chore: add c++ tests for generator derivation (AztecProtocol#6528)

This PR adds some tests just to give ground truth values for
`hash_to_curve` and `derive_generators` which can replicated in test
suites for reimplementations of this logic
[elsewhere](noir-lang/noir#4871)

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

@@ -2,6 +2,7 @@ add_subdirectory(hmac)
 add_subdirectory(blake2s)
 add_subdirectory(blake3s)
 add_subdirectory(blake3s_full)
+add_subdirectory(generators)
 add_subdirectory(keccak)
 add_subdirectory(pedersen_commitment)
 add_subdirectory(pedersen_hash)

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

@@ -0,0 +1 @@
+barretenberg_module(crypto_generator_data ecc)

barretenberg/cpp/src/barretenberg/crypto/generators/generator_data.test.cpp

@@ -0,0 +1,45 @@
+#include "generator_data.hpp"
+#include "barretenberg/crypto/pedersen_commitment/c_bind.hpp"
+#include "barretenberg/ecc/curves/grumpkin/grumpkin.hpp"
+#include <gtest/gtest.h>
+#include <vector>
+
+namespace bb::crypto {
+
+TEST(GeneratorContext, DeriveDefaultGenerators)
+{
+    auto default_generators = generator_data<curve::Grumpkin>::make_precomputed_generators();
+    std::vector<grumpkin::g1::affine_element> expected_default_generators;
+
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("083e7911d835097629f0067531fc15cafd79a89beecb39903f69572c636f4a5a")),
+          fr(uint256_t("1a7f5efaad7f315c25a918f30cc8d7333fccab7ad7c90f14de81bcc528f9935d")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("054aa86a73cb8a34525e5bbed6e43ba1198e860f5f3950268f71df4591bde402")),
+          fr(uint256_t("209dcfbf2cfb57f9f6046f44d71ac6faf87254afc7407c04eb621a6287cac126")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("1c44f2a5207c81c28a8321a5815ce8b1311024bbed131819bbdaf5a2ada84748")),
+          fr(uint256_t("03aaee36e6422a1d0191632ac6599ae9eba5ac2c17a8c920aa3caf8b89c5f8a8")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("26d8b1160c6821a30c65f6cb47124afe01c29f4338f44d4a12c9fccf22fb6fb2")),
+          fr(uint256_t("05c70c3b9c0d25a4c100e3a27bf3cc375f8af8cdd9498ec4089a823d7464caff")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("20ed9c6a1d27271c4498bfce0578d59db1adbeaa8734f7facc097b9b994fcf6e")),
+          fr(uint256_t("29cd7d370938b358c62c4a00f73a0d10aba7e5aaa04704a0713f891ebeb92371")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("0224a8abc6c8b8d50373d64cd2a1ab1567bf372b3b1f7b861d7f01257052d383")),
+          fr(uint256_t("2358629b90eafb299d6650a311e79914b0215eb0a790810b26da5a826726d711")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("0f106f6d46bc904a5290542490b2f238775ff3c445b2f8f704c466655f460a2a")),
+          fr(uint256_t("29ab84d472f1d33f42fe09c47b8f7710f01920d6155250126731e486877bcf27")) }));
+    expected_default_generators.emplace_back(grumpkin::g1::affine_element(
+        { fr(uint256_t("0298f2e42249f0519c8a8abd91567ebe016e480f219b8c19461d6a595cc33696")),
+          fr(uint256_t("035bec4b8520a4ece27bd5aafabee3dfe1390d7439c419a8c55aceb207aac83b")) }));
+
+    EXPECT_EQ(default_generators.size(), expected_default_generators.size());
+    for (size_t i = 0; i < default_generators.size(); ++i) {
+        EXPECT_EQ(default_generators[i], expected_default_generators[i]);
+    }
+}
+
+} // namespace bb::crypto

barretenberg/cpp/src/barretenberg/crypto/pedersen_hash/pedersen.test.cpp

@@ -1,12 +1,23 @@
 #include "pedersen.hpp"
 #include "barretenberg/crypto/generators/generator_data.hpp"
+#include "barretenberg/crypto/pedersen_commitment/c_bind.hpp"
 #include "barretenberg/numeric/uint256/uint256.hpp"
 #include <gtest/gtest.h>
 
 namespace bb::crypto {
 
 using bb::fr;
 
+TEST(Pedersen, DeriveLengthGenerator)
+{
+    auto generator = pedersen_hash::length_generator;
+    std::cout << generator << std::endl;
+    EXPECT_EQ(generator,
+              grumpkin::g1::affine_element(
+                  fr(uint256_t("0x2df8b940e5890e4e1377e05373fae69a1d754f6935e6a780b666947431f2cdcd")),
+                  fr(uint256_t("0x2ecd88d15967bc53b885912e0d16866154acb6aac2d3f85e27ca7eefb2c19083"))));
+}
+
 TEST(Pedersen, Hash)
 {
     auto x = pedersen_hash::Fq::one();

barretenberg/cpp/src/barretenberg/ecc/groups/affine_element.test.cpp

@@ -12,6 +12,7 @@
 #include <fstream>
 #include <gtest/gtest.h>
 #include <iterator>
+#include <tuple>
 
 using ::testing::Each;
 using ::testing::ElementsAreArray;
@@ -254,4 +255,31 @@ TYPED_TEST(TestAffineElement, BatchEndomoprhismByMinusOne)
     } else {
         GTEST_SKIP();
     }
-}
+}
+
+TEST(AffineElement, HashToCurve)
+{
+    std::vector<std::tuple<std::vector<uint8_t>, grumpkin::g1::affine_element>> test_vectors;
+    test_vectors.emplace_back(std::vector<uint8_t>(),
+                              grumpkin::g1::affine_element(
+                                  fr(uint256_t("24c4cb9c1206ab5470592f237f1698abe684dadf0ab4d7a132c32b2134e2c12e")),
+                                  fr(uint256_t("0668b8d61a317fb34ccad55c930b3554f1828a0e5530479ecab4defe6bbc0b2e"))));
+
+    test_vectors.emplace_back(std::vector<uint8_t>{ 1 },
+                              grumpkin::g1::affine_element(
+                                  fr(uint256_t("107f1b633c6113f3222f39f6256f0546b41a4880918c86864b06471afb410454")),
+                                  fr(uint256_t("050cd3823d0c01590b6a50adcc85d2ee4098668fd28805578aa05a423ea938c6"))));
+
+    // "hello world"
+    test_vectors.emplace_back(std::vector<uint8_t>{ 0x68, 0x65, 0x6c, 0x6c, 0x6f, 0x20, 0x77, 0x6f, 0x72, 0x6c, 0x64 },
+                              grumpkin::g1::affine_element(
+                                  fr(uint256_t("037c5c229ae495f6e8d1b4bf7723fafb2b198b51e27602feb8a4d1053d685093")),
+                                  fr(uint256_t("10cf9596c5b2515692d930efa2cf3817607e4796856a79f6af40c949b066969f"))));
+
+    for (std::tuple<std::vector<uint8_t>, grumpkin::g1::affine_element> test_case : test_vectors) {
+        auto result = grumpkin::g1::affine_element::hash_to_curve(std::get<0>(test_case), 0);
+        auto expected_result = std::get<1>(test_case);
+        std::cout << result << std::endl;
+        EXPECT_TRUE(result == expected_result);
+    }
+}