diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.test.cpp
index 6085671fb0a..511228ac251 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_format.test.cpp
@@ -107,8 +107,8 @@ TEST_F(AcirFormatTests, TestLogicGateFromNoirCircuit)
     };
 
     LogicConstraint logic_constraint{
-        .a = 0,
-        .b = 1,
+        .a = WitnessOrConstant<bb::fr>::from_index(0),
+        .b = WitnessOrConstant<bb::fr>::from_index(1),
         .result = 2,
         .num_bits = 32,
         .is_xor_gate = 1,
@@ -510,7 +510,33 @@ TEST_F(AcirFormatTests, TestKeccakPermutation)
 {
     Keccakf1600
         keccak_permutation{
-            .state = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25 },
+             .state = { 
+                WitnessOrConstant<bb::fr>::from_index(1),
+                WitnessOrConstant<bb::fr>::from_index(2),
+                WitnessOrConstant<bb::fr>::from_index(3),
+                WitnessOrConstant<bb::fr>::from_index(4),
+                WitnessOrConstant<bb::fr>::from_index(5),
+                WitnessOrConstant<bb::fr>::from_index(6),
+                WitnessOrConstant<bb::fr>::from_index(7),
+                WitnessOrConstant<bb::fr>::from_index(8),
+                WitnessOrConstant<bb::fr>::from_index(9),
+                WitnessOrConstant<bb::fr>::from_index(10),
+                WitnessOrConstant<bb::fr>::from_index(11),
+                WitnessOrConstant<bb::fr>::from_index(12),
+                WitnessOrConstant<bb::fr>::from_index(13),
+                WitnessOrConstant<bb::fr>::from_index(14),
+                WitnessOrConstant<bb::fr>::from_index(15),
+                WitnessOrConstant<bb::fr>::from_index(16),
+                WitnessOrConstant<bb::fr>::from_index(17),
+                WitnessOrConstant<bb::fr>::from_index(18),
+                WitnessOrConstant<bb::fr>::from_index(19),
+                WitnessOrConstant<bb::fr>::from_index(20),
+                WitnessOrConstant<bb::fr>::from_index(21),
+                WitnessOrConstant<bb::fr>::from_index(22),
+                WitnessOrConstant<bb::fr>::from_index(23),
+                WitnessOrConstant<bb::fr>::from_index(24),
+                WitnessOrConstant<bb::fr>::from_index(25),
+ },
             .result = { 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
                         39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 },
         };
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_to_constraint_buf.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_to_constraint_buf.cpp
index 2a7882a2080..d50bcd90495 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_to_constraint_buf.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/acir_to_constraint_buf.cpp
@@ -195,19 +195,19 @@ uint32_t get_witness_from_function_input(Program::FunctionInput input)
     return input_witness.value.value;
 }
 
-WitnessConstant<bb::fr> parse_input(Program::FunctionInput input)
+WitnessOrConstant<bb::fr> parse_input(Program::FunctionInput input)
 {
-    WitnessConstant result = std::visit(
+    WitnessOrConstant result = std::visit(
         [&](auto&& e) {
             using T = std::decay_t<decltype(e)>;
             if constexpr (std::is_same_v<T, Program::ConstantOrWitnessEnum::Witness>) {
-                return WitnessConstant<bb::fr>{
+                return WitnessOrConstant<bb::fr>{
                     .index = e.value.value,
                     .value = bb::fr::zero(),
                     .is_constant = false,
                 };
             } else if constexpr (std::is_same_v<T, Program::ConstantOrWitnessEnum::Constant>) {
-                return WitnessConstant<bb::fr>{
+                return WitnessOrConstant<bb::fr>{
                     .index = 0,
                     .value = uint256_t(e.value),
                     .is_constant = true,
@@ -215,7 +215,7 @@ WitnessConstant<bb::fr> parse_input(Program::FunctionInput input)
             } else {
                 ASSERT(false);
             }
-            return WitnessConstant<bb::fr>{
+            return WitnessOrConstant<bb::fr>{
                 .index = 0,
                 .value = bb::fr::zero(),
                 .is_constant = true,
@@ -223,33 +223,6 @@ WitnessConstant<bb::fr> parse_input(Program::FunctionInput input)
         },
         input.input.value);
     return result;
-
-    // WitnessConstant result = std::visit(
-    //     [&](auto&& e) {
-    //         using T = std::decay_t<decltype(e)>;
-    //         if constexpr (std::is_same_v<T, Program::FunctionInput::Witness>) {
-    //             return WitnessConstant<bb::fr>{
-    //                 .index = e.value.witness.value,
-    //                 .value = bb::fr::zero(),
-    //                 .is_constant = false,
-    //             };
-    //         } else if constexpr (std::is_same_v<T, Program::FunctionInput::Constant>) {
-    //             return WitnessConstant<bb::fr>{
-    //                 .index = 0,
-    //                 .value = uint256_t(e.value.constant),
-    //                 .is_constant = true,
-    //             };
-    //         } else {
-    //             ASSERT(false);
-    //         }
-    //         return WitnessConstant<bb::fr>{
-    //             .index = 0,
-    //             .value = bb::fr::zero(),
-    //             .is_constant = true,
-    //         };
-    //     },
-    //     input.value);
-    // return result;
 }
 
 void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
@@ -261,8 +234,8 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
         [&](auto&& arg) {
             using T = std::decay_t<decltype(arg)>;
             if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::AND>) {
-                auto lhs_input = get_witness_from_function_input(arg.lhs);
-                auto rhs_input = get_witness_from_function_input(arg.rhs);
+                auto lhs_input = parse_input(arg.lhs);
+                auto rhs_input = parse_input(arg.rhs);
                 af.logic_constraints.push_back(LogicConstraint{
                     .a = lhs_input,
                     .b = rhs_input,
@@ -272,8 +245,8 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 });
                 af.original_opcode_indices.logic_constraints.push_back(opcode_index);
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::XOR>) {
-                auto lhs_input = get_witness_from_function_input(arg.lhs);
-                auto rhs_input = get_witness_from_function_input(arg.rhs);
+                auto lhs_input = parse_input(arg.lhs);
+                auto rhs_input = parse_input(arg.rhs);
                 af.logic_constraints.push_back(LogicConstraint{
                     .a = lhs_input,
                     .b = rhs_input,
@@ -292,29 +265,9 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
 
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::AES128Encrypt>) {
                 af.aes128_constraints.push_back(AES128Constraint{
-                    .inputs = map(arg.inputs,
-                                  [](auto& e) {
-                                      return AES128Input{
-                                          .witness = get_witness_from_function_input(e),
-                                          .num_bits = e.num_bits,
-                                      };
-                                  }),
-                    .iv = map(arg.iv,
-                              [](auto& e) {
-                                  auto witness = get_witness_from_function_input(e);
-                                  return AES128Input{
-                                      .witness = witness,
-                                      .num_bits = e.num_bits,
-                                  };
-                              }),
-                    .key = map(arg.key,
-                               [](auto& e) {
-                                   auto input_witness = get_witness_from_function_input(e);
-                                   return AES128Input{
-                                       .witness = input_witness,
-                                       .num_bits = e.num_bits,
-                                   };
-                               }),
+                    .inputs = map(arg.inputs, [](auto& e) { return parse_input(e); }),
+                    .iv = map(arg.iv, [](auto& e) { return parse_input(e); }),
+                    .key = map(arg.key, [](auto& e) { return parse_input(e); }),
                     .outputs = map(arg.outputs, [](auto& e) { return e.value; }),
                 });
                 af.original_opcode_indices.aes128_constraints.push_back(opcode_index);
@@ -335,22 +288,8 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
 
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::Sha256Compression>) {
                 af.sha256_compression.push_back(Sha256Compression{
-                    .inputs = map(arg.inputs,
-                                  [](auto& e) {
-                                      auto input_witness = get_witness_from_function_input(e);
-                                      return Sha256Input{
-                                          .witness = input_witness,
-                                          .num_bits = e.num_bits,
-                                      };
-                                  }),
-                    .hash_values = map(arg.hash_values,
-                                       [](auto& e) {
-                                           auto input_witness = get_witness_from_function_input(e);
-                                           return Sha256Input{
-                                               .witness = input_witness,
-                                               .num_bits = e.num_bits,
-                                           };
-                                       }),
+                    .inputs = map(arg.inputs, [](auto& e) { return parse_input(e); }),
+                    .hash_values = map(arg.hash_values, [](auto& e) { return parse_input(e); }),
                     .result = map(arg.outputs, [](auto& e) { return e.value; }),
                 });
                 af.original_opcode_indices.sha256_compression.push_back(opcode_index);
@@ -358,9 +297,8 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 af.blake2s_constraints.push_back(Blake2sConstraint{
                     .inputs = map(arg.inputs,
                                   [](auto& e) {
-                                      auto input_witness = get_witness_from_function_input(e);
                                       return Blake2sInput{
-                                          .witness = input_witness,
+                                          .blackbox_input = parse_input(e),
                                           .num_bits = e.num_bits,
                                       };
                                   }),
@@ -371,9 +309,8 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 af.blake3_constraints.push_back(Blake3Constraint{
                     .inputs = map(arg.inputs,
                                   [](auto& e) {
-                                      auto input_witness = get_witness_from_function_input(e);
                                       return Blake3Input{
-                                          .witness = input_witness,
+                                          .blackbox_input = parse_input(e),
                                           .num_bits = e.num_bits,
                                       };
                                   }),
@@ -437,12 +374,12 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 });
                 af.original_opcode_indices.multi_scalar_mul_constraints.push_back(opcode_index);
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::EmbeddedCurveAdd>) {
-                auto input_1_x = get_witness_from_function_input(arg.input1[0]);
-                auto input_1_y = get_witness_from_function_input(arg.input1[1]);
-                auto input_1_infinite = get_witness_from_function_input(arg.input1[2]);
-                auto input_2_x = get_witness_from_function_input(arg.input2[0]);
-                auto input_2_y = get_witness_from_function_input(arg.input2[1]);
-                auto input_2_infinite = get_witness_from_function_input(arg.input2[2]);
+                auto input_1_x = parse_input(arg.input1[0]);
+                auto input_1_y = parse_input(arg.input1[1]);
+                auto input_1_infinite = parse_input(arg.input1[2]);
+                auto input_2_x = parse_input(arg.input2[0]);
+                auto input_2_y = parse_input(arg.input2[1]);
+                auto input_2_infinite = parse_input(arg.input2[2]);
 
                 af.ec_add_constraints.push_back(EcAdd{
                     .input1_x = input_1_x,
@@ -473,11 +410,7 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 af.original_opcode_indices.keccak_constraints.push_back(opcode_index);
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::Keccakf1600>) {
                 af.keccak_permutations.push_back(Keccakf1600{
-                    .state = map(arg.inputs,
-                                 [](auto& e) {
-                                     auto input_witness = get_witness_from_function_input(e);
-                                     return input_witness;
-                                 }),
+                    .state = map(arg.inputs, [](auto& e) { return parse_input(e); }),
                     .result = map(arg.outputs, [](auto& e) { return e.value; }),
                 });
                 af.original_opcode_indices.keccak_permutations.push_back(opcode_index);
@@ -551,11 +484,7 @@ void handle_blackbox_func_call(Program::Opcode::BlackBoxFuncCall const& arg,
                 af.original_opcode_indices.bigint_operations.push_back(opcode_index);
             } else if constexpr (std::is_same_v<T, Program::BlackBoxFuncCall::Poseidon2Permutation>) {
                 af.poseidon2_constraints.push_back(Poseidon2Constraint{
-                    .state = map(arg.inputs,
-                                 [](auto& e) {
-                                     auto input_witness = get_witness_from_function_input(e);
-                                     return input_witness;
-                                 }),
+                    .state = map(arg.inputs, [](auto& e) { return parse_input(e); }),
                     .result = map(arg.outputs, [](auto& e) { return e.value; }),
                     .len = arg.len,
                 });
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.cpp
index c835322b52c..1605cf8eaf7 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.cpp
@@ -1,4 +1,5 @@
 #include "aes128_constraint.hpp"
+#include "barretenberg/dsl/acir_format/acir_format.hpp"
 #include "barretenberg/stdlib/encryption/aes128/aes128.hpp"
 #include <cstdint>
 #include <cstdio>
@@ -14,20 +15,21 @@ template <typename Builder> void create_aes128_constraints(Builder& builder, con
     using field_ct = bb::stdlib::field_t<Builder>;
 
     // Packs 16 bytes from the inputs (plaintext, iv, key) into a field element
-    const auto convert_input = [&](std::span<const AES128Input, std::dynamic_extent> inputs, size_t padding) {
-        field_ct converted = 0;
-        for (size_t i = 0; i < 16 - padding; ++i) {
-            converted *= 256;
-            field_ct byte = field_ct::from_witness_index(&builder, inputs[i].witness);
-            converted += byte;
-        }
-        for (size_t i = 0; i < padding; ++i) {
-            converted *= 256;
-            field_ct byte = padding;
-            converted += byte;
-        }
-        return converted;
-    };
+    const auto convert_input =
+        [&](std::span<const WitnessOrConstant<bb::fr>, std::dynamic_extent> inputs, size_t padding, Builder& builder) {
+            field_ct converted = 0;
+            for (size_t i = 0; i < 16 - padding; ++i) {
+                converted *= 256;
+                field_ct byte = to_field_ct(inputs[i], builder);
+                converted += byte;
+            }
+            for (size_t i = 0; i < padding; ++i) {
+                converted *= 256;
+                field_ct byte = padding;
+                converted += byte;
+            }
+            return converted;
+        };
 
     // Packs 16 bytes from the outputs (witness indexes) into a field element for comparison
     const auto convert_output = [&](std::span<const uint32_t, 16> outputs) {
@@ -47,11 +49,14 @@ template <typename Builder> void create_aes128_constraints(Builder& builder, con
     for (size_t i = 0; i < constraint.inputs.size(); i += 16) {
         field_ct to_add;
         if (i + 16 > constraint.inputs.size()) {
-            to_add = convert_input(
-                std::span<const AES128Input, std::dynamic_extent>{ &constraint.inputs[i], 16 - padding_size },
-                padding_size);
+            to_add =
+                convert_input(std::span<const WitnessOrConstant<bb::fr>, std::dynamic_extent>{ &constraint.inputs[i],
+                                                                                               16 - padding_size },
+                              padding_size,
+                              builder);
         } else {
-            to_add = convert_input(std::span<const AES128Input, 16>{ &constraint.inputs[i], 16 }, 0);
+            to_add =
+                convert_input(std::span<const WitnessOrConstant<bb::fr>, 16>{ &constraint.inputs[i], 16 }, 0, builder);
         }
         converted_inputs.emplace_back(to_add);
     }
@@ -63,7 +68,7 @@ template <typename Builder> void create_aes128_constraints(Builder& builder, con
     }
 
     const std::vector<field_ct> output_bytes = bb::stdlib::aes128::encrypt_buffer_cbc<Builder>(
-        converted_inputs, convert_input(constraint.iv, 0), convert_input(constraint.key, 0));
+        converted_inputs, convert_input(constraint.iv, 0, builder), convert_input(constraint.key, 0, builder));
 
     for (size_t i = 0; i < output_bytes.size(); ++i) {
         builder.assert_equal(output_bytes[i].normalize().witness_index, converted_outputs[i].normalize().witness_index);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.hpp
index 3149210a8be..fe3a78c058f 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/aes128_constraint.hpp
@@ -1,5 +1,7 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
+#include "barretenberg/stdlib/primitives/field/field.hpp"
 #include <array>
 #include <cstdint>
 #include <vector>
@@ -16,9 +18,9 @@ struct AES128Input {
 };
 
 struct AES128Constraint {
-    std::vector<AES128Input> inputs;
-    std::array<AES128Input, 16> iv;
-    std::array<AES128Input, 16> key;
+    std::vector<WitnessOrConstant<bb::fr>> inputs;
+    std::array<WitnessOrConstant<bb::fr>, 16> iv;
+    std::array<WitnessOrConstant<bb::fr>, 16> key;
     std::vector<uint32_t> outputs;
 
     // For serialization, update with any new fields
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.cpp
index f38b1e2b0dc..00978243476 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.cpp
@@ -18,13 +18,13 @@ template <typename Builder> void create_blake2s_constraints(Builder& builder, co
     // Get the witness assignment for each witness index
     // Write the witness assignment to the byte_array
     for (const auto& witness_index_num_bits : constraint.inputs) {
-        auto witness_index = witness_index_num_bits.witness;
+        auto witness_index = witness_index_num_bits.blackbox_input;
         auto num_bits = witness_index_num_bits.num_bits;
 
         // XXX: The implementation requires us to truncate the element to the nearest byte and not bit
         auto num_bytes = round_to_nearest_byte(num_bits);
 
-        field_ct element = field_ct::from_witness_index(&builder, witness_index);
+        field_ct element = to_field_ct(witness_index, builder);
         byte_array_ct element_bytes(element, num_bytes);
 
         arr.write(element_bytes);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.hpp
index d0fd67eaa55..10f10f69af2 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake2s_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <array>
 #include <cstdint>
@@ -7,11 +8,11 @@
 namespace acir_format {
 
 struct Blake2sInput {
-    uint32_t witness;
+    WitnessOrConstant<bb::fr> blackbox_input;
     uint32_t num_bits;
 
     // For serialization, update with any new fields
-    MSGPACK_FIELDS(witness, num_bits);
+    MSGPACK_FIELDS(blackbox_input, num_bits);
     friend bool operator==(Blake2sInput const& lhs, Blake2sInput const& rhs) = default;
 };
 
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.cpp
index 71fc56301a1..94cb3845e06 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.cpp
@@ -16,13 +16,13 @@ template <typename Builder> void create_blake3_constraints(Builder& builder, con
     // Get the witness assignment for each witness index
     // Write the witness assignment to the byte_array
     for (const auto& witness_index_num_bits : constraint.inputs) {
-        auto witness_index = witness_index_num_bits.witness;
+        auto witness_index = witness_index_num_bits.blackbox_input;
         auto num_bits = witness_index_num_bits.num_bits;
 
         // XXX: The implementation requires us to truncate the element to the nearest byte and not bit
         auto num_bytes = round_to_nearest_byte(num_bits);
 
-        field_ct element = field_ct::from_witness_index(&builder, witness_index);
+        field_ct element = to_field_ct(witness_index, builder);
         byte_array_ct element_bytes(element, num_bytes);
 
         arr.write(element_bytes);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.hpp
index f5a9c0e546b..2a0ebc3835c 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/blake3_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <array>
 #include <cstdint>
@@ -7,11 +8,11 @@
 namespace acir_format {
 
 struct Blake3Input {
-    uint32_t witness;
+    WitnessOrConstant<bb::fr> blackbox_input;
     uint32_t num_bits;
 
     // For serialization, update with any new fields
-    MSGPACK_FIELDS(witness, num_bits);
+    MSGPACK_FIELDS(blackbox_input, num_bits);
     friend bool operator==(Blake3Input const& lhs, Blake3Input const& rhs) = default;
 };
 
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.cpp
index 86bde0342fe..cd05eb150ac 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.cpp
@@ -12,24 +12,39 @@ void create_ec_add_constraint(Builder& builder, const EcAdd& input, bool has_val
 {
     // Input to cycle_group points
     using cycle_group_ct = bb::stdlib::cycle_group<Builder>;
-    using field_ct = bb::stdlib::field_t<Builder>;
     using bool_ct = bb::stdlib::bool_t<Builder>;
 
-    auto x1 = field_ct::from_witness_index(&builder, input.input1_x);
-    auto y1 = field_ct::from_witness_index(&builder, input.input1_y);
-    auto x2 = field_ct::from_witness_index(&builder, input.input2_x);
-    auto y2 = field_ct::from_witness_index(&builder, input.input2_y);
-    auto infinite1 = bool_ct(field_ct::from_witness_index(&builder, input.input1_infinite));
-    auto infinite2 = bool_ct(field_ct::from_witness_index(&builder, input.input2_infinite));
+    auto x1 = to_field_ct(input.input1_x, builder);
+    auto y1 = to_field_ct(input.input1_y, builder);
+    auto x2 = to_field_ct(input.input2_x, builder);
+
+    auto y2 = to_field_ct(input.input2_y, builder);
+
+    auto infinite1 = bool_ct(to_field_ct(input.input1_infinite, builder));
+
+    auto infinite2 = bool_ct(to_field_ct(input.input2_infinite, builder));
+
     if (!has_valid_witness_assignments) {
         auto g1 = bb::grumpkin::g1::affine_one;
         // We need to have correct values representing points on the curve
-        builder.variables[input.input1_x] = g1.x;
-        builder.variables[input.input1_y] = g1.y;
-        builder.variables[input.input1_infinite] = bb::fr(0);
-        builder.variables[input.input2_x] = g1.x;
-        builder.variables[input.input2_y] = g1.y;
-        builder.variables[input.input2_infinite] = bb::fr(0);
+        if (!x1.is_constant()) {
+            builder.variables[x1.witness_index] = g1.x;
+        }
+        if (!y1.is_constant()) {
+            builder.variables[y1.witness_index] = g1.y;
+        }
+        if (!infinite1.is_constant()) {
+            builder.variables[infinite1.witness_index] = bb::fr(0);
+        }
+        if (!x2.is_constant()) {
+            builder.variables[x2.witness_index] = g1.x;
+        }
+        if (!y2.is_constant()) {
+            builder.variables[y2.witness_index] = g1.y;
+        }
+        if (!infinite2.is_constant()) {
+            builder.variables[infinite2.witness_index] = bb::fr(0);
+        }
     }
     cycle_group_ct input1_point(x1, y1, infinite1);
     cycle_group_ct input2_point(x2, y2, infinite2);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.hpp
index 6c33bee13ee..1a83d549ee4 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.hpp
@@ -1,16 +1,17 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <cstdint>
 
 namespace acir_format {
 
 struct EcAdd {
-    uint32_t input1_x;
-    uint32_t input1_y;
-    uint32_t input1_infinite;
-    uint32_t input2_x;
-    uint32_t input2_y;
-    uint32_t input2_infinite;
+    WitnessOrConstant<bb::fr> input1_x;
+    WitnessOrConstant<bb::fr> input1_y;
+    WitnessOrConstant<bb::fr> input1_infinite;
+    WitnessOrConstant<bb::fr> input2_x;
+    WitnessOrConstant<bb::fr> input2_y;
+    WitnessOrConstant<bb::fr> input2_infinite;
     uint32_t result_x;
     uint32_t result_y;
     uint32_t result_infinite;
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.test.cpp
index 9ff5123ffd1..9f43d49c875 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/ec_operations.test.cpp
@@ -40,12 +40,12 @@ size_t generate_ec_add_constraint(EcAdd& ec_add_constraint, WitnessVector& witne
     witness_values.push_back(fr(0));
     witness_values.push_back(fr(0));
     ec_add_constraint = EcAdd{
-        .input1_x = 1,
-        .input1_y = 2,
-        .input1_infinite = 7,
-        .input2_x = 3,
-        .input2_y = 4,
-        .input2_infinite = 7,
+        .input1_x = WitnessOrConstant<bb::fr>::from_index(1),
+        .input1_y = WitnessOrConstant<bb::fr>::from_index(2),
+        .input1_infinite = WitnessOrConstant<bb::fr>::from_index(7),
+        .input2_x = WitnessOrConstant<bb::fr>::from_index(3),
+        .input2_y = WitnessOrConstant<bb::fr>::from_index(4),
+        .input2_infinite = WitnessOrConstant<bb::fr>::from_index(7),
         .result_x = 5,
         .result_y = 6,
         .result_infinite = 8,
@@ -129,52 +129,52 @@ TEST_F(EcOperations, TestECMultiScalarMul)
         fr(0),
     };
     msm_constrain = MultiScalarMul{
-        .points = { WitnessConstant<fr>{
+        .points = { WitnessOrConstant<fr>{
                         .index = 1,
                         .value = fr(0),
                         .is_constant = false,
                     },
-                    WitnessConstant<fr>{
+                    WitnessOrConstant<fr>{
                         .index = 2,
                         .value = fr(0),
                         .is_constant = false,
                     },
-                    WitnessConstant<fr>{
+                    WitnessOrConstant<fr>{
                         .index = 3,
                         .value = fr(0),
                         .is_constant = false,
                     },
-                    WitnessConstant<fr>{
+                    WitnessOrConstant<fr>{
                         .index = 1,
                         .value = fr(0),
                         .is_constant = false,
                     },
-                    WitnessConstant<fr>{
+                    WitnessOrConstant<fr>{
                         .index = 2,
                         .value = fr(0),
                         .is_constant = false,
                     },
-                    WitnessConstant<fr>{
+                    WitnessOrConstant<fr>{
                         .index = 3,
                         .value = fr(0),
                         .is_constant = false,
                     } },
-        .scalars = { WitnessConstant<fr>{
+        .scalars = { WitnessOrConstant<fr>{
                          .index = 4,
                          .value = fr(0),
                          .is_constant = false,
                      },
-                     WitnessConstant<fr>{
+                     WitnessOrConstant<fr>{
                          .index = 5,
                          .value = fr(0),
                          .is_constant = false,
                      },
-                     WitnessConstant<fr>{
+                     WitnessOrConstant<fr>{
                          .index = 4,
                          .value = fr(0),
                          .is_constant = false,
                      },
-                     WitnessConstant<fr>{
+                     WitnessOrConstant<fr>{
                          .index = 5,
                          .value = fr(0),
                          .is_constant = false,
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/honk_recursion_constraint.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/honk_recursion_constraint.test.cpp
index af86ada3185..b87bd4c9e39 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/honk_recursion_constraint.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/honk_recursion_constraint.test.cpp
@@ -39,8 +39,8 @@ class AcirHonkRecursionConstraint : public ::testing::Test {
         };
 
         LogicConstraint logic_constraint{
-            .a = 0,
-            .b = 1,
+            .a = WitnessOrConstant<bb::fr>::from_index(0),
+            .b = WitnessOrConstant<bb::fr>::from_index(1),
             .result = 2,
             .num_bits = 32,
             .is_xor_gate = 1,
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.cpp
index 13c72f0f231..54139dba07d 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.cpp
@@ -51,7 +51,7 @@ template <typename Builder> void create_keccak_permutations(Builder& builder, co
     // Get the witness assignment for each witness index
     // Write the witness assignment to the byte_array
     for (size_t i = 0; i < constraint.state.size(); ++i) {
-        state[i] = field_ct::from_witness_index(&builder, constraint.state[i]);
+        state[i] = to_field_ct(constraint.state[i], builder);
     }
 
     std::array<field_ct, 25> output_state = bb::stdlib::keccak<Builder>::permutation_opcode(state, &builder);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.hpp
index 6ae65a6e8d2..2bf194dfd9f 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/keccak_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <array>
 #include <cstdint>
@@ -16,7 +17,7 @@ struct HashInput {
 };
 
 struct Keccakf1600 {
-    std::array<uint32_t, 25> state;
+    std::array<WitnessOrConstant<bb::fr>, 25> state;
     std::array<uint32_t, 25> result;
 
     // For serialization, update with any new fields
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.cpp
index de6c2842d1d..cea21fc25ba 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.cpp
@@ -7,16 +7,16 @@ using namespace bb::plonk;
 
 template <typename Builder>
 void create_logic_gate(Builder& builder,
-                       const uint32_t a,
-                       const uint32_t b,
+                       const WitnessOrConstant<bb::fr> a,
+                       const WitnessOrConstant<bb::fr> b,
                        const uint32_t result,
                        const size_t num_bits,
                        const bool is_xor_gate)
 {
     using field_ct = bb::stdlib::field_t<Builder>;
 
-    field_ct left = field_ct::from_witness_index(&builder, a);
-    field_ct right = field_ct::from_witness_index(&builder, b);
+    field_ct left = to_field_ct(a, builder);
+    field_ct right = to_field_ct(b, builder);
 
     field_ct res = bb::stdlib::logic<Builder>::create_logic_constraint(left, right, num_bits, is_xor_gate);
     field_ct our_res = field_ct::from_witness_index(&builder, result);
@@ -24,14 +24,14 @@ void create_logic_gate(Builder& builder,
 }
 
 template void create_logic_gate<bb::MegaCircuitBuilder>(bb::MegaCircuitBuilder& builder,
-                                                        const uint32_t a,
-                                                        const uint32_t b,
+                                                        const WitnessOrConstant<bb::fr> a,
+                                                        const WitnessOrConstant<bb::fr> b,
                                                         const uint32_t result,
                                                         const size_t num_bits,
                                                         const bool is_xor_gate);
 template void create_logic_gate<bb::UltraCircuitBuilder>(bb::UltraCircuitBuilder& builder,
-                                                         const uint32_t a,
-                                                         const uint32_t b,
+                                                         const WitnessOrConstant<bb::fr> a,
+                                                         const WitnessOrConstant<bb::fr> b,
                                                          const uint32_t result,
                                                          const size_t num_bits,
                                                          const bool is_xor_gate);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.hpp
index 16b17f73830..a7af4832ee0 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/logic_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include "barretenberg/stdlib/primitives/circuit_builders/circuit_builders_fwd.hpp"
 #include <cstdint>
@@ -8,8 +9,8 @@ namespace acir_format {
 using Builder = bb::UltraCircuitBuilder;
 
 struct LogicConstraint {
-    uint32_t a;
-    uint32_t b;
+    WitnessOrConstant<bb::fr> a;
+    WitnessOrConstant<bb::fr> b;
     uint32_t result;
     uint32_t num_bits;
     uint32_t is_xor_gate;
@@ -21,10 +22,14 @@ struct LogicConstraint {
 };
 
 template <typename Builder>
-void create_logic_gate(
-    Builder& builder, uint32_t a, uint32_t b, uint32_t result, std::size_t num_bits, bool is_xor_gate);
+void create_logic_gate(Builder& builder,
+                       WitnessOrConstant<bb::fr> a,
+                       WitnessOrConstant<bb::fr> b,
+                       uint32_t result,
+                       std::size_t num_bits,
+                       bool is_xor_gate);
 
-void xor_gate(Builder& builder, uint32_t a, uint32_t b, uint32_t result);
+void xor_gate(Builder& builder, WitnessOrConstant<bb::fr> a, WitnessOrConstant<bb::fr> b, uint32_t result);
 
-void and_gate(Builder& builder, uint32_t a, uint32_t b, uint32_t result);
+void and_gate(Builder& builder, WitnessOrConstant<bb::fr> a, WitnessOrConstant<bb::fr> b, uint32_t result);
 } // namespace acir_format
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.cpp
index 398c794dea1..1baf25b97ec 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.cpp
@@ -25,21 +25,9 @@ template <typename Builder> void create_multi_scalar_mul_constraint(Builder& bui
         field_ct point_x;
         field_ct point_y;
         bool_ct infinite;
-        if (input.points[i].is_constant) {
-            point_x = field_ct(input.points[i].value);
-        } else {
-            point_x = field_ct::from_witness_index(&builder, input.points[i].index);
-        }
-        if (input.points[i + 1].is_constant) {
-            point_y = field_ct(input.points[i + 1].value);
-        } else {
-            point_y = field_ct::from_witness_index(&builder, input.points[i + 1].index);
-        }
-        if (input.points[i + 2].is_constant) {
-            infinite = bool_ct(field_ct(input.points[i + 2].value));
-        } else {
-            infinite = bool_ct(field_ct::from_witness_index(&builder, input.points[i + 2].index));
-        }
+        point_x = to_field_ct(input.points[i], builder);
+        point_y = to_field_ct(input.points[i + 1], builder);
+        infinite = bool_ct(to_field_ct(input.points[i + 2], builder));
         cycle_group_ct input_point(point_x, point_y, infinite);
         // Reconstruct the scalar from the low and high limbs
         field_ct scalar_low_as_field;
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.hpp
index ef980a99ab6..0d13aaca513 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/multi_scalar_mul.hpp
@@ -2,22 +2,15 @@
 #include "barretenberg/serialize/msgpack.hpp"
 #include "barretenberg/stdlib/primitives/field/field.hpp"
 #include "serde/index.hpp"
+#include "witness_constant.hpp"
 #include <cstdint>
 #include <vector>
 
 namespace acir_format {
 
-template <typename FF> struct WitnessConstant {
-    uint32_t index;
-    FF value;
-    bool is_constant;
-    MSGPACK_FIELDS(index, value, is_constant);
-    friend bool operator==(WitnessConstant const& lhs, WitnessConstant const& rhs) = default;
-};
-
 struct MultiScalarMul {
-    std::vector<WitnessConstant<bb::fr>> points;
-    std::vector<WitnessConstant<bb::fr>> scalars;
+    std::vector<WitnessOrConstant<bb::fr>> points;
+    std::vector<WitnessOrConstant<bb::fr>> scalars;
 
     uint32_t out_point_x;
     uint32_t out_point_y;
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.cpp
index 1a8e0821070..03ecef4efbe 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.cpp
@@ -20,7 +20,7 @@ template <typename Builder> void create_poseidon2_permutations(Builder& builder,
     // Write the witness assignment to the byte_array state
     State state;
     for (size_t i = 0; i < constraint.state.size(); ++i) {
-        state[i] = field_ct::from_witness_index(&builder, constraint.state[i]);
+        state[i] = to_field_ct(constraint.state[i], builder);
     }
     State output_state;
     output_state = stdlib::Poseidon2Permutation<Poseidon2Params, Builder>::permutation(&builder, state);
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.hpp
index 342d709fd59..b2ee452bcd3 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <cstdint>
 #include <vector>
@@ -6,7 +7,7 @@
 namespace acir_format {
 
 struct Poseidon2Constraint {
-    std::vector<uint32_t> state;
+    std::vector<WitnessOrConstant<bb::fr>> state;
     std::vector<uint32_t> result;
     uint32_t len;
 
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.test.cpp
index cc144fa6fd9..b140797cf9e 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/poseidon2_constraint.test.cpp
@@ -8,6 +8,7 @@
 
 #include <cstdint>
 #include <gtest/gtest.h>
+#include <strings.h>
 #include <vector>
 
 namespace acir_format::tests {
@@ -29,7 +30,12 @@ TEST_F(Poseidon2Tests, TestPoseidon2Permutation)
 {
     Poseidon2Constraint
         poseidon2_constraint{
-            .state = { 1, 2, 3, 4, },
+            .state = { 
+                WitnessOrConstant<bb::fr>::from_index(1),
+                WitnessOrConstant<bb::fr>::from_index(2),
+                WitnessOrConstant<bb::fr>::from_index(3),
+                WitnessOrConstant<bb::fr>::from_index(4),
+ },
             .result = { 5, 6, 7, 8, },
             .len = 4,
         };
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/recursion_constraint.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/recursion_constraint.test.cpp
index 76e6d72bad1..abc6b33cb07 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/recursion_constraint.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/recursion_constraint.test.cpp
@@ -37,8 +37,8 @@ Builder create_inner_circuit()
     };
 
     LogicConstraint logic_constraint{
-        .a = 0,
-        .b = 1,
+        .a = WitnessOrConstant<bb::fr>::from_index(0),
+        .b = WitnessOrConstant<bb::fr>::from_index(1),
         .result = 2,
         .num_bits = 32,
         .is_xor_gate = 1,
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.cpp
index eef6327ab12..99f88882937 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.cpp
@@ -56,16 +56,12 @@ void create_sha256_compression_constraints(Builder& builder, const Sha256Compres
     // because of the lookup-tables.
     size_t i = 0;
     for (const auto& witness_index_num_bits : constraint.inputs) {
-        auto witness_index = witness_index_num_bits.witness;
-        field_ct element = field_ct::from_witness_index(&builder, witness_index);
-        inputs[i] = element;
+        inputs[i] = to_field_ct(witness_index_num_bits, builder);
         ++i;
     }
     i = 0;
     for (const auto& witness_index_num_bits : constraint.hash_values) {
-        auto witness_index = witness_index_num_bits.witness;
-        field_ct element = field_ct::from_witness_index(&builder, witness_index);
-        hash_inputs[i] = element;
+        hash_inputs[i] = to_field_ct(witness_index_num_bits, builder);
         ++i;
     }
 
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.hpp
index 1843aa5198d..4b243b5b6ab 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.hpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.hpp
@@ -1,4 +1,5 @@
 #pragma once
+#include "barretenberg/dsl/acir_format/witness_constant.hpp"
 #include "barretenberg/serialize/msgpack.hpp"
 #include <array>
 #include <cstdint>
@@ -25,8 +26,8 @@ struct Sha256Constraint {
 };
 
 struct Sha256Compression {
-    std::array<Sha256Input, 16> inputs;
-    std::array<Sha256Input, 8> hash_values;
+    std::array<WitnessOrConstant<bb::fr>, 16> inputs;
+    std::array<WitnessOrConstant<bb::fr>, 8> hash_values;
     std::array<uint32_t, 8> result;
 
     friend bool operator==(Sha256Compression const& lhs, Sha256Compression const& rhs) = default;
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.test.cpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.test.cpp
index 72936adc776..39163fc7a6f 100644
--- a/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.test.cpp
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/sha256_constraint.test.cpp
@@ -21,13 +21,13 @@ class Sha256Tests : public ::testing::Test {
 TEST_F(Sha256Tests, TestSha256Compression)
 {
 
-    std::array<Sha256Input, 16> inputs;
+    std::array<WitnessOrConstant<bb::fr>, 16> inputs;
     for (size_t i = 0; i < 16; ++i) {
-        inputs[i] = { .witness = static_cast<uint32_t>(i + 1), .num_bits = 32 };
+        inputs[i] = WitnessOrConstant<bb::fr>::from_index(static_cast<uint32_t>(i + 1));
     }
-    std::array<Sha256Input, 8> hash_values;
+    std::array<WitnessOrConstant<bb::fr>, 8> hash_values;
     for (size_t i = 0; i < 8; ++i) {
-        hash_values[i] = { .witness = static_cast<uint32_t>(i + 17), .num_bits = 32 };
+        hash_values[i] = WitnessOrConstant<bb::fr>::from_index(static_cast<uint32_t>(i + 17));
     }
     Sha256Compression sha256_compression{
         .inputs = inputs,
diff --git a/barretenberg/cpp/src/barretenberg/dsl/acir_format/witness_constant.hpp b/barretenberg/cpp/src/barretenberg/dsl/acir_format/witness_constant.hpp
new file mode 100644
index 00000000000..554c8ddf657
--- /dev/null
+++ b/barretenberg/cpp/src/barretenberg/dsl/acir_format/witness_constant.hpp
@@ -0,0 +1,33 @@
+#pragma once
+#include "barretenberg/serialize/msgpack.hpp"
+#include "barretenberg/stdlib/primitives/field/field.hpp"
+
+namespace acir_format {
+template <typename FF> struct WitnessOrConstant {
+
+    uint32_t index;
+    FF value;
+    bool is_constant;
+    MSGPACK_FIELDS(index, value, is_constant);
+    friend bool operator==(WitnessOrConstant const& lhs, WitnessOrConstant const& rhs) = default;
+    static WitnessOrConstant from_index(uint32_t index)
+    {
+        return WitnessOrConstant{
+            .index = index,
+            .value = FF::zero(),
+            .is_constant = false,
+        };
+    }
+};
+
+template <typename Builder, typename FF>
+bb::stdlib::field_t<Builder> to_field_ct(const WitnessOrConstant<FF>& input, Builder& builder)
+{
+    using field_ct = bb::stdlib::field_t<Builder>;
+    if (input.is_constant) {
+        return field_ct(input.value);
+    }
+    return field_ct::from_witness_index(&builder, input.index);
+}
+
+} // namespace acir_format
\ No newline at end of file