added c++ example Poseidon-hash

examples/c++/Poseidon-hash/CMakeLists.txt

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+cmake_minimum_required(VERSION 3.18)
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CUDA_STANDARD 17)
+set(CMAKE_CUDA_STANDARD_REQUIRED TRUE)
+set(CMAKE_CXX_STANDARD_REQUIRED TRUE)
+if (${CMAKE_VERSION} VERSION_LESS "3.24.0")
+    set(CMAKE_CUDA_ARCHITECTURES ${CUDA_ARCH})
+else()
+    set(CMAKE_CUDA_ARCHITECTURES native) # on 3.24+, on earlier it is ignored, and the target is not passed
+endif ()
+project(icicle LANGUAGES CUDA CXX)
+
+set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} --expt-relaxed-constexpr")
+set(CMAKE_CUDA_FLAGS_RELEASE "")
+set(CMAKE_CUDA_FLAGS_DEBUG "${CMAKE_CUDA_FLAGS_DEBUG} -g -G -O0")
+# change the path to your Icicle location
+include_directories("../../../icicle")
+add_executable(
+  example
+  example.cu
+)
+
+find_library(NVML_LIBRARY nvidia-ml PATHS /usr/local/cuda-12.0/targets/x86_64-linux/lib/stubs/ )
+target_link_libraries(example ${NVML_LIBRARY})
+set_target_properties(example PROPERTIES CUDA_SEPARABLE_COMPILATION ON)

examples/c++/Poseidon-hash/README.md

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+# Icicle example: build a Merkle tree using Poseidon hash
+
+## Best-Practices
+
+We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
+
+## Key-Takeaway
+
+`Icicle` provides CUDA C++ template `poseidon_hash` to accelerate the popular [Poseidon hash function](https://www.poseidon-hash.info/).
+
+## Concise Usage Explanation
+
+```c++
+#include "appUtils/poseidon/poseidon.cu"
+...
+poseidon_hash<scalar_t, arity+1>(input, output, n, constants, config);
+```
+
+**Parameters:**
+
+- **`scalar_t`:** a scalar field of the selected curve. Currently only `BLS12-381`.
+You can think of field's elements as 32-byte integers modulo `p`, where `p` is a prime number, specific to this field.
+
+- **arity:** number of elements in a hashed block.
+
+- **n:** number of blocks we hash in parallel.
+
+- **input, output:** `scalar_t` arrays of size $arity*n$ and $n$ respectively.
+
+- **constants:** are defined as below
+
+```c++
+device_context::DeviceContext ctx= device_context::get_default_device_context();
+PoseidonConstants<scalar_t> constants;
+init_optimized_poseidon_constants<scalar_t>(ctx, &constants);
+```
+
+## What's in the example
+
+1. Define the size of the example: the height of the full binary Merkle tree. 
+2. Hash blocks in parallel. The tree width determines the number of blocks to hash.
+3. Build a Merkle tree from the hashes.
+4. Use the tree to generate a membership proof for one of computed hashes.
+5. Validate the hash membership.
+6. Tamper the hash.
+7. Invalidate the membership of the tempered hash.
+
+## Details
+
+### Merkle tree structure
+
+Our Merkle tree is a **full binary tree** stored in a 1D array.
+The tree nodes are stored following a level-first traversal of the binary tree.
+For a given level, we use offset to number elements from left to right. The node numbers on the figure below correspond to their locations in the array.
+
+```text
+        Tree        Level
+          0         0 
+        /   \
+       1     2      1
+      / \   / \
+     3   4 5   6    2
+
+1D array representation: {0, 1, 2, 3, 4, 5, 6}
+```
+
+### Membership proof structure
+
+We use two arrays:
+
+- position (left/right) of the node along the path toward the root
+- hash of a second node with the same parent

examples/c++/Poseidon-hash/compile.sh

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+#!/bin/bash
+
+# Exit immediately on error
+set -e
+
+rm -rf build
+mkdir -p build
+cmake -S . -B build
+cmake --build build

examples/c++/Poseidon-hash/example.cu

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+#include <chrono>
+#include <fstream>
+#include <iostream>
+
+// select the curve (only 2 available so far)
+#define CURVE_ID 2
+// include Poseidon template
+#include "appUtils/poseidon/poseidon.cu"
+using namespace poseidon;
+using namespace curve_config;
+
+device_context::DeviceContext ctx= device_context::get_default_device_context();
+
+// location of a tree node in the array for a given level and offset
+inline uint32_t tree_index(uint32_t level, uint32_t offset) { return (1 << level) - 1 + offset; }
+
+// We assume the tree has leaves already set, compute all other levels
+void build_tree(
+  const uint32_t tree_height, scalar_t* tree, PoseidonConstants<scalar_t> * constants, PoseidonConfig config)
+{
+  for (uint32_t level = tree_height - 1; level > 0; level--) {
+    const uint32_t next_level = level - 1;
+    const uint32_t next_level_width = 1 << next_level;
+    poseidon_hash<scalar_t, 2+1>(
+      &tree[tree_index(level, 0)], &tree[tree_index(next_level, 0)], next_level_width, *constants, config);
+  }
+}
+
+// linear search leaves for a given hash, return offset
+uint32_t query_membership(scalar_t query, scalar_t* tree, const uint32_t tree_height)
+{
+  const uint32_t tree_width = (1 << (tree_height - 1));
+  for (uint32_t i = 0; i < tree_width; i++) {
+    const scalar_t leaf = tree[tree_index(tree_height - 1, i)];
+    if (leaf == query) {
+      return i; // found the hash
+    }
+  }
+  return tree_height; // hash not found
+}
+
+void generate_proof(
+  uint32_t position,
+  scalar_t* tree,
+  const uint32_t tree_height,
+  uint32_t* proof_lr,
+  scalar_t* proof_hash)
+{
+  uint32_t level_index = position;
+  for (uint32_t level = tree_height - 1; level > 0; level--) {
+    uint32_t lr;
+    uint32_t neighbour_index;
+    lr = level_index % 2;
+    if (lr == 0) {
+      // left
+      neighbour_index = level_index + 1;
+    } else {
+      // right
+      neighbour_index = level_index - 1;
+    }
+    proof_lr[level] = lr;
+    proof_hash[level] = tree[tree_index(level, neighbour_index)];
+    level_index /= 2;
+  }
+  // the proof must match this:
+  proof_hash[0] = tree[tree_index(0, 0)];
+}
+
+uint32_t validate_proof(
+  const scalar_t hash,
+  const uint32_t tree_height,
+  const uint32_t* proof_lr,
+  const scalar_t* proof_hash,
+  PoseidonConstants<scalar_t> * constants,
+  PoseidonConfig config)
+{
+  scalar_t hashes_in[2], hash_out[1], level_hash;
+  level_hash = hash;
+  for (uint32_t level = tree_height - 1; level > 0; level--) {
+    if (proof_lr[level] == 0) {
+      hashes_in[0] = level_hash;
+      hashes_in[1] = proof_hash[level];
+    } else {
+      hashes_in[0] = proof_hash[level];
+      hashes_in[1] = level_hash;
+    }
+    // next level hash
+    poseidon_hash<scalar_t, 2+1>(hashes_in, hash_out, 1, *constants, config);
+    level_hash = hash_out[0];
+  }
+  return proof_hash[0] == level_hash;
+}
+
+int main(int argc, char* argv[])
+{
+  std::cout << "1. Defining the size of the example: height of the full binary Merkle tree" << std::endl;
+  const uint32_t tree_height = 21;
+  std::cout << "Tree height: " << tree_height << std::endl;
+  const uint32_t tree_arity = 2;
+  const uint32_t leaf_level = tree_height - 1;
+  const uint32_t tree_width = 1 << leaf_level;
+  std::cout << "Tree width: " << tree_width << std::endl;
+  const uint32_t tree_size = (1 << tree_height) - 1;
+  std::cout << "Tree size: " << tree_size << std::endl;
+  scalar_t* tree = static_cast<scalar_t*>(malloc(tree_size * sizeof(scalar_t)));
+
+  std::cout << "2. Hashing blocks in parallel" << std::endl;
+  const uint32_t data_arity = 4;
+  std::cout << "Block size (arity): " << data_arity << std::endl;
+  std::cout << "Initializing blocks..." << std::endl;
+  scalar_t d = scalar_t::zero();
+  scalar_t* data = static_cast<scalar_t*>(malloc(tree_width * data_arity * sizeof(scalar_t)));
+  for (uint32_t i = 0; i < tree_width * data_arity; i++) {
+    data[i] = d;
+    d = d + scalar_t::one();
+  }
+  std::cout << "Hashing blocks into tree leaves..." << std::endl;
+  PoseidonConstants<scalar_t> constants;
+  init_optimized_poseidon_constants<scalar_t>(data_arity, ctx, &constants);
+  PoseidonConfig config = default_poseidon_config<scalar_t>(data_arity+1); 
+  poseidon_hash<curve_config::scalar_t, data_arity+1>(data, &tree[tree_index(leaf_level, 0)], tree_width, constants, config);
+
+  std::cout << "3. Building Merkle tree" << std::endl;
+  // Poseidon<BLS12_381::scalar_t> tree_poseidon(tree_arity, stream);
+  PoseidonConstants<scalar_t> tree_constants;
+  init_optimized_poseidon_constants<scalar_t>(tree_arity, ctx, &tree_constants);
+  PoseidonConfig tree_config = default_poseidon_config<scalar_t>(tree_arity+1);
+  build_tree(tree_height, tree, &tree_constants, tree_config);
+
+  std::cout << "4. Generate membership proof" << std::endl;
+  uint32_t position = tree_width - 1;
+  std::cout << "Using the hash for block: " << position << std::endl;
+  scalar_t query = tree[tree_index(leaf_level, position)];
+  uint32_t query_position = query_membership(query, tree, tree_height);
+  // allocate arrays for the proof
+  uint32_t* proof_lr = static_cast<uint32_t*>(malloc(tree_height * sizeof(uint32_t)));
+  scalar_t* proof_hash = static_cast<scalar_t*>(malloc(tree_height * sizeof(scalar_t)));
+  generate_proof(query_position, tree, tree_height, proof_lr, proof_hash);
+
+  std::cout << "5. Validate the hash membership" << std::endl;
+  uint32_t validated;
+  const scalar_t hash = tree[tree_index(leaf_level, query_position)];
+  validated = validate_proof(hash, tree_height, proof_lr, proof_hash, &tree_constants, tree_config);
+  std::cout << "Validated: " << validated << std::endl;
+
+  std::cout << "6. Tamper the hash" << std::endl;
+  const scalar_t tampered_hash = hash + scalar_t::one();
+  validated = validate_proof(tampered_hash, tree_height, proof_lr, proof_hash, &tree_constants, tree_config);
+  
+  std::cout << "7. Invalidate tamper hash membership" << std::endl;
+  std::cout << "Validated: " << validated << std::endl;
+  return 0;
+}

examples/c++/Poseidon-hash/run.sh

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+#!/bin/bash
+./build/example