From e480a587917ee5688904476eb94dd30ab1618f0d Mon Sep 17 00:00:00 2001
From: codygunton <codygunton@gmail.com>
Date: Tue, 10 Sep 2024 21:49:59 +0000
Subject: [PATCH] Fold alphas [no-ci]

---
 .../utils/batch_mul_native.hpp                | 14 +++++++++++
 .../protogalaxy/protogalaxy_verifier.cpp      | 24 +++++++------------
 .../barretenberg/ultra_honk/decider_keys.hpp  | 15 ++++++++++++
 3 files changed, 38 insertions(+), 15 deletions(-)

diff --git a/barretenberg/cpp/src/barretenberg/commitment_schemes/utils/batch_mul_native.hpp b/barretenberg/cpp/src/barretenberg/commitment_schemes/utils/batch_mul_native.hpp
index 7ae350363e4a..507e2a6d2ba8 100644
--- a/barretenberg/cpp/src/barretenberg/commitment_schemes/utils/batch_mul_native.hpp
+++ b/barretenberg/cpp/src/barretenberg/commitment_schemes/utils/batch_mul_native.hpp
@@ -34,4 +34,18 @@ static Commitment batch_mul_native(const std::vector<Commitment>& _points, const
     }
     return result;
 }
+
+/**
+ * @brief Utility for native batch multiplication of group elements
+ * @note This is used only for native verification and is not optimized for efficiency
+ */
+template <typename FF> static FF linear_combination(const std::vector<FF>& as, const std::vector<FF>& bs)
+{
+    FF result = as[0] * bs[0];
+    for (size_t idx = 1; idx < as.size(); ++idx) {
+        result += as[idx] * bs[idx];
+    }
+    return result;
+}
+
 } // namespace bb
diff --git a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
index aefcd02c92d9..0b8ce58db3e8 100644
--- a/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
+++ b/barretenberg/cpp/src/barretenberg/protogalaxy/protogalaxy_verifier.cpp
@@ -121,28 +121,22 @@ std::shared_ptr<typename DeciderVerificationKeys::DeciderVK> ProtogalaxyVerifier
         update_gate_challenges(perturbator_challenge, accumulator->gate_challenges, deltas);
 
     // // Fold the commitments
-    size_t commitment_idx = 0;
+    idx = 0;
     for (auto& folded_commitment : next_accumulator->verification_key->get_all()) {
-        folded_commitment =
-            batch_mul_native(keys_to_fold.get_precomputed_commitments_at_index(commitment_idx), lagranges);
-        commitment_idx++;
+        folded_commitment = batch_mul_native(keys_to_fold.get_precomputed_commitments_at_index(idx), lagranges);
+        idx++;
     }
-    commitment_idx = 0;
+    idx = 0;
     for (auto& folded_commitment : next_accumulator->witness_commitments.get_all()) {
-        folded_commitment = batch_mul_native(keys_to_fold.get_witness_commitments_at_index(commitment_idx), lagranges);
-        commitment_idx++;
+        folded_commitment = batch_mul_native(keys_to_fold.get_witness_commitments_at_index(idx), lagranges);
+        idx++;
     }
 
     // Fold the relation parameters
-    size_t alpha_idx = 0;
+    idx = 0;
     for (auto& alpha : next_accumulator->alphas) {
-        alpha = FF(0);
-        size_t vk_idx = 0;
-        for (auto& key : keys_to_fold) {
-            alpha += key->alphas[alpha_idx] * lagranges[vk_idx];
-            vk_idx++;
-        }
-        alpha_idx++;
+        alpha = linear_combination(keys_to_fold.get_alphas_at_index(idx), lagranges);
+        idx++;
     }
     auto& expected_parameters = next_accumulator->relation_parameters;
     for (size_t vk_idx = 0; vk_idx < NUM_KEYS; vk_idx++) {
diff --git a/barretenberg/cpp/src/barretenberg/ultra_honk/decider_keys.hpp b/barretenberg/cpp/src/barretenberg/ultra_honk/decider_keys.hpp
index 0736603b0b19..c39ebe74d37d 100644
--- a/barretenberg/cpp/src/barretenberg/ultra_honk/decider_keys.hpp
+++ b/barretenberg/cpp/src/barretenberg/ultra_honk/decider_keys.hpp
@@ -86,6 +86,7 @@ template <typename Flavor_, size_t NUM_ = 2> struct DeciderProvingKeys_ {
 template <typename Flavor_, size_t NUM_ = 2> struct DeciderVerificationKeys_ {
     static_assert(NUM_ > 1, "Must have at least two decider verification keys.");
     using Flavor = Flavor_;
+    using FF = typename Flavor_::FF;
     using Commitment = typename Flavor_::Commitment;
     using VerificationKey = typename Flavor::VerificationKey;
     using DeciderVK = DeciderVerificationKey_<Flavor>;
@@ -141,5 +142,19 @@ template <typename Flavor_, size_t NUM_ = 2> struct DeciderVerificationKeys_ {
 
         return result;
     }
+
+    /**
+     * @brief Get the witness commitments at a given index
+     * @details This is similar to get_precomputed_commitments_at_index, but for witness commitments.
+     */
+    std::vector<FF> get_alphas_at_index(const size_t idx) const
+    {
+        std::vector<FF> result(NUM);
+        for (auto [elt, key] : zip_view(result, _data)) {
+            elt = key->alphas[idx];
+        }
+
+        return result;
+    }
 };
 } // namespace bb