diff --git a/hydra/garaga/modulo_circuit_structs.py b/hydra/garaga/modulo_circuit_structs.py
index 1a6a7ff1..245b6689 100644
--- a/hydra/garaga/modulo_circuit_structs.py
+++ b/hydra/garaga/modulo_circuit_structs.py
@@ -1015,22 +1015,45 @@ def extract_from_circuit_output(
     ) -> str:
         raise NotImplementedError("Never used in practice")
 
+    def serialize_input_signature(self) -> str:
+        bits = self.bits
+        if bits <= 288:
+            return f"{self.name}:MillerLoopResultScalingFactor<u288>"
+        else:
+            return f"{self.name}:MillerLoopResultScalingFactor<u384>"
+
     def dump_to_circuit_input(self) -> str:
         code = ""
+        bits = self.bits
+        if bits <= 288:
+            next_fn = "next_u288"
+        else:
+            next_fn = "next_2"
         for mem_name in self.members_names:
-            code += f"circuit_inputs = circuit_inputs.next_2({self.name}.{mem_name});\n"
+            code += (
+                f"circuit_inputs = circuit_inputs.{next_fn}({self.name}.{mem_name});\n"
+            )
         return code
 
     def serialize(self, raw: bool = False) -> str:
         assert len(self.elmts) == 6
-        raw_struct = f"{self.__class__.__name__}{{{','.join([f'{self.members_names[i]}: {int_to_u384(self.elmts[i].value)}' for i in range(len(self))])}}}"
+        bits = self.bits
+        if bits <= 288:
+            curve_id = 0
+        else:
+            curve_id = 1
+        raw_struct = f"{self.__class__.__name__}{{{','.join([f'{self.members_names[i]}: {int_to_u2XX(self.elmts[i].value, curve_id=curve_id)}' for i in range(len(self))])}}}"
         if raw:
             return raw_struct
         else:
             return f"let {self.name}:{self.__class__.__name__} = {raw_struct};\n"
 
     def _serialize_to_calldata(self) -> list[int]:
-        return io.bigint_split_array(self.elmts, prepend_length=False)
+        bits = self.bits
+        if bits <= 288:
+            return io.bigint_split_array(self.elmts, n_limbs=3, prepend_length=False)
+        else:
+            return io.bigint_split_array(self.elmts, n_limbs=4, prepend_length=False)
 
     def __len__(self) -> int:
         if self.elmts is not None:
diff --git a/src/src/circuits/multi_pairing_check.cairo b/src/src/circuits/multi_pairing_check.cairo
index 494975b5..b0acf040 100644
--- a/src/src/circuits/multi_pairing_check.cairo
+++ b/src/src/circuits/multi_pairing_check.cairo
@@ -2213,7 +2213,7 @@ fn run_BLS12_381_MP_CHECK_INIT_BIT_3P_2F_circuit(
     return (Q0, new_lhs);
 }
 fn run_BLS12_381_MP_CHECK_PREPARE_LAMBDA_ROOT_circuit(
-    lambda_root_inverse: E12D<u384>, z: u384, scaling_factor: MillerLoopResultScalingFactor
+    lambda_root_inverse: E12D<u384>, z: u384, scaling_factor: MillerLoopResultScalingFactor<u384>
 ) -> (u384, u384, u384) {
     // CONSTANT stack
     let in0 = CE::<CI<0>> {}; // 0x0
@@ -5334,7 +5334,7 @@ fn run_BN254_MP_CHECK_INIT_BIT_3P_2F_circuit(
 fn run_BN254_MP_CHECK_PREPARE_LAMBDA_ROOT_circuit(
     lambda_root: E12D<u288>,
     z: u384,
-    scaling_factor: MillerLoopResultScalingFactor,
+    scaling_factor: MillerLoopResultScalingFactor<u288>,
     c_inv: E12D<u288>,
     c_0: u384
 ) -> (u384, u384, u384, u384, u384, u384, u384) {
@@ -5678,12 +5678,12 @@ fn run_BN254_MP_CHECK_PREPARE_LAMBDA_ROOT_circuit(
     circuit_inputs = circuit_inputs.next_u288(lambda_root.w10); // in55
     circuit_inputs = circuit_inputs.next_u288(lambda_root.w11); // in56
     circuit_inputs = circuit_inputs.next_2(z); // in57
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w0); // in58
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w2); // in59
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w4); // in60
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w6); // in61
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w8); // in62
-    circuit_inputs = circuit_inputs.next_2(scaling_factor.w10); // in63
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w0); // in58
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w2); // in59
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w4); // in60
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w6); // in61
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w8); // in62
+    circuit_inputs = circuit_inputs.next_u288(scaling_factor.w10); // in63
     circuit_inputs = circuit_inputs.next_u288(c_inv.w0); // in64
     circuit_inputs = circuit_inputs.next_u288(c_inv.w1); // in65
     circuit_inputs = circuit_inputs.next_u288(c_inv.w2); // in66
diff --git a/src/src/definitions.cairo b/src/src/definitions.cairo
index fbb14622..43a15fc8 100644
--- a/src/src/definitions.cairo
+++ b/src/src/definitions.cairo
@@ -556,13 +556,13 @@ impl E12DSerde288 of Serde<E12D<u288>> {
 }
 
 #[derive(Copy, Drop, Debug, PartialEq, Serde)]
-struct MillerLoopResultScalingFactor {
-    w0: u384,
-    w2: u384,
-    w4: u384,
-    w6: u384,
-    w8: u384,
-    w10: u384,
+struct MillerLoopResultScalingFactor<T> {
+    w0: T,
+    w2: T,
+    w4: T,
+    w6: T,
+    w8: T,
+    w10: T,
 }
 #[derive(Copy, Drop, Debug, PartialEq, Serde)]
 struct E12DMulQuotient {
diff --git a/src/src/groth16.cairo b/src/src/groth16.cairo
index 7c1045a0..85669393 100644
--- a/src/src/groth16.cairo
+++ b/src/src/groth16.cairo
@@ -253,7 +253,7 @@ fn multi_pairing_check_bn254_3P_2F_with_extra_miller_loop_result(
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair2, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u288(mpcheck_hint.lambda_root, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u288(mpcheck_hint.lambda_root_inverse, s0, s1, s2);
-    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor(mpcheck_hint.w, s0, s1, s2);
+    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor_u288(mpcheck_hint.w, s0, s1, s2);
     // Hash Ris to obtain base random coefficient c0
     let (s0, s1, s2) = hashing::hash_E12D_u288_transcript(mpcheck_hint.Ris, s0, s1, s2);
 
@@ -514,7 +514,7 @@ fn multi_pairing_check_bls12_381_3P_2F_with_extra_miller_loop_result(
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair1, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair2, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u384(hint.lambda_root_inverse, s0, s1, s2);
-    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor(hint.w, s0, s1, s2);
+    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor_u384(hint.w, s0, s1, s2);
     // Hash Ris to obtain base random coefficient c0
     let (s0, s1, s2) = hashing::hash_E12D_u384_transcript(hint.Ris, s0, s1, s2);
     let mut c_i: u384 = s1.into();
diff --git a/src/src/pairing_check.cairo b/src/src/pairing_check.cairo
index 32bf416b..b7fae0dc 100644
--- a/src/src/pairing_check.cairo
+++ b/src/src/pairing_check.cairo
@@ -41,7 +41,7 @@ use garaga::basic_field_ops::{compute_yInvXnegOverY_BN254, compute_yInvXnegOverY
 struct MPCheckHintBN254 {
     lambda_root: E12D<u288>,
     lambda_root_inverse: E12D<u288>,
-    w: MillerLoopResultScalingFactor,
+    w: MillerLoopResultScalingFactor<u288>,
     Ris: Span<E12D<u288>>,
     big_Q: Array<u288>,
 }
@@ -49,7 +49,7 @@ struct MPCheckHintBN254 {
 #[derive(Drop, Serde)]
 struct MPCheckHintBLS12_381 {
     lambda_root_inverse: E12D<u384>,
-    w: MillerLoopResultScalingFactor,
+    w: MillerLoopResultScalingFactor<u384>,
     Ris: Span<E12D<u384>>,
     big_Q: Array<u384>,
 }
@@ -70,7 +70,7 @@ fn multi_pairing_check_bn254_2P_2F(
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair1, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u288(hint.lambda_root, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u288(hint.lambda_root_inverse, s0, s1, s2);
-    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor(hint.w, s0, s1, s2);
+    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor_u288(hint.w, s0, s1, s2);
     // Hash Ris to obtain base random coefficient c0
     let (s0, s1, s2) = hashing::hash_E12D_u288_transcript(hint.Ris, s0, s1, s2);
     let mut c_i: u384 = s1.into();
@@ -233,7 +233,7 @@ fn multi_pairing_check_bls12_381_2P_2F(
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair0, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_G1G2Pair(pair1, s0, s1, s2);
     let (s0, s1, s2) = hashing::hash_E12D_u384(hint.lambda_root_inverse, s0, s1, s2);
-    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor(hint.w, s0, s1, s2);
+    let (s0, s1, s2) = hashing::hash_MillerLoopResultScalingFactor_u384(hint.w, s0, s1, s2);
     // Hash Ris to obtain base random coefficient c0
     let (s0, s1, s2) = hashing::hash_E12D_u384_transcript(hint.Ris, s0, s1, s2);
 
diff --git a/src/src/tests/pairing_tests.cairo b/src/src/tests/pairing_tests.cairo
index 39d9fbf9..2a582fb5 100644
--- a/src/src/tests/pairing_tests.cairo
+++ b/src/src/tests/pairing_tests.cairo
@@ -4097,12 +4097,12 @@ mod pairing_tests {
                 }
             },
             w: MillerLoopResultScalingFactor {
-                w0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w2: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w4: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w6: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w8: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w10: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }
+                w0: u288 { limb0: 0x1, limb1: 0x0, limb2: 0x0 },
+                w2: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w4: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w6: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w8: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w10: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }
             },
             Ris: array![
                 E12D {
@@ -11917,12 +11917,12 @@ mod pairing_tests {
                 }
             },
             w: MillerLoopResultScalingFactor {
-                w0: u384 { limb0: 0x1, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w2: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w4: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w6: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w8: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 },
-                w10: u384 { limb0: 0x0, limb1: 0x0, limb2: 0x0, limb3: 0x0 }
+                w0: u288 { limb0: 0x1, limb1: 0x0, limb2: 0x0 },
+                w2: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w4: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w6: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w8: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 },
+                w10: u288 { limb0: 0x0, limb1: 0x0, limb2: 0x0 }
             },
             Ris: array![
                 E12D {
diff --git a/src/src/utils/hashing.cairo b/src/src/utils/hashing.cairo
index c54fa3b8..f8711137 100644
--- a/src/src/utils/hashing.cairo
+++ b/src/src/utils/hashing.cairo
@@ -177,8 +177,8 @@ pub fn hash_E12D_u288(
 
 // Apply sponge construction to a MillerLoopResultScalingFactor element from an initial state (s0,
 // s1, s2)
-pub fn hash_MillerLoopResultScalingFactor(
-    elmt: MillerLoopResultScalingFactor, mut s0: felt252, mut s1: felt252, mut s2: felt252
+pub fn hash_MillerLoopResultScalingFactor_u384(
+    elmt: MillerLoopResultScalingFactor<u384>, mut s0: felt252, mut s1: felt252, mut s2: felt252
 ) -> (felt252, felt252, felt252) {
     let base: felt252 = 79228162514264337593543950336; // 2**96
 
@@ -203,6 +203,32 @@ pub fn hash_MillerLoopResultScalingFactor(
     return (_s0, _s1, _s2);
 }
 
+pub fn hash_MillerLoopResultScalingFactor_u288(
+    elmt: MillerLoopResultScalingFactor<u288>, mut s0: felt252, mut s1: felt252, mut s2: felt252
+) -> (felt252, felt252, felt252) {
+    let base: felt252 = 79228162514264337593543950336; // 2**96
+
+    let in_1 = s0 + elmt.w0.limb0.into() + base * elmt.w0.limb1.into();
+    let in_2 = s1 + elmt.w0.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, s2);
+    let in_1 = _s0 + elmt.w2.limb0.into() + base * elmt.w2.limb1.into();
+    let in_2 = _s1 + elmt.w2.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2);
+    let in_1 = _s0 + elmt.w4.limb0.into() + base * elmt.w4.limb1.into();
+    let in_2 = _s1 + elmt.w4.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2);
+    let in_1 = _s0 + elmt.w6.limb0.into() + base * elmt.w6.limb1.into();
+    let in_2 = _s1 + elmt.w6.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2);
+    let in_1 = _s0 + elmt.w8.limb0.into() + base * elmt.w8.limb1.into();
+    let in_2 = _s1 + elmt.w8.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2);
+    let in_1 = _s0 + elmt.w10.limb0.into() + base * elmt.w10.limb1.into();
+    let in_2 = _s1 + elmt.w10.limb2.into();
+    let (_s0, _s1, _s2) = hades_permutation(in_1, in_2, _s2);
+    return (_s0, _s1, _s2);
+}
+
 // Apply sponge construction to a sequence of E12D elements from an initial state (s0, s1, s2)
 pub fn hash_E12D_u384_transcript(
     transcript: Span<E12D<u384>>, mut s0: felt252, mut s1: felt252, mut s2: felt252