fix: set denominator to 1 during verification of dsl/big-field divisi…

…on (#5188)

This PR solve the verification issue with bigint division in Noir:
noir-lang/noir#4530

---------

Co-authored-by: Tom French <15848336+TomAFrench@users.noreply.github.com>
Co-authored-by: Rumata888 <isennovskiy@gmail.com>

barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.cpp

@@ -100,11 +100,12 @@ void build_constraints(Builder& builder, AcirFormat const& constraint_system, bo
 
     // Add big_int constraints
     DSLBigInts<Builder> dsl_bigints;
+    dsl_bigints.set_builder(&builder);
     for (const auto& constraint : constraint_system.bigint_from_le_bytes_constraints) {
         create_bigint_from_le_bytes_constraint(builder, constraint, dsl_bigints);
     }
     for (const auto& constraint : constraint_system.bigint_operations) {
-        create_bigint_operations_constraint<Builder>(constraint, dsl_bigints);
+        create_bigint_operations_constraint<Builder>(constraint, dsl_bigints, has_valid_witness_assignments);
     }
     for (const auto& constraint : constraint_system.bigint_to_le_bytes_constraints) {
         create_bigint_to_le_bytes_constraint(builder, constraint, dsl_bigints);

barretenberg/cpp/src/barretenberg/dsl/acir_format/bigint_constraint.cpp

@@ -2,6 +2,7 @@
 #include "barretenberg/common/assert.hpp"
 #include "barretenberg/dsl/types.hpp"
 #include "barretenberg/numeric/uint256/uint256.hpp"
+#include "barretenberg/numeric/uintx/uintx.hpp"
 #include "barretenberg/stdlib/primitives/bigfield/bigfield.hpp"
 #include <cstddef>
 #include <cstdint>
@@ -34,14 +35,16 @@ ModulusId modulus_param_to_id(ModulusParam param)
         secp256r1::FrParams::modulus_2 == param.modulus_2 && secp256r1::FrParams::modulus_3 == param.modulus_3) {
         return ModulusId::SECP256R1_FR;
     }
-
     return ModulusId::UNKNOWN;
 }
 
 template void create_bigint_operations_constraint<UltraCircuitBuilder>(const BigIntOperation& input,
-                                                                       DSLBigInts<UltraCircuitBuilder>& dsl_bigint);
+                                                                       DSLBigInts<UltraCircuitBuilder>& dsl_bigint,
+                                                                       bool has_valid_witness_assignments);
 template void create_bigint_operations_constraint<GoblinUltraCircuitBuilder>(
-    const BigIntOperation& input, DSLBigInts<GoblinUltraCircuitBuilder>& dsl_bigint);
+    const BigIntOperation& input,
+    DSLBigInts<GoblinUltraCircuitBuilder>& dsl_bigint,
+    bool has_valid_witness_assignments);
 template void create_bigint_addition_constraint<UltraCircuitBuilder>(const BigIntOperation& input,
                                                                      DSLBigInts<UltraCircuitBuilder>& dsl_bigint);
 template void create_bigint_addition_constraint<GoblinUltraCircuitBuilder>(
@@ -55,9 +58,11 @@ template void create_bigint_mul_constraint<UltraCircuitBuilder>(const BigIntOper
 template void create_bigint_mul_constraint<GoblinUltraCircuitBuilder>(
     const BigIntOperation& input, DSLBigInts<GoblinUltraCircuitBuilder>& dsl_bigint);
 template void create_bigint_div_constraint<UltraCircuitBuilder>(const BigIntOperation& input,
-                                                                DSLBigInts<UltraCircuitBuilder>& dsl_bigint);
-template void create_bigint_div_constraint<GoblinUltraCircuitBuilder>(
-    const BigIntOperation& input, DSLBigInts<GoblinUltraCircuitBuilder>& dsl_bigint);
+                                                                DSLBigInts<UltraCircuitBuilder>& dsl_bigint,
+                                                                bool has_valid_witness_assignments);
+template void create_bigint_div_constraint<GoblinUltraCircuitBuilder>(const BigIntOperation& input,
+                                                                      DSLBigInts<GoblinUltraCircuitBuilder>& dsl_bigint,
+                                                                      bool has_valid_witness_assignments);
 
 template <typename Builder>
 void create_bigint_addition_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigint)
@@ -198,8 +203,18 @@ void create_bigint_mul_constraint(const BigIntOperation& input, DSLBigInts<Build
 }
 
 template <typename Builder>
-void create_bigint_div_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigint)
+void create_bigint_div_constraint(const BigIntOperation& input,
+                                  DSLBigInts<Builder>& dsl_bigint,
+                                  bool has_valid_witness_assignments)
 {
+    if (!has_valid_witness_assignments) {
+        // Asserts catch the case where the divisor is zero, so we need to provide a different value (1) to avoid the
+        // assert
+        std::array<uint32_t, 5> limbs_idx;
+        dsl_bigint.get_witness_idx_of_limbs(input.rhs, limbs_idx);
+        dsl_bigint.set_value(1, limbs_idx);
+    }
+
     switch (dsl_bigint.get_modulus_id(input.lhs)) {
     case ModulusId::BN254_FR: {
         auto lhs = dsl_bigint.bn254_fr(input.lhs);
@@ -244,7 +259,9 @@ void create_bigint_div_constraint(const BigIntOperation& input, DSLBigInts<Build
 }
 
 template <typename Builder>
-void create_bigint_operations_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigint)
+void create_bigint_operations_constraint(const BigIntOperation& input,
+                                         DSLBigInts<Builder>& dsl_bigint,
+                                         bool has_valid_witness_assignments)
 {
     switch (input.opcode) {
     case BigIntOperationType::Add: {
@@ -260,7 +277,7 @@ void create_bigint_operations_constraint(const BigIntOperation& input, DSLBigInt
         break;
     }
     case BigIntOperationType::Div: {
-        create_bigint_div_constraint<Builder>(input, dsl_bigint);
+        create_bigint_div_constraint<Builder>(input, dsl_bigint, has_valid_witness_assignments);
         break;
     }
     default: {

barretenberg/cpp/src/barretenberg/dsl/acir_format/bigint_constraint.hpp

@@ -1,6 +1,8 @@
 #pragma once
 #include "barretenberg/dsl/types.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
+
+#include <array>
 #include <cstdint>
 #include <vector>
 
@@ -77,9 +79,13 @@ template <typename Builder> class DSLBigInts {
     std::map<uint32_t, big_secp256r1_fq> m_secp256r1_fq;
     std::map<uint32_t, big_secp256r1_fr> m_secp256r1_fr;
 
+    Builder* builder;
+
   public:
     DSLBigInts() = default;
 
+    void set_builder(Builder* ctx) { builder = ctx; }
+
     ModulusId get_modulus_id(uint32_t bigint_id)
     {
         if (this->m_bn254_fq.contains(bigint_id)) {
@@ -104,6 +110,62 @@ template <typename Builder> class DSLBigInts {
         return ModulusId::UNKNOWN;
     }
 
+    /// Set value of the witnesses representing the bigfield element
+    /// so that the bigfield value is the input value.
+    /// The input value is decomposed into the binary basis for the binary limbs
+    /// The input array must be:
+    /// the 4 witness index of the binary limbs, and the index of the prime limb
+    void set_value(uint256_t value, const std::array<uint32_t, 5> limbs_idx)
+    {
+        uint256_t limb_modulus = uint256_t(1) << big_bn254_fq::NUM_LIMB_BITS;
+        builder->variables[limbs_idx[4]] = value;
+        for (uint32_t i = 0; i < 4; i++) {
+            uint256_t limb = value % limb_modulus;
+            value = (value - limb) / limb_modulus;
+            builder->variables[limbs_idx[i]] = limb;
+        }
+    }
+
+    /// Utility function that retrieve the witness indexes of a bigfield element
+    /// for use in set_value()
+    void get_witness_idx_of_limbs(uint32_t bigint_id, std::array<uint32_t, 5>& limbs_idx)
+    {
+        if (m_bn254_fr.contains(bigint_id)) {
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = m_bn254_fr[bigint_id].binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = m_bn254_fr[bigint_id].prime_basis_limb.witness_index;
+        } else if (m_bn254_fq.contains(bigint_id)) {
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = m_bn254_fq[bigint_id].binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = m_bn254_fq[bigint_id].prime_basis_limb.witness_index;
+        } else if (m_secp256k1_fq.contains(bigint_id)) {
+            auto big_field = m_secp256k1_fq[bigint_id];
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = big_field.binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = big_field.prime_basis_limb.witness_index;
+        } else if (m_secp256k1_fr.contains(bigint_id)) {
+            auto big_field = m_secp256k1_fr[bigint_id];
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = big_field.binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = big_field.prime_basis_limb.witness_index;
+        } else if (m_secp256r1_fr.contains(bigint_id)) {
+            auto big_field = m_secp256r1_fr[bigint_id];
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = big_field.binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = big_field.prime_basis_limb.witness_index;
+        } else if (m_secp256r1_fq.contains(bigint_id)) {
+            auto big_field = m_secp256r1_fq[bigint_id];
+            for (uint32_t i = 0; i < 4; i++) {
+                limbs_idx[i] = big_field.binary_basis_limbs[i].element.witness_index;
+            }
+            limbs_idx[4] = big_field.prime_basis_limb.witness_index;
+        }
+    }
     big_bn254_fr bn254_fr(uint32_t bigint_id)
     {
         if (this->m_bn254_fr.contains(bigint_id)) {
@@ -192,14 +254,14 @@ void create_bigint_to_le_bytes_constraint(Builder& builder,
                                           DSLBigInts<Builder>& dsl_bigints);
 
 template <typename Builder>
-void create_bigint_operations_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints);
+void create_bigint_operations_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints, bool);
 template <typename Builder>
 void create_bigint_addition_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints);
 template <typename Builder>
 void create_bigint_sub_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints);
 template <typename Builder>
 void create_bigint_mul_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints);
 template <typename Builder>
-void create_bigint_div_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints);
+void create_bigint_div_constraint(const BigIntOperation& input, DSLBigInts<Builder>& dsl_bigints, bool);
 
 } // namespace acir_format

barretenberg/cpp/src/barretenberg/dsl/acir_format/bigint_constraint.test.cpp

@@ -392,4 +392,78 @@ TEST_F(BigIntTests, TestBigIntConstraintReuse2)
     EXPECT_EQ(verifier.verify_proof(proof), true);
 }
 
+TEST_F(BigIntTests, TestBigIntDIV)
+{
+    // 6 / 3 = 2
+    // 6 = bigint(1) = from_bytes(w(1))
+    // 3 = bigint(2) = from_bytes(w(2))
+    // 2 = bigint(3) = to_bytes(w(3))
+    BigIntOperation div_constraint{
+        .lhs = 1,
+        .rhs = 2,
+        .result = 3,
+        .opcode = BigIntOperationType::Div,
+    };
+
+    BigIntFromLeBytes from_le_bytes_constraint_bigint1{
+        .inputs = { 1 },
+        .modulus = { 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF, 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA,
+                     0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF },
+        .result = 1,
+    };
+    BigIntFromLeBytes from_le_bytes_constraint_bigint2{
+        .inputs = { 2 },
+        .modulus = { 0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF, 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA,
+                     0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF },
+        .result = 2,
+    };
+
+    BigIntToLeBytes result3_to_le_bytes{
+        .input = 3, .result = { 3 }, //
+    };
+
+    AcirFormat constraint_system{
+        .varnum = 5,
+        .recursive = false,
+        .public_inputs = {},
+        .logic_constraints = {},
+        .range_constraints = {},
+        .sha256_constraints = {},
+        .sha256_compression = {},
+        .schnorr_constraints = {},
+        .ecdsa_k1_constraints = {},
+        .ecdsa_r1_constraints = {},
+        .blake2s_constraints = {},
+        .blake3_constraints = {},
+        .keccak_constraints = {},
+        .keccak_var_constraints = {},
+        .keccak_permutations = {},
+        .pedersen_constraints = {},
+        .pedersen_hash_constraints = {},
+        .poseidon2_constraints = {},
+        .fixed_base_scalar_mul_constraints = {},
+        .ec_add_constraints = {},
+        .recursion_constraints = {},
+        .bigint_from_le_bytes_constraints = { from_le_bytes_constraint_bigint1, from_le_bytes_constraint_bigint2 },
+        .bigint_to_le_bytes_constraints = { result3_to_le_bytes },
+        .bigint_operations = { div_constraint },
+        .constraints = {},
+        .block_constraints = {},
+
+    };
+
+    WitnessVector witness{
+        0, 6, 3, 2, 0,
+    };
+    auto builder = create_circuit(constraint_system, /*size_hint*/ 0, witness);
+    auto composer = Composer();
+    auto prover = composer.create_ultra_with_keccak_prover(builder);
+    auto proof = prover.construct_proof();
+    EXPECT_TRUE(CircuitChecker::check(builder));
+
+    auto builder2 = create_circuit(constraint_system, /*size_hint*/ 0, WitnessVector{});
+    EXPECT_TRUE(CircuitChecker::check(builder));
+    auto verifier2 = composer.create_ultra_with_keccak_verifier(builder);
+    EXPECT_EQ(verifier2.verify_proof(proof), true);
+}
 } // namespace acir_format::tests