nLevels-1].st_na + sm[nLevels-1].st_iold + sm[nLevels-1].st_inew + sm[nLevels-1].st_i0 === 1;
+
+    component levels[nLevels];
+    for (var i=nLevels-1; i != -1; i--) {
+        levels[i] = SMTVerifierLevel();
+
+        levels[i].st_top <== sm[i].st_top;
+        levels[i].st_i0 <== sm[i].st_i0;
+        levels[i].st_inew <== sm[i].st_inew;
+        levels[i].st_iold <== sm[i].st_iold;
+        levels[i].st_na <== sm[i].st_na;
+
+        levels[i].sibling <== siblings[i];
+        levels[i].old1leaf <== hash1Old.out;
+        levels[i].new1leaf <== hash1New.out;
+
+        levels[i].lrbit <== n2bNew.out[i];
+        if (i==nLevels-1) {
+            levels[i].child <== 0;
+        } else {
+            levels[i].child <== levels[i+1].root;
+        }
+    }
+
+
+    // Check that if checking for non inclussuin and isOld0==0 then key!=old
+    component areKeyEquals = IsEqual();
+    areKeyEquals.in[0] <== oldKey;
+    areKeyEquals.in[1] <== key;
+
+    component keysOk = MultiAND(4);
+    keysOk.in[0] <== fnc;
+    keysOk.in[1] <== 1-isOld0;
+    keysOk.in[2] <== areKeyEquals.out;
+    keysOk.in[3] <== enabled;
+
+    keysOk.out === 0;
+
+    // Check the root
+    component checkRoot = ForceEqualIfEnabled();
+    checkRoot.enabled <== enabled;
+    checkRoot.in[0] <== levels[0].root;
+    checkRoot.in[1] <== root;
+
+    // levels[0].root === root;
+
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifierlevel.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifierlevel.circom
@@ -0,0 +1,71 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/******
+
+SMTVerifierLevel
+
+This circuit has 1 hash
+
+Outputs according to the state.
+
+State        root
+=====        =======
+top          H'(child, sibling)
+i0           0
+iold         old1leaf
+inew         new1leaf
+na           0
+
+H' is the Hash function with the inputs shifted acordingly.
+
+*****/
+
+
+template SMTVerifierLevel() {
+    signal input st_top;
+    signal input st_i0;
+    signal input st_iold;
+    signal input st_inew;
+    signal input st_na;
+
+    signal output root;
+    signal input sibling;
+    signal input old1leaf;
+    signal input new1leaf;
+    signal input lrbit;
+    signal input child;
+
+    signal aux[2];
+
+    component proofHash = SMTHash2();
+    component switcher = Switcher();
+
+    switcher.L <== child;
+    switcher.R <== sibling;
+
+    switcher.sel <== lrbit;
+    proofHash.L <== switcher.outL;
+    proofHash.R <== switcher.outR;
+
+    aux[0] <== proofHash.out * st_top;
+    aux[1] <== old1leaf*st_iold;
+
+    root <== aux[0] + aux[1] + new1leaf*st_inew;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifiersm.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/smt/smtverifiersm.circom
@@ -0,0 +1,105 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+Each level in the SMTVerifier has a state.
+
+This is the state machine.
+
+The signals are
+
+levIns: 1 if we are in the level where the insertion should happen
+xor: 1 if the bitKey of the old and new keys are different in this level
+is0: Input that indicates that the oldKey is 0
+fnc:  0 -> VERIFY INCLUSION
+      1 -> VERIFY NOT INCLUSION
+
+err state is not a state itself. It's a lack of state.
+
+The end of the last level will have to be `na`
+
+   levIns=0                                                                                any
+     ┌────┐                                                                              ┌────┐
+     │    │                                                                              │    │
+     │    ▼                          levIns=1                                            ▼    │
+     │    ###########                is0=1      ###########                    ###########    │
+     │   #           #               fnc=1     #           #       any        #           #   │
+     └──#    top      # ─────────────────────▶#     i0      #───────────────▶#    na       #──┘
+         ##         ## ──────────┐             ##         ##         ┌───────▶##         ##
+           ########─────────────┐│               #########           │┌────────▶#########
+                                ││ levIns=1                          ││
+                                ││ is0=0        ###########          ││
+                                ││ fnc=1       #           #       any│
+                                │└──────────▶ #    iold     #────────┘│
+                                │              ##         ##          │
+                                │                #########            │
+                                │                                     │
+                                │  levIns=1     ###########           │
+                                │  fnc=0       #           #        any
+                                └────────────▶#    inew     #─────────┘
+                                               ##         ##
+                                                 #########
+
+ */
+
+
+template SMTVerifierSM() {
+    signal input is0;
+    signal input levIns;
+    signal input fnc;
+
+    signal input prev_top;
+    signal input prev_i0;
+    signal input prev_iold;
+    signal input prev_inew;
+    signal input prev_na;
+
+    signal output st_top;
+    signal output st_i0;
+    signal output st_iold;
+    signal output st_inew;
+    signal output st_na;
+
+    signal prev_top_lev_ins;
+    signal prev_top_lev_ins_fnc;
+
+    prev_top_lev_ins <== prev_top * levIns;
+    prev_top_lev_ins_fnc <== prev_top_lev_ins*fnc;  // prev_top * levIns * fnc
+
+    // st_top = prev_top * (1-levIns)
+    //    = + prev_top
+    //      - prev_top * levIns
+    st_top <== prev_top - prev_top_lev_ins;
+
+    // st_inew = prev_top * levIns * (1-fnc)
+    //   = + prev_top * levIns
+    //     - prev_top * levIns * fnc
+    st_inew <== prev_top_lev_ins - prev_top_lev_ins_fnc;
+
+    // st_iold = prev_top * levIns * (1-is0)*fnc
+    //   = + prev_top * levIns * fnc
+    //     - prev_top * levIns * fnc * is0
+    st_iold <== prev_top_lev_ins_fnc * (1 - is0);
+
+    // st_i0 = prev_top * levIns * is0
+    //  = + prev_top * levIns * is0
+    st_i0 <== prev_top_lev_ins * is0;
+
+    st_na <== prev_na + prev_inew + prev_iold + prev_i0;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/switcher.circom
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/circuits/switcher.circom
@@ -0,0 +1,40 @@
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of circom (Zero Knowledge Circuit Compiler).
+
+    circom is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    circom is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with circom. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+    Assume sel is binary.
+
+    If sel == 0 then outL = L and outR=R
+    If sel == 1 then outL = R and outR=L
+
+ */
+
+template Switcher() {
+    signal input sel;
+    signal input L;
+    signal input R;
+    signal output outL;
+    signal output outR;
+
+    signal aux;
+
+    aux <== (R-L)*sel;    // We create aux in order to have only one multiplication
+    outL <==  aux + L;
+    outR <== -aux + R;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/root_transfer.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/root_transfer.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_diagram_0.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_diagram_0.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_diagram_1.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_diagram_1.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_hash.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_hash.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_levins.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_levins.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_sm.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_sm.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_verifier_sm.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/smt_verifier_sm.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/voting.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/voting.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/window.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/window.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/window_chain.monopic
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/doc/window_chain.monopic
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/index.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/index.js
@@ -0,0 +1,6 @@
+exports.smt = require("./src/smt");
+exports.eddsa = require("./src/eddsa");
+exports.mimc7 = require("./src/mimc7");
+exports.mimcsponge = require("./src/mimcsponge");
+exports.babyJub = require("./src/babyjub");
+exports.pedersenHash = require("./src/pedersenHash");
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/package-lock.json
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/package-lock.json
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/package.json
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/package.json
@@ -0,0 +1,39 @@
+{
+  "name": "circomlib",
+  "version": "0.0.12",
+  "description": "Basic circuits library for Circom",
+  "main": "index.js",
+  "directories": {
+    "test": "test"
+  },
+  "scripts": {
+    "test": "mocha --max-old-space-size=4000"
+  },
+  "keywords": [
+    "pedersen",
+    "hash",
+    "ethereum",
+    "circuit",
+    "circom",
+    "zksnark"
+  ],
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/iden3/circomlib.git"
+  },
+  "author": "0Kims",
+  "license": "GPL-3.0",
+  "dependencies": {
+    "blake-hash": "^1.1.0",
+    "blake2b": "^2.1.3",
+    "snarkjs": "0.1.11",
+    "typedarray-to-buffer": "^3.1.5",
+    "web3": "^1.0.0-beta.55"
+  },
+  "devDependencies": {
+    "circom": "0.0.28",
+    "eslint-plugin-mocha": "^5.2.0",
+    "ganache-cli": "^6.4.4",
+    "mocha": "^5.2.0"
+  }
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/babyjub.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/babyjub.js
@@ -0,0 +1,109 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+
+exports.addPoint = addPoint;
+exports.mulPointEscalar = mulPointEscalar;
+exports.inCurve = inCurve;
+exports.inSubgroup = inSubgroup;
+exports.packPoint = packPoint;
+exports.unpackPoint = unpackPoint;
+exports.Generator = [
+    bigInt("995203441582195749578291179787384436505546430278305826713579947235728471134"),
+    bigInt("5472060717959818805561601436314318772137091100104008585924551046643952123905")
+];
+exports.Base8 = [
+    bigInt("5299619240641551281634865583518297030282874472190772894086521144482721001553"),
+    bigInt("16950150798460657717958625567821834550301663161624707787222815936182638968203")
+];
+exports.order = bigInt("21888242871839275222246405745257275088614511777268538073601725287587578984328");
+exports.subOrder = exports.order.shr(3);
+exports.p = bn128.r;
+exports.A = bigInt("168700");
+exports.D = bigInt("168696");
+
+
+function addPoint(a,b) {
+    const q = bn128.r;
+
+    const res = [];
+
+    /* does the equivalent of:
+     res[0] = bigInt((a[0]*b[1] + b[0]*a[1]) *  bigInt(bigInt("1") + d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+    res[1] = bigInt((a[1]*b[1] - cta*a[0]*b[0]) * bigInt(bigInt("1") - d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
+    */
+    res[0] = bigInt((bigInt(a[0]).mul(b[1]).add(bigInt(b[0]).mul(a[1]))).mul(bigInt(bigInt("1").add(exports.D.mul(a[0]).mul(b[0]).mul(a[1]).mul(b[1]))).inverse(q))).affine(q);
+    res[1] = bigInt((bigInt(a[1]).mul(b[1]).sub(exports.A.mul(a[0]).mul(b[0]))).mul(bigInt(bigInt("1").sub(exports.D.mul(a[0]).mul(b[0]).mul(a[1]).mul(b[1]))).inverse(q))).affine(q);
+
+    return res;
+}
+
+function mulPointEscalar(base, e) {
+    let res = [bigInt("0"),bigInt("1")];
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = addPoint(res, exp);
+        }
+        exp = addPoint(exp, exp);
+        rem = rem.shr(1);
+    }
+
+    return res;
+}
+
+function inSubgroup(P) {
+    if (!inCurve(P)) return false;
+    const res= mulPointEscalar(P, exports.subOrder);
+    return (res[0].equals(bigInt(0))) && (res[1].equals(bigInt(1)));
+}
+
+function inCurve(P) {
+    const F = bn128.Fr;
+
+    const x2 = F.square(P[0]);
+    const y2 = F.square(P[1]);
+
+    if (!F.equals(
+        F.add(F.mul(exports.A, x2), y2),
+        F.add(F.one, F.mul(F.mul(x2, y2), exports.D)))) return false;
+
+    return true;
+}
+
+function packPoint(P) {
+    const buff = bigInt.leInt2Buff(P[1], 32);
+    if (P[0].greater(exports.p.shr(1))) {
+        buff[31] = buff[31] | 0x80;
+    }
+    return buff;
+}
+
+function unpackPoint(_buff) {
+    const F = bn128.Fr;
+
+    const buff = Buffer.from(_buff);
+    let sign = false;
+    const P = new Array(2);
+    if (buff[31] & 0x80) {
+        sign = true;
+        buff[31] = buff[31] & 0x7F;
+    }
+    P[1] = bigInt.leBuff2int(buff);
+    if (P[1].greaterOrEquals(exports.p)) return null;
+
+    const y2 = F.square(P[1]);
+
+    let x = F.sqrt(F.div(
+        F.sub(F.one, y2),
+        F.sub(exports.A, F.mul(exports.D, y2))));
+
+    if (x == null) return null;
+
+    if (sign) x = F.neg(x);
+
+    P[0] = F.affine(x);
+
+    return P;
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/eddsa.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/eddsa.js
@@ -0,0 +1,223 @@
+const createBlakeHash = require("blake-hash");
+const bigInt = require("snarkjs").bigInt;
+const babyJub = require("./babyjub");
+const pedersenHash = require("./pedersenHash").hash;
+const mimc7 = require("./mimc7");
+const poseidon = require("./poseidon.js");
+const mimcsponge = require("./mimcsponge");
+
+exports.prv2pub= prv2pub;
+exports.sign = sign;
+exports.signMiMC = signMiMC;
+exports.signPoseidon = signPoseidon;
+exports.signMiMCSponge = signMiMCSponge;
+exports.verify = verify;
+exports.verifyMiMC = verifyMiMC;
+exports.verifyPoseidon = verifyPoseidon;
+exports.verifyMiMCSponge = verifyMiMCSponge;
+exports.packSignature = packSignature;
+exports.unpackSignature = unpackSignature;
+exports.pruneBuffer = pruneBuffer;
+
+
+function pruneBuffer(_buff) {
+    const buff = Buffer.from(_buff);
+    buff[0] = buff[0] & 0xF8;
+    buff[31] = buff[31] & 0x7F;
+    buff[31] = buff[31] | 0x40;
+    return buff;
+}
+
+function prv2pub(prv) {
+    const sBuff = pruneBuffer(createBlakeHash("blake512").update(prv).digest().slice(0,32));
+    let s = bigInt.leBuff2int(sBuff);
+    const A = babyJub.mulPointEscalar(babyJub.Base8, s.shr(3));
+    return A;
+}
+
+function sign(prv, msg) {
+    const h1 = createBlakeHash("blake512").update(prv).digest();
+    const sBuff = pruneBuffer(h1.slice(0,32));
+    const s = bigInt.leBuff2int(sBuff);
+    const A = babyJub.mulPointEscalar(babyJub.Base8, s.shr(3));
+
+    const rBuff = createBlakeHash("blake512").update(Buffer.concat([h1.slice(32,64), msg])).digest();
+    let r = bigInt.leBuff2int(rBuff);
+    r = r.mod(babyJub.subOrder);
+    const R8 = babyJub.mulPointEscalar(babyJub.Base8, r);
+    const R8p = babyJub.packPoint(R8);
+    const Ap = babyJub.packPoint(A);
+    const hmBuff = pedersenHash(Buffer.concat([R8p, Ap, msg]));
+    const hm = bigInt.leBuff2int(hmBuff);
+    const S = r.add(hm.mul(s)).mod(babyJub.subOrder);
+    return {
+        R8: R8,
+        S: S
+    };
+}
+
+function signMiMC(prv, msg) {
+    const h1 = createBlakeHash("blake512").update(prv).digest();
+    const sBuff = pruneBuffer(h1.slice(0,32));
+    const s = bigInt.leBuff2int(sBuff);
+    const A = babyJub.mulPointEscalar(babyJub.Base8, s.shr(3));
+
+    const msgBuff = bigInt.leInt2Buff(msg, 32);
+    const rBuff = createBlakeHash("blake512").update(Buffer.concat([h1.slice(32,64), msgBuff])).digest();
+    let r = bigInt.leBuff2int(rBuff);
+    r = r.mod(babyJub.subOrder);
+    const R8 = babyJub.mulPointEscalar(babyJub.Base8, r);
+    const hm = mimc7.multiHash([R8[0], R8[1], A[0], A[1], msg]);
+    const S = r.add(hm.mul(s)).mod(babyJub.subOrder);
+    return {
+        R8: R8,
+        S: S
+    };
+}
+
+function signMiMCSponge(prv, msg) {
+    const h1 = createBlakeHash("blake512").update(prv).digest();
+    const sBuff = pruneBuffer(h1.slice(0,32));
+    const s = bigInt.leBuff2int(sBuff);
+    const A = babyJub.mulPointEscalar(babyJub.Base8, s.shr(3));
+
+    const msgBuff = bigInt.leInt2Buff(msg, 32);
+    const rBuff = createBlakeHash("blake512").update(Buffer.concat([h1.slice(32,64), msgBuff])).digest();
+    let r = bigInt.leBuff2int(rBuff);
+    r = r.mod(babyJub.subOrder);
+    const R8 = babyJub.mulPointEscalar(babyJub.Base8, r);
+    const hm = mimcsponge.multiHash([R8[0], R8[1], A[0], A[1], msg]);
+    const S = r.add(hm.mul(s)).mod(babyJub.subOrder);
+    return {
+        R8: R8,
+        S: S
+    };
+}
+
+function signPoseidon(prv, msg) {
+    const h1 = createBlakeHash("blake512").update(prv).digest();
+    const sBuff = pruneBuffer(h1.slice(0,32));
+    const s = bigInt.leBuff2int(sBuff);
+    const A = babyJub.mulPointEscalar(babyJub.Base8, s.shr(3));
+
+    const msgBuff = bigInt.leInt2Buff(msg, 32);
+    const rBuff = createBlakeHash("blake512").update(Buffer.concat([h1.slice(32,64), msgBuff])).digest();
+    let r = bigInt.leBuff2int(rBuff);
+    r = r.mod(babyJub.subOrder);
+    const R8 = babyJub.mulPointEscalar(babyJub.Base8, r);
+    const hash = poseidon.createHash(6, 8, 57);
+    const hm = hash([R8[0], R8[1], A[0], A[1], msg]);
+    const S = r.add(hm.mul(s)).mod(babyJub.subOrder);
+    return {
+        R8: R8,
+        S: S
+    };
+}
+
+function verify(msg, sig, A) {
+    // Check parameters
+    if (typeof sig != "object") return false;
+    if (!Array.isArray(sig.R8)) return false;
+    if (sig.R8.length!= 2) return false;
+    if (!babyJub.inCurve(sig.R8)) return false;
+    if (!Array.isArray(A)) return false;
+    if (A.length!= 2) return false;
+    if (!babyJub.inCurve(A)) return false;
+    if (sig.S>= babyJub.subOrder) return false;
+
+    const R8p = babyJub.packPoint(sig.R8);
+    const Ap = babyJub.packPoint(A);
+    const hmBuff = pedersenHash(Buffer.concat([R8p, Ap, msg]));
+    const hm = bigInt.leBuff2int(hmBuff);
+
+    const Pleft = babyJub.mulPointEscalar(babyJub.Base8, sig.S);
+    let Pright = babyJub.mulPointEscalar(A, hm.mul(bigInt("8")));
+    Pright = babyJub.addPoint(sig.R8, Pright);
+
+    if (!Pleft[0].equals(Pright[0])) return false;
+    if (!Pleft[1].equals(Pright[1])) return false;
+    return true;
+}
+
+function verifyMiMC(msg, sig, A) {
+    // Check parameters
+    if (typeof sig != "object") return false;
+    if (!Array.isArray(sig.R8)) return false;
+    if (sig.R8.length!= 2) return false;
+    if (!babyJub.inCurve(sig.R8)) return false;
+    if (!Array.isArray(A)) return false;
+    if (A.length!= 2) return false;
+    if (!babyJub.inCurve(A)) return false;
+    if (sig.S>= babyJub.subOrder) return false;
+
+    const hm = mimc7.multiHash([sig.R8[0], sig.R8[1], A[0], A[1], msg]);
+
+    const Pleft = babyJub.mulPointEscalar(babyJub.Base8, sig.S);
+    let Pright = babyJub.mulPointEscalar(A, hm.mul(bigInt("8")));
+    Pright = babyJub.addPoint(sig.R8, Pright);
+
+    if (!Pleft[0].equals(Pright[0])) return false;
+    if (!Pleft[1].equals(Pright[1])) return false;
+    return true;
+}
+
+
+function verifyPoseidon(msg, sig, A) {
+    // Check parameters
+    if (typeof sig != "object") return false;
+    if (!Array.isArray(sig.R8)) return false;
+    if (sig.R8.length!= 2) return false;
+    if (!babyJub.inCurve(sig.R8)) return false;
+    if (!Array.isArray(A)) return false;
+    if (A.length!= 2) return false;
+    if (!babyJub.inCurve(A)) return false;
+    if (sig.S>= babyJub.subOrder) return false;
+
+    const hash = poseidon.createHash(6, 8, 57);
+    const hm = hash([sig.R8[0], sig.R8[1], A[0], A[1], msg]);
+
+    const Pleft = babyJub.mulPointEscalar(babyJub.Base8, sig.S);
+    let Pright = babyJub.mulPointEscalar(A, hm.mul(bigInt("8")));
+    Pright = babyJub.addPoint(sig.R8, Pright);
+
+    if (!Pleft[0].equals(Pright[0])) return false;
+    if (!Pleft[1].equals(Pright[1])) return false;
+    return true;
+}
+
+function verifyMiMCSponge(msg, sig, A) {
+    // Check parameters
+    if (typeof sig != "object") return false;
+    if (!Array.isArray(sig.R8)) return false;
+    if (sig.R8.length!= 2) return false;
+    if (!babyJub.inCurve(sig.R8)) return false;
+    if (!Array.isArray(A)) return false;
+    if (A.length!= 2) return false;
+    if (!babyJub.inCurve(A)) return false;
+    if (sig.S>= babyJub.subOrder) return false;
+
+    const hm = mimcsponge.multiHash([sig.R8[0], sig.R8[1], A[0], A[1], msg]);
+
+    const Pleft = babyJub.mulPointEscalar(babyJub.Base8, sig.S);
+    let Pright = babyJub.mulPointEscalar(A, hm.mul(bigInt("8")));
+    Pright = babyJub.addPoint(sig.R8, Pright);
+
+    if (!Pleft[0].equals(Pright[0])) return false;
+    if (!Pleft[1].equals(Pright[1])) return false;
+    return true;
+}
+
+function packSignature(sig) {
+    const R8p = babyJub.packPoint(sig.R8);
+    const Sp = bigInt.leInt2Buff(sig.S, 32);
+    return Buffer.concat([R8p, Sp]);
+}
+
+function unpackSignature(sigBuff) {
+    return {
+        R8: babyJub.unpackPoint(sigBuff.slice(0,32)),
+        S: bigInt.leBuff2int(sigBuff.slice(32,64))
+    };
+}
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/evmasm.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/evmasm.js
@@ -0,0 +1,197 @@
+// Copyright (c) 2018 Jordi Baylina
+// License: LGPL-3.0+
+//
+
+
+const Web3Utils = require("web3-utils");
+
+class Contract {
+    constructor() {
+        this.code = [];
+        this.labels = {};
+        this.pendingLabels = {};
+    }
+
+    createTxData() {
+        let C;
+
+        // Check all labels are defined
+        const pendingLabels = Object.keys(this.pendingLabels);
+        if (pendingLabels.length>0) {
+            throw new Error("Lables not defined: "+ pendingLabels.join(", "));
+        }
+
+        let setLoaderLength = 0;
+        let genLoadedLength = -1;
+
+        while  (genLoadedLength!=setLoaderLength) {
+            setLoaderLength = genLoadedLength;
+            C = new module.exports();
+            C.codesize();
+            C.push(setLoaderLength);
+            C.push(0);
+            C.codecopy();
+
+            C.push(this.code.length);
+            C.push(0);
+            C.return();
+            genLoadedLength = C.code.length;
+        }
+
+        return Web3Utils.bytesToHex(C.code.concat(this.code));
+    }
+
+    stop() { this.code.push(0x00); }
+    add()  { this.code.push(0x01); }
+    mul()  { this.code.push(0x02); }
+    sub()  { this.code.push(0x03); }
+    div()  { this.code.push(0x04); }
+    sdiv() { this.code.push(0x05); }
+    mod()  { this.code.push(0x06); }
+    smod()  { this.code.push(0x07); }
+    addmod()  { this.code.push(0x08); }
+    mulmod()  { this.code.push(0x09); }
+    exp()  { this.code.push(0x0a); }
+    signextend()  { this.code.push(0x0b); }
+
+    lt()   { this.code.push(0x10); }
+    gt()   { this.code.push(0x11); }
+    slt()  { this.code.push(0x12); }
+    sgt()  { this.code.push(0x13); }
+    eq()   { this.code.push(0x14); }
+    iszero()  { this.code.push(0x15); }
+    and()  { this.code.push(0x16); }
+    or()  { this.code.push(0x17); }
+    shor()  { this.code.push(0x18); }
+    not()  { this.code.push(0x19); }
+    byte()  { this.code.push(0x1a); }
+
+    keccak() { this.code.push(0x20); }
+    sha3() { this.code.push(0x20); }   // alias
+
+    address()  { this.code.push(0x30); }
+    balance()  { this.code.push(0x31); }
+    origin()  { this.code.push(0x32); }
+    caller()  { this.code.push(0x33); }
+    callvalue()  { this.code.push(0x34); }
+    calldataload()  { this.code.push(0x35); }
+    calldatasize()  { this.code.push(0x36); }
+    calldatacopy()  { this.code.push(0x37); }
+    codesize()  { this.code.push(0x38); }
+    codecopy()  { this.code.push(0x39); }
+    gasprice()  { this.code.push(0x3a); }
+    extcodesize()  { this.code.push(0x3b); }
+    extcodecopy()  { this.code.push(0x3c); }
+    returndatasize()  { this.code.push(0x3d); }
+    returndatacopy()  { this.code.push(0x3e); }
+
+    blockhash()  { this.code.push(0x40); }
+    coinbase()  { this.code.push(0x41); }
+    timestamp()  { this.code.push(0x42); }
+    number()  { this.code.push(0x43); }
+    difficulty()  { this.code.push(0x44); }
+    gaslimit()  { this.code.push(0x45); }
+
+    pop()  { this.code.push(0x50); }
+    mload()  { this.code.push(0x51); }
+    mstore()  { this.code.push(0x52); }
+    mstore8()  { this.code.push(0x53); }
+    sload()  { this.code.push(0x54); }
+    sstore()  { this.code.push(0x55); }
+
+    _pushLabel(label) {
+        if (typeof this.labels[label] != "undefined") {
+            this.push(this.labels[label]);
+        } else {
+            this.pendingLabels[label] = this.pendingLabels[label] || [];
+            this.pendingLabels[label].push(this.code.length);
+            this.push("0x000000");
+        }
+    }
+
+    _fillLabel(label) {
+        if (!this.pendingLabels[label]) return;
+
+        let dst = this.labels[label];
+
+        const dst3 = [dst >> 16, (dst >> 8) & 0xFF, dst & 0xFF];
+
+        this.pendingLabels[label].forEach((p) => {
+            for (let i=0; i<3; i++) {
+                this.code[p+i+1] = dst3[i];
+            }
+        });
+
+        delete this.pendingLabels[label];
+    }
+
+
+    jmp(label)  {
+        if (typeof label !== "undefined") {
+            this._pushLabel(label);
+        }
+        this.code.push(0x56);
+    }
+
+    jmpi(label)  {
+        if (typeof label !== "undefined") {
+            this._pushLabel(label);
+        }
+        this.code.push(0x57);
+    }
+
+    pc()  { this.code.push(0x58); }
+    msize()  { this.code.push(0x59); }
+    gas()  { this.code.push(0x5a); }
+    label(name)  {
+        if (typeof this.labels[name] != "undefined") {
+            throw new Error("Label already defined");
+        }
+        this.labels[name] = this.code.length;
+        this.code.push(0x5b);
+
+        this._fillLabel(name);
+    }
+
+    push(data) {
+        const d = Web3Utils.hexToBytes(Web3Utils.toHex(data));
+        if (d.length == 0 || d.length > 32) {
+            throw new Error("Assertion failed");
+        }
+        this.code = this.code.concat([0x5F + d.length], d);
+    }
+
+    dup(n) {
+        if (n < 0 || n >= 16) {
+            throw new Error("Assertion failed");
+        }
+        this.code.push(0x80 + n);
+    }
+
+    swap(n) {
+        if (n < 1 || n > 16) {
+            throw new Error("Assertion failed");
+        }
+        this.code.push(0x8f + n);
+    }
+
+    log0()  { this.code.push(0xa0); }
+    log1()  { this.code.push(0xa1); }
+    log2()  { this.code.push(0xa2); }
+    log3()  { this.code.push(0xa3); }
+    log4()  { this.code.push(0xa4); }
+
+    create()  { this.code.push(0xf0); }
+    call()  { this.code.push(0xf1); }
+    callcode()  { this.code.push(0xf2); }
+    return()  { this.code.push(0xf3); }
+    delegatecall()  { this.code.push(0xf4); }
+
+    staticcall()  { this.code.push(0xfa); }
+    revert()  { this.code.push(0xfd); }
+    invalid()  { this.code.push(0xfe); }
+    selfdestruct()  { this.code.push(0xff); }
+}
+
+module.exports = Contract;
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/g2_gencontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/g2_gencontract.js
@@ -0,0 +1,583 @@
+// Copyright (c) 2018 Jordi Baylina
+// License: LGPL-3.0+
+//
+
+const Contract = require("./evmasm");
+const G2 = require("snarkjs").bn128.G2;
+const bigInt = require("snarkjs").bigInt;
+
+
+function toHex256(a) {
+    let S = a.toString(16);
+    while (S.length < 64) S="0"+S;
+    return "0x" + S;
+}
+
+function createCode(P, w) {
+
+    const C = new Contract();
+
+    const NPOINTS = 1 << (w-1);
+
+    const VAR_POS = C.allocMem(32);
+    const VAR_POINTS = C.allocMem( (NPOINTS)*4*32);
+    const savedP = C.allocMem(32);
+    const savedZ3 = C.allocMem(32);
+
+    // Check selector
+    C.push("0x0100000000000000000000000000000000000000000000000000000000");
+    C.push(0);
+    C.calldataload();
+    C.div();
+    C.push("b65c7c74"); // mulexp(uint256)
+    C.eq();
+    C.jmpi("start");
+    C.invalid();
+
+    C.label("start");
+
+    storeVals();
+
+    C.push( Math.floor(255/w)*w  );                // pos := 255
+    C.push(VAR_POS);
+    C.mstore();
+
+    C.push("21888242871839275222246405745257275088696311157297823662689037894645226208583");
+    C.push(0);
+    C.push(0);
+    C.push(0);
+    C.push(0);
+    C.push(0);
+    C.push(0);
+
+    C.label("begin_loop");      // ACC_X ACC_Y ACC_Z q
+
+    C.internalCall("double");
+
+    // g = (e>>pos)&MASK
+    C.push(4);
+    C.calldataload();           // e ACC_X ACC_Y ACC_Z q
+
+    C.push(VAR_POS);
+    C.mload();                  // pos e ACC_X ACC_Y ACC_Z q
+    C.shr();
+
+    C.push(NPOINTS-1);
+    C.and();                    // g ACC_X ACC_Y ACC_Z q
+
+    C.internalCall("add");      // acc_x acc_y acc_z
+
+    C.push(VAR_POS);
+    C.mload();                  // pos acc_x acc_y acc_z
+    C.dup(0);                   // pos pos acc_x acc_y acc_z
+    C.push(0);                  // 0 pos pos acc_x acc_y acc_z
+    C.eq();                     // eq pos acc_x acc_y acc_z
+    C.jmpi("after_loop");       // pos acc_x acc_y acc_z
+    C.push(w);                  // 5 pos acc_x acc_y acc_z
+    C.sub();                    // pos acc_x acc_y acc_z
+    C.push(VAR_POS);
+    C.mstore();                 // acc_x acc_y acc_z
+    C.jmp("begin_loop");
+    C.label("after_loop");      // pos acc_x acc_y acc_z
+    C.pop();                    // acc_x acc_y acc_z
+
+    C.internalCall("affine");   // acc_x acc_y
+
+    C.push(0);
+    C.mstore();
+    C.push(20);
+    C.mstore();
+    C.push(40);
+    C.mstore();
+    C.push(60);
+    C.mstore();
+
+    C.push("0x80");
+    C.push("0x00");
+    C.return();
+
+
+    double();
+    addPoint();
+    affine();
+
+    return C.createTxData();
+
+    function add(a,b,q) {
+        C.dup(q);
+        C.dup(a+1 + 1);
+        C.dup(b+1 + 2);
+        C.addmod();
+        C.dup(q + 1);
+        C.dup(a + 2);
+        C.dup(b + 3);
+        C.addmod();
+    }
+
+    function sub(a,b,q) {
+        C.dup(q);           // q
+        C.dup(a+1 + 1);     // ai q
+        C.dub(q + 2);       // q ai q
+        C.dup(b+1 + 3);     // bi q ai q
+        C.sub();            // -bi ai q
+        C.addmod();         // ci
+        C.dup(q + 1);       // q ci
+        C.dup(a + 2);       // ar q ci
+        C.dup(q + 3);       // q ar q ci
+        C.dup(b + 4);       // br q ar q ci
+        C.sub();            // -br ar q ci
+        C.addmod();         // cr ci
+    }
+
+    function mul(a, b, q) {
+        C.dup(q);           //  q
+        C.dup(q + 1);       //  q q
+        C.dup(a + 2);       //  ar q q
+        C.dup(b+1 + 3);     //  bi ar q q
+        C.mulmod();         //  ci1 q
+        C.dup(q + 2);       //  q ci1 q
+        C.dup(a+1 + 3);     //  ai q ci1 q
+        C.dup(b + 4);       //  ar ai q ci1 q
+        C.mulmod();         //  ci2 ci1 q
+        C.addmod();         //  ci
+        C.dup(q + 1);       //  q ci
+        C.dup(q + 2);       //  q q ci
+        C.dup(q + 3);       //  q q q ci
+        C.dup(a+1 + 4);     //  ai q q ci
+        C.dup(b+1 + 5);     //  bi ai q q ci
+        C.mulmod();         //  cr2 q q ci
+        C.sub();            //  -cr2 q ci
+        C.dup(q + 3);       //  q -cr2 q ci
+        C.dup(a + 4);       //  ar q -cr2 q ci
+        C.dup(b + 5);       //  br ar q -cr2 q ci
+        C.mulmod();         //  cr1 -cr2 q ci
+        C.addmod();         //  cr ci
+    }
+
+    function square(a, q) {
+        C.dup(q);           //  q
+        C.dup(q + 1);       //  q q
+        C.dup(a + 2);       //  ar q q
+        C.dup(a+1 + 3);     //  ai ar q q
+        C.mulmod();         //  arai q
+        C.dup(0);           //  arai arai q
+        C.addmod();         //  ci
+        C.dup(q + 1);       //  q ci
+        C.dup(q + 2);       //  q q ci
+        C.dup(q + 3);       //  q q q ci
+        C.dup(a+1 + 4);     //  ai q q ci
+        C.dup(a+1 + 5);     //  ai ai q q ci
+        C.mulmod();         //  cr2 q q ci
+        C.sub();            //  -cr2 q ci
+        C.dup(q + 3);       //  q -cr2 q ci
+        C.dup(a + 4);       //  ar q -cr2 q ci
+        C.dup(a + 5);       //  br ar q -cr2 q ci
+        C.mulmod();         //  cr1 -cr2 q ci
+        C.addmod();         //  cr ci
+    }
+
+    function add1(a, q) {
+        C.dup(a+1);         // im
+        C.dup(1 + q);       //  q
+        C.dup(2 + a);       //  re q im
+        C.push(1);          // 1 re q im
+        C.addmod();
+    }
+
+    function cmp(a, b) {
+        C.dup(a);
+        C.dup(b);
+        C.eq();
+        C.dup(a+1);
+        C.dup(a+1);
+        C.and();
+    }
+
+    function rm(a) {
+        if (a>0) C.swap(a);
+        C.pop();
+        if (a>0) C.swap(a);
+        C.pop();
+    }
+
+    function double() {
+        C.label("double");       // xR, xI,    yR, yI,   zR zI, q
+
+        C.dup(4);
+        C.iszero();
+        C.dup(6);
+        C.iszero();
+        C.and();
+        C.jumpi("enddouble");   // X Y Z q
+
+
+        // Z3 = 2*Y*Z // Remove Z
+        mul(2, 4, 6);           // yz X Y Z q
+        rm(6);                  // X Y yz q
+
+        add(4, 4, 6);           // 2yz X Y yz q
+        rm(6);                  // X Y Z3 q
+
+        // A = X^2
+        square(0,6);               // A X Y Z3 q
+
+        // B = Y^2  // Remove Y
+        square(4,8);              // B A X Y Z3 q
+        rm(6);                  // A X B Z3 q
+
+        // C = B^2
+        square(4,8);               // C A X B Z3 q
+
+        // D = (X+B)^2-A-C // Remove X, Remove B
+        add(4,6, 10);           // X+B C A X B Z3 q
+        rm(6);                  // C A X+B B Z3 q
+        rm(6);                  // A X+B C Z3 q
+        square(2,8);            // (X+B)^2 A X+B C Z3 q
+        rm(4);                  // A (X+B)^2 C Z3 q
+        sub(2, 0, 8);           // (X+B)^2-A A (X+B)^2 C Z3 q
+        rm(4);                  // A (X+B)^2-A C Z3 q
+        sub(2, 4, 8);           // (X+B)^2-A-C A (X+B)^2-A C Z3 q
+        rm(4);                  // A D C Z3 q
+
+        // D = D+D
+        add(2,2, 8);            // D+D A D C Z3 q
+        rm(4);                  // A D C Z3 q
+
+        // E=A+A+A
+        add(0, 0, 8);           // 2A A D C Z3 q
+        add(0, 2, 10);          // 3A 2A A D C Z3 q
+        rm(4);                  // 2A 3A D C Z3 q
+        rm(0);                  // E D C Z3 q
+
+        // F=E^2
+        square(0, 8);           // F E D C Z3 q
+
+        // X3= F - 2*D  // Remove F
+        add(4, 4, 10);          // 2D F E D C Z3 q
+        sub(2, 0, 12);          // F-2D 2D F E D C Z3 q
+        rm(4);                  // 2D X3 E D C Z3 q
+        rm(0);                  // X3 E D C Z3 q
+
+        // Y3 = E * (D - X3) - 8 * C  // Remove D C  E
+
+        sub(4, 0, 10);          // D-X3 X3 E D C Z3 q
+        rm(6);                  // X3 E D-X3 C Z3 q
+        mul(2, 4, 10);          // E*(D-X3) X3 E D-X3 C Z3 q
+        rm(6);                  // X3 E E*(D-X3) C Z3 q
+        rm(2);                  // X3 E*(D-X3) C Z3 q
+        add(4, 4, 8);           // 2C X3 E*(D-X3) C Z3 q
+        rm(6);                  // X3 E*(D-X3) 2C Z3 q
+        add(4, 4, 8);           // 4C X3 E*(D-X3) 2C Z3 q
+        rm(6);                  // X3 E*(D-X3) 4C Z3 q
+        add(4, 4, 8);           // 8C X3 E*(D-X3) 4C Z3 q
+        rm(6);                  // X3 E*(D-X3) 8C Z3 q
+        sub(2, 4, 8);           // E*(D-X3)-8C X3 E*(D-X3) 8C Z3 q
+        rm(6);                  // X3 E*(D-X3) Y3 Z3 q
+        rm(2);                  // X3 Y3 Z3 q
+
+        C.label("enddouble");
+        C.returnCall();
+    }
+
+    function addPoint() {     // p, xR, xI,    yR, yI,   zR zI, q
+
+
+        C.dup(0);           // p p X2 Y2 Z2 q
+
+        C.push(savedP);
+        C.mstore();
+
+        C.iszero();         // X2 Y2 Z2 q
+        C.jumpi("endpadd");
+
+
+        C.dup(4);
+        C.iszero();
+        C.dup(6);
+        C.iszero();
+        C.and();
+        C.jumpi("returnP");   // X2 Y2 Z2 q
+
+
+
+        // lastZ3 = (Z2+1)^2 - Z2^2
+        add1(4, 6);         // Z2+1 X2 Y2 Z2 q
+        square(0, 8);       // (Z2+1)^2 Z2+1 X2 Y2 Z2 q
+        rm(2);              // (Z2+1)^2 X2 Y2 Z2 q
+        square(6, 8);       // Z2^2 (Z2+1)^2 X2 Y2 Z2 q
+
+
+        sub(2, 0, 10);      // (Z2+1)^2-Z2^2 Z2^2 (Z2+1)^2 X2 Y2 Z2 q
+
+        saveZ3();           // Z2^2 (Z2+1)^2 X2 Y2 Z2 q
+        rm(2);              // Z2^2 X2 Y2 Z2 q
+
+        // U2 = X2
+        // S2 = Y2          // Z2^2 U2 S2 Z2 q
+
+
+        // U1 = X1 * Z2^2
+        loadX();            // X1 Z2^2 U2 S2 Z2 q
+        mul(0, 2, 10);      // X1*Z2^2 X1 Z2^2 U2 S2 Z2 q
+        rm(2);              // X1*Z2^2 Z2^2 U2 S2 Z2 q
+
+
+        mul(2, 8, 10);      // Z2^3 U1 Z2^2 U2 S2 Z2 q
+        rm(4);              // U1 Z2^3 U2 S2 Z2 q
+        rm(8);              // Z2^3 U2 S2 U1 q
+
+        // S1 = Y1 * Z1^3
+        loadY();            // Y1 Z2^3 U2 S2 U1 q
+        mul(0, 2, 10);      // S1 Y1 Z2^3 U2 S2 U1 q
+        rm(4);              // Y1 S1 U2 S2 U1 q
+        rm(0);              // S1 U2 S2 U1 q
+
+        cmp(0, 4);          // c1 S1 U2 S2 U1 q
+        cmp(3, 7);          // c2 c1 S1 U2 S2 U1 q
+        C.and();            // c2&c1 S1 U2 S2 U1 q
+        C.jumpi("double1"); // S1 U2 S2 U1 q
+
+
+        // Returns the double
+
+        // H = U2-U1  // Remove U2
+        C.sub(4, 8, 10);    // H S1 U2 S2 U1 q
+        rm(4);              // S1 H S2 U1 q
+
+        // // r = 2 * (S2-S1)  // Remove S2
+        C.sub(4, 4, 8);     // S1-S2 S1 H S2 U1 q
+        rm(6);              // S1 H S1-S2 U1 q
+        C.add(4, 4, 8);     // 2*(S1-S2) S1 H S1-S2 U1 q
+        rm(6);              // S1 H r U1 q
+
+        // I = (2 * H)^2
+        C.add(2, 2, 8);     // 2*H S1 H r U1 q
+        C.square(0, 10);    // (2*H)^2 2*H S1 H r U1 q
+        rm(2);              // I S1 H r U1 q
+
+        // V = U1 * I
+        mul(8, 0, 10);      // V I S1 H r U1 q
+        rm(10);             // I S1 H r V q
+
+        // J = H * I // Remove I
+        mul(4, 0, 10);      // J I S1 H r V q
+        rm(2);              // J S1 H r V q
+
+        // X3 = r^2 - J - 2 * V
+
+        // S1J2 = (S1*J)*2  // Remove S1
+        mul(2, 0, 10);      // S1*J J S1 H r V q
+        rm(4);              // J S1*J H r V q
+        add(2,2, 10);       // (S1*J)*2 J S1*J H r V q
+        rm(4);              // J S1J2 H r V q
+
+        // X3 = r^2 - J - 2 * V
+        square(6, 10);      // r^2 J S1J2 H r V q
+        sub(0, 2, 12);      // r^2-J r^2 J S1J2 H r V q
+        rm(2);              // r^2-J J S1J2 H r V q
+        rm(2);              // r^2-J S1J2 H r V q
+        add(8, 8, 10);      // 2*V r^2-J S1J2 H r V q
+        sub(2, 0, 12);      // r^2-J-2*V 2*V r^2-J S1J2 H r V q
+        rm(4);              // 2*V  X3 S1J2 H r V q
+        rm(0);              // X3 S1J2 H r V q
+
+        // Y3 = r * (V-X3)-S1J2
+
+        sub(8, 0, 10);      // V-X3 X3 S1J2 H r V q
+        rm(10);             // X3 S1J2 H r V-X3 q
+        mul(6, 8, 10);      // r*(V-X3) X3 S1J2 H r V-X3 q
+        rm(8);              // X3 S1J2 H r*(V-X3) V-X3 q
+        rm(8);              // S1J2 H r*(V-X3) X3 q
+        sub(4, 0, 8);       // Y3 S1J2 H r*(V-X3) X3 q
+        rm(6);              // S1J2 H Y3 X3 q
+        rm(0);              // H Y3 X3 q
+
+        // Z3 = lastZ * H
+        loadZ3();           // lastZ3 H Y3 X3 q
+        mul(0, 2, 8);       // Z3 lastZ3 H Y3 X3 q
+        rm(4);              // lastZ3 Z3 Y3 X3 q
+        rm(0);              // Z3 Y3 X3 q
+
+        C.swap(1);
+        C.swap(5);
+        C.swap(1);
+        C.swap(4);          // X3 Y3 Z3 q
+
+        // returns the point in memory
+        C.label("returnP"); // X Y Z q
+        rm(0);
+        rm(0);
+        rm(0);
+        C.push(0);
+        C.push(1);
+        loadX();
+        loadY();
+        C.jump("endpadd");
+
+        C.label("double1"); // S1 U2 S2 U1 q
+        rm(0);
+        rm(0);
+        rm(0);
+        rm(0);
+        C.push(0);
+        C.push(1);
+        loadX();
+        loadY();
+        C.jump("double");
+
+        C.label("endpadd");
+        C.returnCall();
+
+        function loadX() {
+            C.push(savedP);
+            C.mload();                  // p
+            C.push(32);
+            C.mul();                    // P*32
+            C.push(VAR_POINTS+32);
+            C.add();                    // P*32+32
+            C.dup();                    // P*32+32 P*32+32
+            C.mload();                  // im P*32+32
+            C.swap(1);                  // P*32+32 im
+            C.push(0x20);               // 32 P*32+32 im
+            C.sub();                    // P*32 im
+            C.mload();                  // re im
+        }
+
+        function loadY() {
+            C.push(savedP);
+            C.mload();                  // p
+            C.push(32);
+            C.mul();                    // P*32
+            C.push(VAR_POINTS+32*3);
+            C.add();                    // P*32+32
+            C.dup();                    // P*32+32 P*32+32
+            C.mload();                  // im P*32+32
+            C.swap(1);                  // P*32+32 im
+            C.push(0x20);               // 32 P*32+32 im
+            C.sub();                    // P*32 im
+            C.mload();                  // re im
+        }
+
+        function loadZ3() {
+            C.push(savedZ3+32);
+            C.mload();                  // p
+            C.push(savedZ3);
+            C.mload();
+        }
+
+        function saveZ3() {
+            C.push(savedZ3);
+            C.mstore();
+            C.push(savedZ3+32);
+            C.mstore();
+        }
+    }
+
+    function affine() { // X Y Z q
+        // If Z2=0 return 0
+        C.label("affine");
+        C.dup(4);
+        C.dup(5 + 1);
+        C.or();
+        C.jumpi("notZero");     // X Y Z q
+        rm(0);
+        rm(0);
+        C.push(0);
+        C.push(0);
+
+        C.jmp("endAffine");
+        C.label("notZero");
+
+        inverse2(4,6);          // Z_inv X Y Z q
+        square(2, 8);           // Z2_inv Z_inv X Y Z q
+        mul(0, 2, 10);          // Z3_inv Z2_inv Z_inv X Y Z q
+        rm(4);                  // Z2_inv Z3_inv X Y Z q
+        C.push(1);
+        C.push(0);              // 1 Z2_inv Z3_inv X Y Z q
+        rm(10);                 // Z2_inv Z3_inv X Y 1 q
+        mul(2, 6, 10);          // YI Z2_inv Z3_inv X Y 1 q
+        rm(8);                  // Z2_inv Z3_inv X YI 1 q
+        mul(0, 4, 10);          // XI Z2_inv Z3_inv X YI 1 q
+        rm(6);                  // Z2_inv Z3_inv XI YI 1 q
+        rm(0);                  // Z3_inv XI YI 1 q
+        rm(0);                  // XI YI 1 q
+        C.label("endAffine");
+        C.returnCall();
+    }
+
+    function inverse2(a, q) {
+        C.dup(q);           // q
+        C.dup(q + 1);       // q q
+        C.push(2);          // 2 q q
+        C.sub();            // q-2 q
+        C.dup(q + 2);       // q q-2 q
+        C.dup(q + 3);       // q q q-2 q
+        C.dup(a + 4);       // ar q q q-2 q
+        C.dup(a + 5);       // ar ar q q q-2 q
+        C.mulmod();         // t0 q q-2 q
+
+        C.dup(q   + 4);     // q t0 q q-2 q
+        C.dup(a+1 + 5);     // ai q t0 q q-2 q
+        C.dup(a+1 + 6);     // ai ai q t0 q q-2 q
+        C.mulmod();         // t1 t0 q q-2 q
+
+        C.addmod();         // t2 q-2 q
+        C.expmod();         // t3
+
+        C.dup(q + 1);       // q t3
+        C.dup(q + 2);       // q q t3
+        C.dup(q + 3);       // q q q t3
+        C.dup(1);           // t3 q q q t3
+        C.sub();            // -t3 q q t3
+        C.dup(a+1 + 3);     // ai -t3 q q t3
+        C.mulmod();         // ii q t3
+        C.swap(2);          // t3 q ii
+        C.dup(a + 3);       // ar t3 q ii
+        C.mulmod();         // ir ii
+    }
+
+    function storeVals() {
+        C.push(VAR_POINTS);                 // p
+        for (let i=0; i<NPOINTS; i++) {
+            const MP = G2.affine(G2.mulScalar(P, bigInt(i)));
+            for (let j=0; j<2; j++) {
+                for (let k=0; k<2; k++) {
+                    C.push(toHex256(MP[j][k]));     // MP[0][0] p
+                    C.dup(1);                       // p MP[0][0] p
+                    C.mstore();                     // p
+                    C.push(32);                     // 32 p
+                    C.add();                        // p+32
+                }
+            }
+        }
+    }
+
+}
+
+module.exports.abi = [
+    {
+        "constant": true,
+        "inputs": [
+            {
+                "name": "escalar",
+                "type": "uint256"
+            }
+        ],
+        "name": "mulexp",
+        "outputs": [
+            {
+                "name": "",
+                "type": "uint256"
+            },
+            {
+                "name": "",
+                "type": "uint256"
+            }
+        ],
+        "payable": false,
+        "stateMutability": "pure",
+        "type": "function"
+    }
+];
+
+module.exports.createCode = createCode;
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc7.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc7.js
@@ -0,0 +1,64 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+const Web3Utils = require("web3-utils");
+const F = bn128.Fr;
+
+const SEED = "mimc";
+const NROUNDS = 91;
+
+exports.getIV = (seed) => {
+    if (typeof seed === "undefined") seed = SEED;
+    const c = Web3Utils.keccak256(seed+"_iv");
+    const cn = bigInt(Web3Utils.toBN(c).toString());
+    const iv = cn.mod(F.q);
+    return iv;
+};
+
+exports.getConstants = (seed, nRounds) => {
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRounds === "undefined") nRounds = NROUNDS;
+    const cts = new Array(nRounds);
+    let c = Web3Utils.keccak256(SEED);
+    for (let i=1; i<nRounds; i++) {
+        c = Web3Utils.keccak256(c);
+
+        const n1 = Web3Utils.toBN(c).mod(Web3Utils.toBN(F.q.toString()));
+        const c2 = Web3Utils.padLeft(Web3Utils.toHex(n1), 64);
+        cts[i] = bigInt(Web3Utils.toBN(c2).toString());
+    }
+    cts[0] = bigInt(0);
+    return cts;
+};
+
+const cts = exports.getConstants(SEED, 91);
+
+exports.hash =  (_x_in, _k) =>{
+    const x_in = bigInt(_x_in);
+    const k = bigInt(_k);
+    let r;
+    for (let i=0; i<NROUNDS; i++) {
+        const c = cts[i];
+        const t = (i==0) ? F.add(x_in, k) : F.add(F.add(r, k), c);
+        r = F.exp(t, 7);
+    }
+    return F.affine(F.add(r, k));
+};
+
+exports.multiHash = (arr, key) => {
+    let r;
+    if (typeof(key) === "undefined") {
+        r = F.zero;
+    } else {
+        r = key;
+    }
+    for (let i=0; i<arr.length; i++) {
+        r = F.add(
+            F.add(
+                r,
+                arr[i]
+            ),
+            exports.hash(bigInt(arr[i]), r)
+        );
+    }
+    return F.affine(r);
+};
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_gencontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_gencontract.js
@@ -0,0 +1,114 @@
+// Copyright (c) 2018 Jordi Baylina
+// License: LGPL-3.0+
+//
+
+const Web3Utils = require("web3-utils");
+
+const Contract = require("./evmasm");
+
+function createCode(seed, n) {
+
+    let ci = Web3Utils.keccak256(seed);
+
+    const C = new Contract();
+
+    C.push(0x44);
+    C.push("0x00");
+    C.push("0x00");
+    C.calldatacopy();
+    C.push("0x0100000000000000000000000000000000000000000000000000000000");
+    C.push("0x00");
+    C.mload();
+    C.div();
+    C.push("0xd15ca109"); // MiMCpe7(uint256,uint256)
+//    C.push("0x8c42199e"); // MiMCpe7(uint256,uint256,uint256)
+    C.eq();
+    C.jmpi("start");
+    C.invalid();
+
+    C.label("start");
+    C.push("0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001");  // q
+    C.push("0x24");
+    C.mload();          // k q
+
+
+    C.dup(1);           // q k q
+    C.dup(0);           // q q k q
+    C.push("0x04");
+    C.mload();          // x q q k q
+    C.dup(3);           // k x q q k q
+    C.addmod();         // t=x+k q k q
+    C.dup(1);           // q t q k q
+    C.dup(0);           // q q t q k q
+    C.dup(2);           // t q q t q k q
+    C.dup(0);           // t t q q t q k q
+    C.mulmod();         // a=t^2 q t q k q
+    C.dup(1);           // q a q t q k q
+    C.dup(1);           // a q a q t q k q
+    C.dup(0);           // a a q a q t q k q
+    C.mulmod();         // b=t^4 a q t q k q
+    C.mulmod();         // c=t^6 t q k q
+    C.mulmod();         // r=t^7 k q
+
+    for (let i=0; i<n-1; i++) {
+        ci = Web3Utils.keccak256(ci);
+        C.dup(2);       // q r k q
+        C.dup(0);       // q q r k q
+        C.dup(0);       // q q q r k q
+        C.swap(3);      // r q q q k q
+        C.push(ci);     // c r q q k q
+        C.addmod();     // s=c+r q q k q
+        C.dup(3);       // k s q q k q
+        C.addmod();     // t=s+k q k q
+        C.dup(1);       // q t q k q
+        C.dup(0);       // q q t q k q
+        C.dup(2);       // t q q t q k q
+        C.dup(0);       // t t q q t q k q
+        C.mulmod();     // a=t^2 q t q k q
+        C.dup(1);       // q a q t q k q
+        C.dup(1);       // a q a q t q k q
+        C.dup(0);       // a a q a q t q k q
+        C.mulmod();     // b=t^4 a q t q k q
+        C.mulmod();     // c=t^6 t q k q
+        C.mulmod();     // r=t^7 k q
+    }
+
+    C.addmod();     // res=t^7+k
+    C.push("0x00");
+    C.mstore();     // Save it to pos 0;
+    C.push("0x20");
+    C.push("0x00");
+    C.return();
+
+    return C.createTxData();
+}
+
+module.exports.abi = [
+    {
+        "constant": true,
+        "inputs": [
+            {
+                "name": "in_x",
+                "type": "uint256"
+            },
+            {
+                "name": "in_k",
+                "type": "uint256"
+            }
+        ],
+        "name": "MiMCpe7",
+        "outputs": [
+            {
+                "name": "out_x",
+                "type": "uint256"
+            }
+        ],
+        "payable": false,
+        "stateMutability": "pure",
+        "type": "function"
+    }
+];
+
+module.exports.createCode = createCode;
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_print_iv.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_print_iv.js
@@ -0,0 +1,3 @@
+const mimc7 = require("./mimc7.js");
+
+console.log("IV: "+mimc7.getIV().toString());
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_printconstants.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_printconstants.js
@@ -0,0 +1,13 @@
+const mimc7 = require("./mimc7.js");
+
+const nRounds = 91;
+let S = "[\n";
+const cts = mimc7.getConstants();
+for (let i=0; i<nRounds; i++) {
+    S = S + cts[i].toString();
+    if (i<nRounds-1) S = S + ",";
+    S=S+"\n";
+}
+S = S + "]\n";
+
+console.log(S);
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_printcontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimc_printcontract.js
@@ -0,0 +1,13 @@
+const mimcGenContract = require("./mimc_gencontract");
+
+const SEED = "mimc";
+
+let nRounds;
+if (typeof process.argv[2] != "undefined") {
+    nRounds = parseInt(process.argv[2]);
+} else {
+    nRounds = 91;
+}
+
+console.log(mimcGenContract.createCode(SEED, nRounds));
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge.js
@@ -0,0 +1,86 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+const Web3Utils = require("web3-utils");
+const F = bn128.Fr;
+
+const SEED = "mimcsponge";
+const NROUNDS = 220;
+
+exports.getIV = (seed) => {
+    if (typeof seed === "undefined") seed = SEED;
+    const c = Web3Utils.keccak256(seed+"_iv");
+    const cn = bigInt(Web3Utils.toBN(c).toString());
+    const iv = cn.mod(F.q);
+    return iv;
+};
+
+exports.getConstants = (seed, nRounds) => {
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRounds === "undefined") nRounds = NROUNDS;
+    const cts = new Array(nRounds);
+    let c = Web3Utils.keccak256(SEED);
+    for (let i=1; i<nRounds; i++) {
+        c = Web3Utils.keccak256(c);
+
+        const n1 = Web3Utils.toBN(c).mod(Web3Utils.toBN(F.q.toString()));
+        const c2 = Web3Utils.padLeft(Web3Utils.toHex(n1), 64);
+        cts[i] = bigInt(Web3Utils.toBN(c2).toString());
+    }
+    cts[0] = bigInt(0);
+    cts[cts.length - 1] = bigInt(0);
+    return cts;
+};
+
+const cts = exports.getConstants(SEED, NROUNDS);
+
+exports.hash = (_xL_in, _xR_in, _k) =>{
+    let xL = bigInt(_xL_in);
+    let xR = bigInt(_xR_in);
+    const k = bigInt(_k);
+    for (let i=0; i<NROUNDS; i++) {
+        const c = cts[i];
+        const t = (i==0) ? F.add(xL, k) : F.add(F.add(xL, k), c);
+        const xR_tmp = bigInt(xR);
+        if (i < (NROUNDS - 1)) {
+          xR = xL;
+          xL = F.add(xR_tmp, F.exp(t, 5));
+        } else {
+          xR = F.add(xR_tmp, F.exp(t, 5));
+        }
+    }
+    return {
+      xL: F.affine(xL),
+      xR: F.affine(xR),
+    };
+};
+
+exports.multiHash = (arr, key, numOutputs) => {
+    if (typeof(numOutputs) === "undefined") {
+      numOutputs = 1;
+    }
+    if (typeof(key) === "undefined") {
+        key = F.zero;
+    }
+
+    let R = F.zero;
+    let C = F.zero;
+
+    for (let i=0; i<arr.length; i++) {
+      R = F.add(R, bigInt(arr[i]));
+      const S = exports.hash(R, C, key);
+      R = S.xL;
+      C = S.xR;
+    }
+    let outputs = [R];
+    for (let i=1; i < numOutputs; i++) {
+      const S = exports.hash(R, C, key);
+      R = S.xL;
+      C = S.xR;
+      outputs.push(R);
+    }
+    if (numOutputs == 1) {
+      return F.affine(outputs[0]);
+    } else {
+      return outputs.map(x => F.affine(x));
+    }
+};
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_gencontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_gencontract.js
@@ -0,0 +1,128 @@
+// Copyright (c) 2018 Jordi Baylina
+// License: LGPL-3.0+
+//
+
+const Web3Utils = require("web3-utils");
+
+const Contract = require("./evmasm");
+
+function createCode(seed, n) {
+
+    let ci = Web3Utils.keccak256(seed);
+
+    const C = new Contract();
+
+    C.push(0x64);
+    C.push("0x00");
+    C.push("0x00");
+    C.calldatacopy();
+    C.push("0x0100000000000000000000000000000000000000000000000000000000");
+    C.push("0x00");
+    C.mload();
+    C.div();
+    C.push("0x3f1a1187"); // MiMCSponge(uint256,uint256,uint256)
+    C.eq();
+    C.jmpi("start");
+    C.invalid();
+
+    C.label("start");
+    C.push("0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001");  // q
+    C.push("0x44");
+    C.mload();          // k q
+    C.push("0x04");
+    C.mload();          // xL k q
+    C.dup(2);           // q xL k q
+    C.push("0x24");
+    C.mload();          // xR q xL k q
+    C.dup(1);           // q xR q xL k q
+    C.dup(0);           // q q xR q xL k q
+    C.dup(4);           // xL q q xR q xL k q
+    C.dup(6);           // k xL q q xR q xL k q
+    C.addmod();         // t=k+xL q xR q xL k q
+    C.dup(1);           // q t q xR q xL k q
+    C.dup(0);           // q q t q xR q xL k q
+    C.dup(2);           // t q q t q xR q xL k q
+    C.dup(0);           // t t q q t q xR q xL k q
+    C.mulmod();         // b=t^2 q t q xR q xL k q
+    C.dup(0);           // b b q t q xR q xL k q
+    C.mulmod();         // c=t^4 t q xR q xL k q
+    C.mulmod();         // d=t^5 xR q xL k q
+    C.addmod();         // e=t^5+xR xL k q (for next round: xL xR k q)
+
+    for (let i=0; i<n-1; i++) {
+        if (i < n-2) {
+          ci = Web3Utils.keccak256(ci);
+        } else {
+          ci = "0x00";
+        }
+        C.swap(1);      // xR xL k q
+        C.dup(3);       // q xR xL k q
+        C.dup(3);       // k q xR xL k q
+        C.dup(1);       // q k q xR xL k q
+        C.dup(4);       // xL q k q xR xL k q
+        C.push(ci);     // ci xL q k q xR xL k q
+        C.addmod();     // a=ci+xL k q xR xL k q
+        C.addmod();     // t=a+k xR xL k q
+        C.dup(4);       // q t xR xL k q
+        C.swap(1);      // t q xR xL k q
+        C.dup(1);       // q t q xR xL k q
+        C.dup(0);       // q q t q xR xL k q
+        C.dup(2);       // t q q t q xR xL k q
+        C.dup(0);       // t t q q t q xR xL k q
+        C.mulmod();     // b=t^2 q t q xR xL k q
+        C.dup(0);       // b b q t q xR xL k q
+        C.mulmod();     // c=t^4 t q xR xL k q
+        C.mulmod();     // d=t^5 xR xL k q
+        C.dup(4);       // q d xR xL k q
+        C.swap(2);      // xR d q xL k q
+        C.addmod();     // e=t^5+xR xL k q (for next round: xL xR k q)
+    }
+
+    C.push("0x20");
+    C.mstore();     // Save it to pos 0;
+    C.push("0x00");
+    C.mstore();     // Save it to pos 1;
+    C.push("0x40");
+    C.push("0x00");
+    C.return();
+
+    return C.createTxData();
+}
+
+module.exports.abi = [
+    {
+        "constant": true,
+        "inputs": [
+            {
+                "name": "xL_in",
+                "type": "uint256"
+            },
+            {
+                "name": "xR_in",
+                "type": "uint256"
+            },
+            {
+                "name": "k",
+                "type": "uint256"
+            }
+        ],
+        "name": "MiMCSponge",
+        "outputs": [
+            {
+                "name": "xL",
+                "type": "uint256"
+            },
+            {
+                "name": "xR",
+                "type": "uint256"
+            }
+        ],
+        "payable": false,
+        "stateMutability": "pure",
+        "type": "function"
+    }
+];
+
+module.exports.createCode = createCode;
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_printconstants.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_printconstants.js
@@ -0,0 +1,13 @@
+const mimcsponge = require("./mimcsponge.js");
+
+const nRounds = 220;
+let S = "[\n";
+const cts = mimcsponge.getConstants();
+for (let i=0; i<nRounds; i++) {
+    S = S + cts[i].toString();
+    if (i<nRounds-1) S = S + ",";
+    S=S+"\n";
+}
+S = S + "]\n";
+
+console.log(S);
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_printcontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/mimcsponge_printcontract.js
@@ -0,0 +1,13 @@
+const mimcGenContract = require("./mimcsponge_gencontract");
+
+const SEED = "mimcsponge";
+
+let nRounds;
+if (typeof process.argv[2] != "undefined") {
+    nRounds = parseInt(process.argv[2]);
+} else {
+    nRounds = 220;
+}
+
+console.log(mimcGenContract.createCode(SEED, nRounds));
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/pedersenHash.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/pedersenHash.js
@@ -0,0 +1,111 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+const babyJub = require("./babyjub");
+const createBlakeHash = require("blake-hash");
+
+const GENPOINT_PREFIX = "PedersenGenerator";
+const windowSize = 4;
+const nWindowsPerSegment = 50;
+
+exports.hash = pedersenHash;
+exports.getBasePoint = getBasePoint;
+
+function pedersenHash(msg) {
+    const bitsPerSegment = windowSize*nWindowsPerSegment;
+    const bits = buffer2bits(msg);
+
+    const nSegments = Math.floor((bits.length - 1)/(windowSize*nWindowsPerSegment)) +1;
+
+    let accP = [bigInt.zero,bigInt.one];
+
+    for (let s=0; s<nSegments; s++) {
+        let nWindows;
+        if (s == nSegments-1) {
+            nWindows = Math.floor(((bits.length - (nSegments - 1)*bitsPerSegment) - 1) / windowSize) +1;
+        } else {
+            nWindows = nWindowsPerSegment;
+        }
+        let escalar = bigInt.zero;
+        let exp = bigInt.one;
+        for (let w=0; w<nWindows; w++) {
+            let o = s*bitsPerSegment + w*windowSize;
+            let acc = bigInt.one;
+            for (let b=0; ((b<windowSize-1)&&(o<bits.length)) ; b++) {
+                if (bits[o]) {
+                    acc = acc.add( bigInt.one.shl(b) );
+                }
+                o++;
+            }
+            if (o<bits.length) {
+                if (bits[o]) {
+                    acc = acc.neg();
+                }
+                o++;
+            }
+            escalar = escalar.add(acc.mul(exp));
+            exp = exp.shl(windowSize+1);
+        }
+
+        if (escalar.lesser(bigInt.zero)) {
+            escalar = babyJub.subOrder.add(escalar);
+        }
+
+        accP = babyJub.addPoint(accP, babyJub.mulPointEscalar(getBasePoint(s), escalar));
+    }
+
+    return babyJub.packPoint(accP);
+}
+
+let bases = [];
+
+function getBasePoint(pointIdx) {
+    if (pointIdx<bases.length) return bases[pointIdx];
+    let p= null;
+    let tryIdx = 0;
+    while (p==null) {
+        const S = GENPOINT_PREFIX + "_" + padLeftZeros(pointIdx, 32) + "_" + padLeftZeros(tryIdx, 32);
+        const h = createBlakeHash("blake256").update(S).digest();
+        h[31] = h[31] & 0xBF;  // Set 255th bit to 0 (256th is the signal and 254th is the last possible bit to 1)
+        p = babyJub.unpackPoint(h);
+        tryIdx++;
+    }
+
+    const p8 = babyJub.mulPointEscalar(p, 8);
+
+    if (!babyJub.inSubgroup(p8)) {
+        throw new Error("Point not in curve");
+    }
+
+    bases[pointIdx] = p8;
+    return p8;
+}
+
+function padLeftZeros(idx, n) {
+    let sidx = "" + idx;
+    while (sidx.length<n) sidx = "0"+sidx;
+    return sidx;
+}
+
+/*
+Input a buffer
+Returns an array of booleans. 0 is LSB of first byte and so on.
+ */
+function buffer2bits(buff) {
+    const res = new Array(buff.length*8);
+    for (let i=0; i<buff.length; i++) {
+        const b = buff[i];
+        res[i*8] = b & 0x01;
+        res[i*8+1] = b & 0x02;
+        res[i*8+2] = b & 0x04;
+        res[i*8+3] = b & 0x08;
+        res[i*8+4] = b & 0x10;
+        res[i*8+5] = b & 0x20;
+        res[i*8+6] = b & 0x40;
+        res[i*8+7] = b & 0x80;
+    }
+    return res;
+}
+
+
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/pedersen_printbases.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/pedersen_printbases.js
@@ -0,0 +1,13 @@
+const pedersenHash = require("./pedersenHash.js");
+
+let nBases;
+if (typeof process.argv[2] != "undefined") {
+    nBases = parseInt(process.argv[2]);
+} else {
+    nBases = 5;
+}
+
+for (let i=0; i < nBases; i++) {
+    const p = pedersenHash.getBasePoint(i);
+    console.log(`[${p[0]},${p[1]}]`);
+}
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon.js
@@ -0,0 +1,116 @@
+const bn128 = require("snarkjs").bn128;
+const bigInt = require("snarkjs").bigInt;
+const blake2b = require('blake2b');
+const assert = require("assert");
+const F = bn128.Fr;
+
+const SEED = "poseidon";
+const NROUNDSF = 8;
+const NROUNDSP = 57;
+const T = 6;
+
+function getPseudoRandom(seed, n) {
+    const res = [];
+    let input = Buffer.from(seed);
+    let h = blake2b(32).update(input).digest()
+    while (res.length<n) {
+        const n = F.affine(bigInt.leBuff2int(h));
+        res.push(n);
+        h = blake2b(32).update(h).digest()
+    }
+
+    return res;
+}
+
+function allDifferent(v) {
+    for (let i=0; i<v.length; i++) {
+        if (v[i].isZero()) return false;
+        for (let j=i+1; j<v.length; j++) {
+            if (v[i].equals(v[j])) return false;
+        }
+    }
+    return true;
+}
+
+exports.getMatrix = (t, seed, nRounds) => {
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRounds === "undefined") nRounds = NROUNDSF + NROUNDSP;
+    if (typeof t === "undefined") t = T;
+    let nonce = "0000";
+    let cmatrix = getPseudoRandom(seed+"_matrix_"+nonce, t*2);
+    while (!allDifferent(cmatrix)) {
+        nonce = (Number(nonce)+1)+"";
+        while(nonce.length<4) nonce = "0"+nonce;
+        cmatrix = getPseudoRandom(seed+"_matrix_"+nonce, t*2);
+    }
+
+    const M = new Array(t);
+    for (let i=0; i<t; i++) {
+        M[i] = new Array(t);
+        for (let j=0; j<t; j++) {
+            M[i][j] = F.affine(F.inverse(F.sub(cmatrix[i], cmatrix[t+j])));
+        }
+    }
+    return M;
+};
+
+exports.getConstants = (t, seed, nRounds) => {
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRounds === "undefined") nRounds = NROUNDSF + NROUNDSP;
+    if (typeof t === "undefined") t = T;
+    const cts = getPseudoRandom(seed+"_constants", nRounds);
+    return cts;
+};
+
+function ark(state, c) {
+    for (let j=0; j<state.length; j++ ) {
+        state[j] = F.add(state[j], c);
+    }
+}
+
+function sigma(a) {
+    return F.mul(a, F.square(F.square(a,a)));
+}
+
+function mix(state, M) {
+    const newState = new Array(state.length);
+    for (let i=0; i<state.length; i++) {
+        newState[i] = F.zero;
+        for (let j=0; j<state.length; j++) {
+            newState[i] = F.add(newState[i], F.mul(M[i][j], state[j]) );
+        }
+    }
+    for (let i=0; i<state.length; i++) state[i] = newState[i];
+}
+
+exports.createHash = (t, nRoundsF, nRoundsP, seed) => {
+
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRoundsF === "undefined") nRoundsF = NROUNDSF;
+    if (typeof nRoundsP === "undefined") nRoundsP = NROUNDSP;
+    if (typeof t === "undefined") t = T;
+
+    assert(nRoundsF % 2 == 0);
+    const C = exports.getConstants(t, seed, nRoundsF + nRoundsP);
+    const M = exports.getMatrix(t, seed, nRoundsF + nRoundsP);
+    return function(inputs) {
+        let state = [];
+        assert(inputs.length < t);
+        assert(inputs.length > 0);
+        for (let i=0; i<inputs.length; i++) state[i] = bigInt(inputs[i]);
+        for (let i=inputs.length; i<t; i++) state[i] = F.zero;
+
+        for (let i=0; i< nRoundsF + nRoundsP; i++) {
+            ark(state, C[i]);
+            if ((i<nRoundsF/2) || (i >= nRoundsF/2 + nRoundsP)) {
+                for (let j=0; j<t; j++) state[j] = sigma(state[j]);
+            } else {
+                state[0] = sigma(state[0]);
+            }
+            mix(state, M);
+        }
+        return F.affine(state[0]);
+    };
+};
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_gencontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_gencontract.js
@@ -0,0 +1,180 @@
+// Copyright (c) 2018 Jordi Baylina
+// License: LGPL-3.0+
+//
+
+const Poseidon = require("./poseidon.js");
+
+const Contract = require("./evmasm");
+
+const SEED = "poseidon";
+const NROUNDSF = 8;
+const NROUNDSP = 57;
+const T = 6;
+
+function toHex256(a) {
+    let S = a.toString(16);
+    while (S.length < 64) S="0"+S;
+    return "0x" + S;
+}
+
+function createCode(t, nRoundsF, nRoundsP, seed) {
+    if (typeof seed === "undefined") seed = SEED;
+    if (typeof nRoundsF === "undefined") nRoundsF = NROUNDSF;
+    if (typeof nRoundsP === "undefined") nRoundsP = NROUNDSP;
+    if (typeof t === "undefined") t = T;
+
+    const K = Poseidon.getConstants(t, seed, nRoundsP + nRoundsF);
+    const M = Poseidon.getMatrix(t, seed, nRoundsP + nRoundsF);
+
+    const C = new Contract();
+
+    function saveM() {
+        for (let i=0; i<t; i++) {
+            for (let j=0; j<t; j++) {
+                C.push(toHex256(M[i][j]));
+                C.push((1+i*t+j)*32);
+                C.mstore();
+            }
+        }
+    }
+
+    function ark(r) {
+        C.push(toHex256(K[r])); // K, st, q
+        for (let i=0; i<t; i++) {
+            C.dup(1+t); // q, K, st, q
+            C.dup(1);   // K, q, K, st, q
+            C.dup(3+i); // st[i], K, q, K, st, q
+            C.addmod(); // newSt[i], K, st, q
+            C.swap(2 + i); // xx, K, st, q
+            C.pop();
+        }
+        C.pop();
+    }
+
+    function sigma(p) {
+        // sq, q
+        C.dup(t);   // q, st, q
+        C.dup(1+p); // st[p] , q , st, q
+        C.dup(1);   // q, st[p] , q , st, q
+        C.dup(0);   // q, q, st[p] , q , st, q
+        C.dup(2);   // st[p] , q, q, st[p] , q , st, q
+        C.dup(0);   // st[p] , st[p] , q, q, st[p] , q , st, q
+        C.mulmod(); // st2[p], q, st[p] , q , st, q
+        C.dup(0);   // st2[p], st2[p], q, st[p] , q , st, q
+        C.mulmod(); // st4[p], st[p] , q , st, q
+        C.mulmod(); // st5[p], st, q
+        C.swap(1+p);
+        C.pop();      // newst, q
+    }
+
+    function mix() {
+        C.label("mix");
+        for (let i=0; i<t; i++) {
+            for (let j=0; j<t; j++) {
+                if (j==0) {
+                    C.dup(i+t);      // q, newSt, oldSt, q
+                    C.push((1+i*t+j)*32);
+                    C.mload();      // M, q, newSt, oldSt, q
+                    C.dup(2+i+j);    // oldSt[j], M, q, newSt, oldSt, q
+                    C.mulmod();      // acc, newSt, oldSt, q
+                } else {
+                    C.dup(1+i+t);    // q, acc, newSt, oldSt, q
+                    C.push((1+i*t+j)*32);
+                    C.mload();      // M, q, acc, newSt, oldSt, q
+                    C.dup(3+i+j);    // oldSt[j], M, q, acc, newSt, oldSt, q
+                    C.mulmod();      // aux, acc, newSt, oldSt, q
+                    C.dup(2+i+t);    // q, aux, acc, newSt, oldSt, q
+                    C.swap(2);       // acc, aux, q, newSt, oldSt, q
+                    C.addmod();      // acc, newSt, oldSt, q
+                }
+            }
+        }
+        for (let i=0; i<t; i++) {
+            C.swap((t -i) + (t -i-1));
+            C.pop();
+        }
+        C.push(0);
+        C.mload();
+        C.jmp();
+    }
+
+
+    // Check selector
+    C.push("0x0100000000000000000000000000000000000000000000000000000000");
+    C.push(0);
+    C.calldataload();
+    C.div();
+    C.push("0xc4420fb4"); // poseidon(uint256[])
+    C.eq();
+    C.jmpi("start");
+    C.invalid();
+
+    C.label("start");
+
+    saveM();
+
+    C.push("0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001");  // q
+
+    // Load 6 values from the call data.
+    // The function has a single array param param
+    // [Selector (4)] [Pointer (32)][Length (32)] [data1 (32)] ....
+    // We ignore the pointer and the length and just load 6 values to the state
+    // (Stack positions 0-5) If the array is shorter, we just set zeros.
+    for (let i=0; i<t; i++) {
+        C.push(0x44+(0x20*(5-i)));
+        C.calldataload();
+    }
+
+    for (let i=0; i<nRoundsF+nRoundsP; i++) {
+        ark(i);
+        if ((i<nRoundsF/2) || (i>=nRoundsP+nRoundsF/2)) {
+            for (let j=0; j<t; j++) {
+                sigma(j);
+            }
+        } else {
+            sigma(0);
+        }
+        const strLabel = "aferMix"+i;
+        C._pushLabel(strLabel);
+        C.push(0);
+        C.mstore();
+        C.jmp("mix");
+        C.label(strLabel);
+    }
+
+    C.push("0x00");
+    C.mstore();     // Save it to pos 0;
+    C.push("0x20");
+    C.push("0x00");
+    C.return();
+
+    mix();
+
+    return C.createTxData();
+}
+
+module.exports.abi = [
+    {
+        "constant": true,
+        "inputs": [
+            {
+                "name": "input",
+                "type": "uint256[]"
+            }
+        ],
+        "name": "poseidon",
+        "outputs": [
+            {
+                "name": "",
+                "type": "uint256"
+            }
+        ],
+        "payable": false,
+        "stateMutability": "pure",
+        "type": "function"
+    }
+];
+
+module.exports.createCode = createCode;
+
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printconstants.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printconstants.js
@@ -0,0 +1,16 @@
+
+
+const Poseidon = require("./poseidon.js");
+
+const C = Poseidon.getConstants();
+
+let S = "[\n";
+
+for (let i=0; i<C.length; i++) {
+    S = S + "    " + C[i].toString();
+    if (i<C.length-1) S = S + ",";
+    S = S + "\n";
+}
+S=S+ "]\n";
+
+console.log(S);
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printcontract.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printcontract.js
@@ -0,0 +1,5 @@
+const poseidonGenContract = require("./poseidon_gencontract");
+
+
+console.log(poseidonGenContract.createCode(6, 8, 57));
+
--- a/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printmatrix.js
+++ b/zkrsa/circom-rsa-verify/circom-bigint/circomlib/src/poseidon_printmatrix.js
@@ -0,0 +1,22 @@
+
+
+const Poseidon = require("./poseidon.js");
+
+const M = Poseidon.getMatrix();
+
+let S = "[\n    ";
+
+for (let i=0; i<M.length; i++) {
+    const LC = M[i];
+    S = S + "[\n";
+    for (let j=0; j<LC.length; j++) {
+        S = S + "        " + M[i][j].toString();
+        if (j<LC.length-1) S = S + ",";
+        S = S + "\n";
+    }
+    S = S + "    ]";
+    if (i<M.length-1) S = S + ",";
+}
+S=S+ "\n]\n";
+
+console.log(S);
--- a/Show More
+++ b/Show More