feat: added poseidon2 hash function to barretenberg/crypto (#3118)

Preliminary work to add Poseidon2 hash function as a standard library
primitive (https://eprint.iacr.org/2023/323.pdf)

Adds Poseidon2 to crypto module, following paper + specification at
https://github.com/C2SP/C2SP/blob/792c1254124f625d459bfe34417e8f6bdd02eb28/poseidon-sponge.md

---------

Co-authored-by: lucasxia01 <[email protected]>

barretenberg/cpp/src/barretenberg/crypto/CMakeLists.txt

@@ -9,3 +9,4 @@ add_subdirectory(schnorr)
 add_subdirectory(sha256)
 add_subdirectory(ecdsa)
 add_subdirectory(aes128)
+add_subdirectory(poseidon2)

barretenberg/cpp/src/barretenberg/crypto/poseidon2/CMakeLists.txt

@@ -0,0 +1 @@
+barretenberg_module(crypto_poseidon2 ecc numeric)

barretenberg/cpp/src/barretenberg/crypto/poseidon2/poseidon2.bench.cpp

@@ -0,0 +1,29 @@
+#include "./poseidon2.hpp"
+#include "barretenberg/ecc/curves/grumpkin/grumpkin.hpp"
+#include <benchmark/benchmark.h>
+
+using namespace benchmark;
+
+grumpkin::fq poseidon_function(const size_t count)
+{
+    std::vector<grumpkin::fq> inputs(count);
+    for (size_t i = 0; i < count; ++i) {
+        inputs[i] = grumpkin::fq::random_element();
+    }
+    std::span tmp(inputs);
+    // hash count many field elements
+    inputs[0] = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>::hash(tmp);
+    return inputs[0];
+}
+
+void native_poseidon2_commitment_bench(State& state) noexcept
+{
+    for (auto _ : state) {
+        const size_t count = (static_cast<size_t>(state.range(0)));
+        (poseidon_function(count));
+    }
+}
+BENCHMARK(native_poseidon2_commitment_bench)->Arg(10)->Arg(1000)->Arg(10000);
+
+BENCHMARK_MAIN();
+// } // namespace crypto

barretenberg/cpp/src/barretenberg/crypto/poseidon2/poseidon2.hpp

@@ -0,0 +1,16 @@
+#pragma once
+
+#include "poseidon2_params.hpp"
+#include "poseidon2_permutation.hpp"
+#include "sponge/sponge.hpp"
+
+namespace crypto {
+
+template <typename Params> class Poseidon2 {
+  public:
+    using FF = typename Params::FF;
+
+    using Sponge = FieldSponge<FF, Params::t - 1, 1, Params::t, Poseidon2Permutation<Params>>;
+    static FF hash(std::span<FF> input) { return Sponge::hash_fixed_length(input); }
+};
+} // namespace crypto

barretenberg/cpp/src/barretenberg/crypto/poseidon2/poseidon2.test.cpp

@@ -0,0 +1,49 @@
+#include "poseidon2.hpp"
+#include "barretenberg/crypto/poseidon2/poseidon2_params.hpp"
+#include "barretenberg/ecc/curves/bn254/bn254.hpp"
+#include <gtest/gtest.h>
+
+using namespace barretenberg;
+
+namespace {
+auto& engine = numeric::random::get_debug_engine();
+}
+
+namespace poseidon2_tests {
+TEST(Poseidon2, BasicTests)
+{
+
+    barretenberg::fr a = barretenberg::fr::random_element(&engine);
+    barretenberg::fr b = barretenberg::fr::random_element(&engine);
+    barretenberg::fr c = barretenberg::fr::random_element(&engine);
+    barretenberg::fr d = barretenberg::fr::random_element(&engine);
+
+    std::vector<barretenberg::fr> input1{ a, b, c, d };
+    std::vector<barretenberg::fr> input2{ d, c, b, a };
+
+    auto r0 = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>::hash(input1);
+    auto r1 = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>::hash(input1);
+    auto r2 = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>::hash(input2);
+
+    EXPECT_EQ(r0, r1);
+    EXPECT_NE(r0, r2);
+}
+
+// N.B. these hardcoded values were extracted from the algorithm being tested. These are NOT independent test vectors!
+// TODO(@zac-williamson #3132): find independent test vectors we can compare against! (very hard to find given
+// flexibility of Poseidon's parametrisation)
+TEST(Poseidon2, ConsistencyCheck)
+{
+    barretenberg::fr a(std::string("9a807b615c4d3e2fa0b1c2d3e4f56789fedcba9876543210abcdef0123456789"));
+    barretenberg::fr b(std::string("9a807b615c4d3e2fa0b1c2d3e4f56789fedcba9876543210abcdef0123456789"));
+    barretenberg::fr c(std::string("0x9a807b615c4d3e2fa0b1c2d3e4f56789fedcba9876543210abcdef0123456789"));
+    barretenberg::fr d(std::string("0x9a807b615c4d3e2fa0b1c2d3e4f56789fedcba9876543210abcdef0123456789"));
+
+    std::array<barretenberg::fr, 4> input{ a, b, c, d };
+    auto result = crypto::Poseidon2<crypto::Poseidon2Bn254ScalarFieldParams>::hash(input);
+
+    barretenberg::fr expected(std::string("0x150c19ae11b3290c137c7a4d760d9482a6581d731535f560c3601d6a766b0937"));
+
+    EXPECT_EQ(result, expected);
+}
+} // namespace poseidon2_tests