feat: add hashing to stdlib transcript (#4161)

Combines native and stdlib transcripts by templating it with a
TranscriptParams parameter. This parameter contains the type of field
element in the proof (bb::fr for native and field_t<Builder> for stdlib)
and conversion functions for converting from the field element to/from
other types.

Adds the stdlib conversion functions, and the convert_challenge function
for native and stdlib for turning a challenge into a bn254 scalar or
grumpkin scalar.

Resolves AztecProtocol/barretenberg#835.

---------

Co-authored-by: codygunton <codygunton@gmail.com>

barretenberg/cpp/src/barretenberg/benchmark/ipa_bench/ipa.bench.cpp

@@ -16,8 +16,8 @@ std::shared_ptr<bb::srs::factories::CrsFactory<curve::Grumpkin>> crs_factory(
 auto ck = std::make_shared<CommitmentKey<Curve>>(1 << MAX_POLYNOMIAL_DEGREE_LOG2, crs_factory);
 auto vk = std::make_shared<VerifierCommitmentKey<Curve>>(1 << MAX_POLYNOMIAL_DEGREE_LOG2, crs_factory);
 
-std::vector<std::shared_ptr<BaseTranscript>> prover_transcripts(MAX_POLYNOMIAL_DEGREE_LOG2 -
-                                                                MIN_POLYNOMIAL_DEGREE_LOG2 + 1);
+std::vector<std::shared_ptr<NativeTranscript>> prover_transcripts(MAX_POLYNOMIAL_DEGREE_LOG2 -
+                                                                  MIN_POLYNOMIAL_DEGREE_LOG2 + 1);
 std::vector<OpeningClaim<Curve>> opening_claims(MAX_POLYNOMIAL_DEGREE_LOG2 - MIN_POLYNOMIAL_DEGREE_LOG2 + 1);
 
 void ipa_open(State& state) noexcept
@@ -36,7 +36,7 @@ void ipa_open(State& state) noexcept
         const OpeningPair<Curve> opening_pair = { x, eval };
         const OpeningClaim<Curve> opening_claim{ opening_pair, ck->commit(poly) };
         // initialize empty prover transcript
-        auto prover_transcript = std::make_shared<BaseTranscript>();
+        auto prover_transcript = std::make_shared<NativeTranscript>();
         state.ResumeTiming();
         // Compute proof
         IPA<Curve>::compute_opening_proof(ck, opening_pair, poly, prover_transcript);
@@ -53,7 +53,7 @@ void ipa_verify(State& state) noexcept
         auto prover_transcript = prover_transcripts[static_cast<size_t>(state.range(0)) - MIN_POLYNOMIAL_DEGREE_LOG2];
         auto opening_claim = opening_claims[static_cast<size_t>(state.range(0)) - MIN_POLYNOMIAL_DEGREE_LOG2];
         // initialize verifier transcript from proof data
-        auto verifier_transcript = std::make_shared<BaseTranscript>(prover_transcript->proof_data);
+        auto verifier_transcript = std::make_shared<NativeTranscript>(prover_transcript->proof_data);
 
         state.ResumeTiming();
         auto result = IPA<Curve>::verify(vk, opening_claim, verifier_transcript);

barretenberg/cpp/src/barretenberg/commitment_schemes/gemini/gemini.hpp

@@ -149,7 +149,7 @@ template <typename Curve> class GeminiVerifier_ {
         }
 
         // compute vector of powers of random evaluation point r
-        const Fr r = transcript->get_challenge("Gemini:r");
+        const Fr r = transcript->template get_challenge<Fr>("Gemini:r");
         std::vector<Fr> r_squares = gemini::squares_of_r(r, num_variables);
 
         // Get evaluations a_i, i = 0,...,m-1 from transcript

barretenberg/cpp/src/barretenberg/commitment_schemes/gemini/gemini.test.cpp

@@ -25,7 +25,7 @@ template <class Curve> class GeminiTest : public CommitmentTest<Curve> {
                                           std::vector<GroupElement> multilinear_commitments,
                                           std::vector<GroupElement> multilinear_commitments_to_be_shifted)
     {
-        auto prover_transcript = BaseTranscript::prover_init_empty();
+        auto prover_transcript = NativeTranscript::prover_init_empty();
 
         const Fr rho = Fr::random_element();
 
@@ -65,7 +65,7 @@ template <class Curve> class GeminiTest : public CommitmentTest<Curve> {
             prover_transcript->send_to_verifier(label, commitment);
         }
 
-        const Fr r_challenge = prover_transcript->get_challenge("Gemini:r");
+        const Fr r_challenge = prover_transcript->get_challenge<Fr>("Gemini:r");
 
         auto prover_output = GeminiProver::compute_fold_polynomial_evaluations(
             multilinear_evaluation_point, std::move(gemini_polynomials), r_challenge);
@@ -79,7 +79,7 @@ template <class Curve> class GeminiTest : public CommitmentTest<Curve> {
         // Check that the Fold polynomials have been evaluated correctly in the prover
         this->verify_batch_opening_pair(prover_output.opening_pairs, prover_output.witnesses);
 
-        auto verifier_transcript = BaseTranscript::verifier_init_empty(prover_transcript);
+        auto verifier_transcript = NativeTranscript::verifier_init_empty(prover_transcript);
 
         // Compute:
         // - Single opening pair: {r, \hat{a}_0}

barretenberg/cpp/src/barretenberg/commitment_schemes/ipa/ipa.hpp

@@ -36,12 +36,12 @@ template <typename Curve> class IPA {
     static void compute_opening_proof(const std::shared_ptr<CK>& ck,
                                       const OpeningPair<Curve>& opening_pair,
                                       const Polynomial& polynomial,
-                                      const std::shared_ptr<BaseTranscript>& transcript)
+                                      const std::shared_ptr<NativeTranscript>& transcript)
     {
         ASSERT(opening_pair.challenge != 0 && "The challenge point should not be zero");
         auto poly_degree = static_cast<size_t>(polynomial.size());
-        transcript->send_to_verifier("IPA:poly_degree", static_cast<uint64_t>(poly_degree));
-        const Fr generator_challenge = transcript->get_challenge("IPA:generator_challenge");
+        transcript->send_to_verifier("IPA:poly_degree", static_cast<uint32_t>(poly_degree));
+        const Fr generator_challenge = transcript->template get_challenge<Fr>("IPA:generator_challenge");
         auto aux_generator = Commitment::one() * generator_challenge;
         // Checks poly_degree is greater than zero and a power of two
         // In the future, we might want to consider if non-powers of two are needed
@@ -138,7 +138,7 @@ template <typename Curve> class IPA {
             transcript->send_to_verifier("IPA:R_" + index, Commitment(R_elements[i]));
 
             // Generate the round challenge.
-            const Fr round_challenge = transcript->get_challenge("IPA:round_challenge_" + index);
+            const Fr round_challenge = transcript->get_challenge<Fr>("IPA:round_challenge_" + index);
             const Fr round_challenge_inv = round_challenge.invert();
 
             auto G_lo = GroupElement::batch_mul_with_endomorphism(
@@ -183,10 +183,12 @@ template <typename Curve> class IPA {
      */
     static bool verify(const std::shared_ptr<VK>& vk,
                        const OpeningClaim<Curve>& opening_claim,
-                       const std::shared_ptr<BaseTranscript>& transcript)
+                       const std::shared_ptr<NativeTranscript>& transcript)
     {
-        auto poly_degree = static_cast<size_t>(transcript->template receive_from_prover<uint64_t>("IPA:poly_degree"));
-        const Fr generator_challenge = transcript->get_challenge("IPA:generator_challenge");
+        auto poly_degree = static_cast<uint32_t>(transcript->template receive_from_prover<typename Curve::BaseField>(
+            "IPA:poly_degree")); // note this is base field because this is a uint32_t, which should map to a bb::fr,
+                                 // not a grumpkin::fr, which is a BaseField element for Grumpkin
+        const Fr generator_challenge = transcript->template get_challenge<Fr>("IPA:generator_challenge");
         auto aux_generator = Commitment::one() * generator_challenge;
 
         auto log_poly_degree = static_cast<size_t>(numeric::get_msb(poly_degree));
@@ -204,7 +206,7 @@ template <typename Curve> class IPA {
             std::string index = std::to_string(i);
             auto element_L = transcript->template receive_from_prover<Commitment>("IPA:L_" + index);
             auto element_R = transcript->template receive_from_prover<Commitment>("IPA:R_" + index);
-            round_challenges[i] = transcript->get_challenge("IPA:round_challenge_" + index);
+            round_challenges[i] = transcript->template get_challenge<Fr>("IPA:round_challenge_" + index);
             round_challenges_inv[i] = round_challenges[i].invert();
 
             msm_elements[2 * i] = element_L;

barretenberg/cpp/src/barretenberg/commitment_schemes/ipa/ipa.test.cpp

@@ -72,11 +72,11 @@ TEST_F(IPATest, Open)
     const OpeningClaim<Curve> opening_claim{ opening_pair, commitment };
 
     // initialize empty prover transcript
-    auto prover_transcript = std::make_shared<BaseTranscript>();
+    auto prover_transcript = std::make_shared<NativeTranscript>();
     IPA::compute_opening_proof(this->ck(), opening_pair, poly, prover_transcript);
 
     // initialize verifier transcript from proof data
-    auto verifier_transcript = std::make_shared<BaseTranscript>(prover_transcript->proof_data);
+    auto verifier_transcript = std::make_shared<NativeTranscript>(prover_transcript->proof_data);
 
     auto result = IPA::verify(this->vk(), opening_claim, verifier_transcript);
     EXPECT_TRUE(result);
@@ -131,7 +131,7 @@ TEST_F(IPATest, GeminiShplonkIPAWithShift)
     batched_commitment_unshifted = commitment1 * rhos[0] + commitment2 * rhos[1];
     batched_commitment_to_be_shifted = commitment2 * rhos[2];
 
-    auto prover_transcript = BaseTranscript::prover_init_empty();
+    auto prover_transcript = NativeTranscript::prover_init_empty();
 
     auto gemini_polynomials = GeminiProver::compute_gemini_polynomials(
         mle_opening_point, std::move(batched_unshifted), std::move(batched_to_be_shifted));
@@ -142,7 +142,7 @@ TEST_F(IPATest, GeminiShplonkIPAWithShift)
         prover_transcript->send_to_verifier(label, commitment);
     }
 
-    const Fr r_challenge = prover_transcript->get_challenge("Gemini:r");
+    const Fr r_challenge = prover_transcript->template get_challenge<Fr>("Gemini:r");
 
     const auto [gemini_opening_pairs, gemini_witnesses] = GeminiProver::compute_fold_polynomial_evaluations(
         mle_opening_point, std::move(gemini_polynomials), r_challenge);
@@ -153,18 +153,18 @@ TEST_F(IPATest, GeminiShplonkIPAWithShift)
         prover_transcript->send_to_verifier(label, evaluation);
     }
 
-    const Fr nu_challenge = prover_transcript->get_challenge("Shplonk:nu");
+    const Fr nu_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:nu");
     auto batched_quotient_Q =
         ShplonkProver::compute_batched_quotient(gemini_opening_pairs, gemini_witnesses, nu_challenge);
     prover_transcript->send_to_verifier("Shplonk:Q", this->ck()->commit(batched_quotient_Q));
 
-    const Fr z_challenge = prover_transcript->get_challenge("Shplonk:z");
+    const Fr z_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:z");
     const auto [shplonk_opening_pair, shplonk_witness] = ShplonkProver::compute_partially_evaluated_batched_quotient(
         gemini_opening_pairs, gemini_witnesses, std::move(batched_quotient_Q), nu_challenge, z_challenge);
 
     IPA::compute_opening_proof(this->ck(), shplonk_opening_pair, shplonk_witness, prover_transcript);
 
-    auto verifier_transcript = BaseTranscript::verifier_init_empty(prover_transcript);
+    auto verifier_transcript = NativeTranscript::verifier_init_empty(prover_transcript);
 
     auto gemini_verifier_claim = GeminiVerifier::reduce_verification(mle_opening_point,
                                                                      batched_evaluation,

barretenberg/cpp/src/barretenberg/commitment_schemes/kzg/kzg.hpp

@@ -31,7 +31,7 @@ template <typename Curve> class KZG {
     static void compute_opening_proof(std::shared_ptr<CK> ck,
                                       const OpeningPair<Curve>& opening_pair,
                                       const Polynomial& polynomial,
-                                      const std::shared_ptr<BaseTranscript>& prover_trancript)
+                                      const std::shared_ptr<NativeTranscript>& prover_trancript)
     {
         Polynomial quotient = polynomial;
         quotient[0] -= opening_pair.evaluation;
@@ -55,7 +55,7 @@ template <typename Curve> class KZG {
      */
     static bool verify(const std::shared_ptr<VK>& vk,
                        const OpeningClaim<Curve>& claim,
-                       const std::shared_ptr<BaseTranscript>& verifier_transcript)
+                       const std::shared_ptr<NativeTranscript>& verifier_transcript)
     {
         auto quotient_commitment = verifier_transcript->template receive_from_prover<Commitment>("KZG:W");
         auto lhs = claim.commitment - (GroupElement::one() * claim.opening_pair.evaluation) +
@@ -82,7 +82,7 @@ template <typename Curve> class KZG {
 
         GroupElement P_0;
         if constexpr (Curve::is_stdlib_type) {
-            auto builder = verifier_transcript->builder;
+            auto builder = quotient_commitment.get_context();
             auto one = Fr(builder, 1);
             std::vector<GroupElement> commitments = { claim.commitment,
                                                       quotient_commitment,

barretenberg/cpp/src/barretenberg/commitment_schemes/kzg/kzg.test.cpp

@@ -39,11 +39,11 @@ TYPED_TEST(KZGTest, single)
     auto opening_pair = OpeningPair<TypeParam>{ challenge, evaluation };
     auto opening_claim = OpeningClaim<TypeParam>{ opening_pair, commitment };
 
-    auto prover_transcript = BaseTranscript::prover_init_empty();
+    auto prover_transcript = NativeTranscript::prover_init_empty();
 
     KZG::compute_opening_proof(this->ck(), opening_pair, witness, prover_transcript);
 
-    auto verifier_transcript = BaseTranscript::verifier_init_empty(prover_transcript);
+    auto verifier_transcript = NativeTranscript::verifier_init_empty(prover_transcript);
     bool verified = KZG::verify(this->vk(), opening_claim, verifier_transcript);
 
     EXPECT_EQ(verified, true);
@@ -109,7 +109,7 @@ TYPED_TEST(KZGTest, GeminiShplonkKzgWithShift)
     batched_commitment_unshifted = commitment1 * rhos[0] + commitment2 * rhos[1];
     batched_commitment_to_be_shifted = commitment2 * rhos[2];
 
-    auto prover_transcript = BaseTranscript::prover_init_empty();
+    auto prover_transcript = NativeTranscript::prover_init_empty();
 
     // Run the full prover PCS protocol:
 
@@ -125,7 +125,7 @@ TYPED_TEST(KZGTest, GeminiShplonkKzgWithShift)
         prover_transcript->send_to_verifier(label, commitment);
     }
 
-    const Fr r_challenge = prover_transcript->get_challenge("Gemini:r");
+    const Fr r_challenge = prover_transcript->template get_challenge<Fr>("Gemini:r");
 
     const auto [gemini_opening_pairs, gemini_witnesses] = GeminiProver::compute_fold_polynomial_evaluations(
         mle_opening_point, std::move(gemini_polynomials), r_challenge);
@@ -139,12 +139,12 @@ TYPED_TEST(KZGTest, GeminiShplonkKzgWithShift)
     // Shplonk prover output:
     // - opening pair: (z_challenge, 0)
     // - witness: polynomial Q - Q_z
-    const Fr nu_challenge = prover_transcript->get_challenge("Shplonk:nu");
+    const Fr nu_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:nu");
     auto batched_quotient_Q =
         ShplonkProver::compute_batched_quotient(gemini_opening_pairs, gemini_witnesses, nu_challenge);
     prover_transcript->send_to_verifier("Shplonk:Q", this->ck()->commit(batched_quotient_Q));
 
-    const Fr z_challenge = prover_transcript->get_challenge("Shplonk:z");
+    const Fr z_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:z");
     const auto [shplonk_opening_pair, shplonk_witness] = ShplonkProver::compute_partially_evaluated_batched_quotient(
         gemini_opening_pairs, gemini_witnesses, std::move(batched_quotient_Q), nu_challenge, z_challenge);
 
@@ -154,7 +154,7 @@ TYPED_TEST(KZGTest, GeminiShplonkKzgWithShift)
 
     // Run the full verifier PCS protocol with genuine opening claims (genuine commitment, genuine evaluation)
 
-    auto verifier_transcript = BaseTranscript::verifier_init_empty(prover_transcript);
+    auto verifier_transcript = NativeTranscript::verifier_init_empty(prover_transcript);
 
     // Gemini verifier output:
     // - claim: d+1 commitments to Fold_{r}^(0), Fold_{-r}^(0), Fold^(l), d+1 evaluations a_0_pos, a_l, l = 0:d-1

barretenberg/cpp/src/barretenberg/commitment_schemes/shplonk/shplonk.hpp

@@ -168,11 +168,11 @@ template <typename Curve> class ShplonkVerifier_ {
 
         const size_t num_claims = claims.size();
 
-        const Fr nu = transcript->get_challenge("Shplonk:nu");
+        const Fr nu = transcript->template get_challenge<Fr>("Shplonk:nu");
 
         auto Q_commitment = transcript->template receive_from_prover<Commitment>("Shplonk:Q");
 
-        const Fr z_challenge = transcript->get_challenge("Shplonk:z");
+        const Fr z_challenge = transcript->template get_challenge<Fr>("Shplonk:z");
 
         // [G] = [Q] - ∑ⱼ ρʲ / ( r − xⱼ )⋅[fⱼ] + G₀⋅[1]
         //     = [Q] - [∑ⱼ ρʲ ⋅ ( fⱼ(X) − vⱼ) / ( r − xⱼ )]

barretenberg/cpp/src/barretenberg/commitment_schemes/shplonk/shplonk.test.cpp

@@ -28,7 +28,7 @@ TYPED_TEST(ShplonkTest, ShplonkSimple)
 
     const size_t n = 16;
 
-    auto prover_transcript = BaseTranscript::prover_init_empty();
+    auto prover_transcript = NativeTranscript::prover_init_empty();
 
     // Generate two random (unrelated) polynomials of two different sizes, as well as their evaluations at a (single but
     // different) random point and their commitments.
@@ -47,11 +47,11 @@ TYPED_TEST(ShplonkTest, ShplonkSimple)
     std::vector<Polynomial> polynomials = { poly1.share(), poly2.share() };
 
     // Execute the shplonk prover functionality
-    const Fr nu_challenge = prover_transcript->get_challenge("Shplonk:nu");
+    const Fr nu_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:nu");
     auto batched_quotient_Q = ShplonkProver::compute_batched_quotient(opening_pairs, polynomials, nu_challenge);
     prover_transcript->send_to_verifier("Shplonk:Q", this->ck()->commit(batched_quotient_Q));
 
-    const Fr z_challenge = prover_transcript->get_challenge("Shplonk:z");
+    const Fr z_challenge = prover_transcript->template get_challenge<Fr>("Shplonk:z");
     const auto [prover_opening_pair, shplonk_prover_witness] =
         ShplonkProver::compute_partially_evaluated_batched_quotient(
             opening_pairs, polynomials, std::move(batched_quotient_Q), nu_challenge, z_challenge);
@@ -64,7 +64,7 @@ TYPED_TEST(ShplonkTest, ShplonkSimple)
     opening_claims.emplace_back(OpeningClaim{ opening_pairs[0], commitment1 });
     opening_claims.emplace_back(OpeningClaim{ opening_pairs[1], commitment2 });
 
-    auto verifier_transcript = BaseTranscript::verifier_init_empty(prover_transcript);
+    auto verifier_transcript = NativeTranscript::verifier_init_empty(prover_transcript);
 
     // Execute the shplonk verifier functionality
     const auto verifier_claim = ShplonkVerifier::reduce_verification(this->vk(), opening_claims, verifier_transcript);