diff --git a/ceno_zkvm/src/instructions.rs b/ceno_zkvm/src/instructions.rs
index 633eaa8db..7b44d052c 100644
--- a/ceno_zkvm/src/instructions.rs
+++ b/ceno_zkvm/src/instructions.rs
@@ -17,7 +17,7 @@ pub trait Instruction<E: ExtensionField> {
     // assign single instance giving step from trace
     fn assign_instance(
         config: &Self::InstructionConfig,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<E::BaseField>],
         step: StepRecord,
     ) -> Result<(), ZKVMError>;
 
@@ -25,8 +25,8 @@ pub trait Instruction<E: ExtensionField> {
         config: &Self::InstructionConfig,
         num_witin: usize,
         steps: Vec<StepRecord>,
-    ) -> Result<RowMajorMatrix<E>, ZKVMError> {
-        let mut raw_witin = RowMajorMatrix::<E>::new(steps.len(), num_witin);
+    ) -> Result<RowMajorMatrix<E::BaseField>, ZKVMError> {
+        let mut raw_witin = RowMajorMatrix::<E::BaseField>::new(steps.len(), num_witin);
         let raw_witin_iter = raw_witin.par_iter_mut();
 
         raw_witin_iter
diff --git a/ceno_zkvm/src/instructions/riscv/addsub.rs b/ceno_zkvm/src/instructions/riscv/addsub.rs
index 20609ff0d..d4de41c0c 100644
--- a/ceno_zkvm/src/instructions/riscv/addsub.rs
+++ b/ceno_zkvm/src/instructions/riscv/addsub.rs
@@ -146,7 +146,7 @@ impl<E: ExtensionField> Instruction<E> for AddInstruction {
     #[allow(clippy::option_map_unit_fn)]
     fn assign_instance(
         config: &Self::InstructionConfig,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<E::BaseField>],
         _step: StepRecord,
     ) -> Result<(), ZKVMError> {
         // TODO use field from step
@@ -192,7 +192,7 @@ impl<E: ExtensionField> Instruction<E> for SubInstruction {
     #[allow(clippy::option_map_unit_fn)]
     fn assign_instance(
         config: &Self::InstructionConfig,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<E::BaseField>],
         _step: StepRecord,
     ) -> Result<(), ZKVMError> {
         // TODO use field from step
diff --git a/ceno_zkvm/src/instructions/riscv/blt.rs b/ceno_zkvm/src/instructions/riscv/blt.rs
index bd71b15ab..036ce6a86 100644
--- a/ceno_zkvm/src/instructions/riscv/blt.rs
+++ b/ceno_zkvm/src/instructions/riscv/blt.rs
@@ -1,3 +1,4 @@
+use goldilocks::SmallField;
 use std::mem::MaybeUninit;
 
 use ff_ext::ExtensionField;
@@ -13,7 +14,7 @@ use crate::{
         Instruction,
     },
     set_val,
-    utils::{i64_to_ext, limb_u8_to_u16},
+    utils::{i64_to_base, limb_u8_to_u16},
 };
 
 use super::{
@@ -53,10 +54,10 @@ pub struct BltInput {
 
 impl BltInput {
     /// TODO: refactor after formalize the interface of opcode inputs
-    pub fn assign<E: ExtensionField>(
+    pub fn assign<F: SmallField, E: ExtensionField<BaseField = F>>(
         &self,
         config: &InstructionConfig<E>,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<F>],
     ) {
         assert!(!self.lhs_limb8.is_empty() && (self.lhs_limb8.len() == self.rhs_limb8.len()));
         // TODO: add boundary check for witin
@@ -64,50 +65,54 @@ impl BltInput {
             lhs_limbs: &self.lhs_limb8,
             rhs_limbs: &self.rhs_limb8,
         };
-        let is_lt = lt_input.assign(instance, &config.is_lt);
+        let is_lt = lt_input.assign::<E::BaseField>(instance, &config.is_lt);
 
-        set_val!(instance, config.pc, { i64_to_ext::<E>(self.pc as i64) });
+        set_val!(instance, config.pc, { i64_to_base::<F>(self.pc as i64) });
         set_val!(instance, config.next_pc, {
             if is_lt {
-                i64_to_ext::<E>(self.pc as i64 + self.imm as i64)
+                i64_to_base::<F>(self.pc as i64 + self.imm as i64)
             } else {
-                i64_to_ext::<E>(self.pc as i64 + PC_STEP_SIZE as i64)
+                i64_to_base::<F>(self.pc as i64 + PC_STEP_SIZE as i64)
             }
         });
-        set_val!(instance, config.ts, { i64_to_ext::<E>(self.ts as i64) });
-        set_val!(instance, config.imm, { i64_to_ext::<E>(self.imm as i64) });
+        set_val!(instance, config.ts, { i64_to_base::<F>(self.ts as i64) });
+        set_val!(instance, config.imm, { i64_to_base::<F>(self.imm as i64) });
         set_val!(instance, config.rs1_id, {
-            i64_to_ext::<E>(self.rs1_id as i64)
+            i64_to_base::<F>(self.rs1_id as i64)
         });
         set_val!(instance, config.rs2_id, {
-            i64_to_ext::<E>(self.rs2_id as i64)
+            i64_to_base::<F>(self.rs2_id as i64)
         });
         set_val!(instance, config.prev_rs1_ts, {
-            i64_to_ext::<E>(self.prev_rs1_ts as i64)
+            i64_to_base::<F>(self.prev_rs1_ts as i64)
         });
         set_val!(instance, config.prev_rs2_ts, {
-            i64_to_ext::<E>(self.prev_rs2_ts as i64)
+            i64_to_base::<F>(self.prev_rs2_ts as i64)
         });
 
         config.lhs_limb8.assign(instance, {
             self.lhs_limb8
                 .iter()
-                .map(|&limb| i64_to_ext(limb as i64))
+                .map(|&limb| i64_to_base::<F>(limb as i64))
                 .collect()
         });
         config.rhs_limb8.assign(instance, {
             self.rhs_limb8
                 .iter()
-                .map(|&limb| i64_to_ext(limb as i64))
+                .map(|&limb| i64_to_base::<F>(limb as i64))
                 .collect()
         });
         let lhs = limb_u8_to_u16(&self.lhs_limb8);
         let rhs = limb_u8_to_u16(&self.rhs_limb8);
         config.lhs.assign(instance, {
-            lhs.iter().map(|&limb| i64_to_ext(limb as i64)).collect()
+            lhs.iter()
+                .map(|&limb| i64_to_base::<F>(limb as i64))
+                .collect()
         });
         config.rhs.assign(instance, {
-            rhs.iter().map(|&limb| i64_to_ext(limb as i64)).collect()
+            rhs.iter()
+                .map(|&limb| i64_to_base::<F>(limb as i64))
+                .collect()
         });
     }
 
@@ -216,7 +221,7 @@ impl<E: ExtensionField> Instruction<E> for BltInstruction {
 
     fn assign_instance(
         config: &Self::InstructionConfig,
-        instance: &mut [std::mem::MaybeUninit<E>],
+        instance: &mut [std::mem::MaybeUninit<E::BaseField>],
         _step: ceno_emul::StepRecord,
     ) -> Result<(), ZKVMError> {
         // take input from _step
@@ -230,18 +235,11 @@ impl<E: ExtensionField> Instruction<E> for BltInstruction {
 mod test {
     use super::*;
     use ceno_emul::StepRecord;
-    use ff_ext::ExtensionField;
     use goldilocks::GoldilocksExt2;
     use itertools::Itertools;
     use multilinear_extensions::mle::IntoMLEs;
 
-    use crate::{
-        circuit_builder::{CircuitBuilder, ConstraintSystem},
-        instructions::Instruction,
-        scheme::mock_prover::MockProver,
-    };
-
-    use super::BltInstruction;
+    use crate::{circuit_builder::ConstraintSystem, scheme::mock_prover::MockProver};
 
     #[test]
     fn test_blt_circuit() -> Result<(), ZKVMError> {
diff --git a/ceno_zkvm/src/instructions/riscv/config.rs b/ceno_zkvm/src/instructions/riscv/config.rs
index 33c0a12ee..e5816b2d3 100644
--- a/ceno_zkvm/src/instructions/riscv/config.rs
+++ b/ceno_zkvm/src/instructions/riscv/config.rs
@@ -1,7 +1,7 @@
 use std::mem::MaybeUninit;
 
-use crate::{expression::WitIn, set_val, utils::i64_to_ext};
-use ff_ext::ExtensionField;
+use crate::{expression::WitIn, set_val, utils::i64_to_base};
+use goldilocks::SmallField;
 use itertools::Itertools;
 
 #[derive(Clone)]
@@ -23,19 +23,19 @@ pub struct MsbInput<'a> {
 }
 
 impl MsbInput<'_> {
-    pub fn assign<E: ExtensionField>(
+    pub fn assign<F: SmallField>(
         &self,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<F>],
         config: &MsbConfig,
     ) -> (u8, u8) {
         let n_limbs = self.limbs.len();
         assert!(n_limbs > 0);
         let mut high_limb = self.limbs[n_limbs - 1];
         let msb = (high_limb >> 7) & 1;
-        set_val!(instance, config.msb, { i64_to_ext::<E>(msb as i64) });
+        set_val!(instance, config.msb, { i64_to_base::<F>(msb as i64) });
         high_limb &= 0b0111_1111;
         set_val!(instance, config.high_limb_no_msb, {
-            i64_to_ext::<E>(high_limb as i64)
+            i64_to_base::<F>(high_limb as i64)
         });
         (msb, high_limb)
     }
@@ -57,9 +57,9 @@ pub struct LtuInput<'a> {
 }
 
 impl LtuInput<'_> {
-    pub fn assign<E: ExtensionField>(
+    pub fn assign<F: SmallField>(
         &self,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<F>],
         config: &LtuConfig,
     ) -> bool {
         let mut idx = 0;
@@ -78,28 +78,28 @@ impl LtuInput<'_> {
             }
         }
         set_val!(instance, config.indexes[idx], {
-            i64_to_ext::<E>(flag as i64)
+            i64_to_base::<F>(flag as i64)
         });
         config.acc_indexes.iter().enumerate().for_each(|(id, wit)| {
             if id <= idx {
-                set_val!(instance, wit, { i64_to_ext::<E>(flag as i64) });
+                set_val!(instance, wit, { i64_to_base::<F>(flag as i64) });
             } else {
-                set_val!(instance, wit, E::ZERO);
+                set_val!(instance, wit, 0);
             }
         });
-        let lhs_ne_byte = i64_to_ext::<E>(self.lhs_limbs[idx] as i64);
-        let rhs_ne_byte = i64_to_ext::<E>(self.rhs_limbs[idx] as i64);
+        let lhs_ne_byte = i64_to_base::<F>(self.lhs_limbs[idx] as i64);
+        let rhs_ne_byte = i64_to_base::<F>(self.rhs_limbs[idx] as i64);
         set_val!(instance, config.lhs_ne_byte, lhs_ne_byte);
         set_val!(instance, config.rhs_ne_byte, rhs_ne_byte);
         set_val!(instance, config.byte_diff_inv, {
             if flag {
                 (lhs_ne_byte - rhs_ne_byte).invert().unwrap()
             } else {
-                E::ONE
+                F::ONE
             }
         });
         let is_ltu = self.lhs_limbs[idx] < self.rhs_limbs[idx];
-        set_val!(instance, config.is_ltu, { i64_to_ext::<E>(is_ltu as i64) });
+        set_val!(instance, config.is_ltu, { i64_to_base::<F>(is_ltu as i64) });
         is_ltu
     }
 }
@@ -120,9 +120,9 @@ pub struct LtInput<'a> {
 }
 
 impl LtInput<'_> {
-    pub fn assign<E: ExtensionField>(
+    pub fn assign<F: SmallField>(
         &self,
-        instance: &mut [MaybeUninit<E>],
+        instance: &mut [MaybeUninit<F>],
         config: &LtConfig,
     ) -> bool {
         let n_limbs = self.lhs_limbs.len();
@@ -145,7 +145,7 @@ impl LtInput<'_> {
             lhs_limbs: &lhs_limbs_no_msb,
             rhs_limbs: &rhs_limbs_no_msb,
         };
-        let is_ltu = ltu_input.assign(instance, &config.is_ltu);
+        let is_ltu = ltu_input.assign::<F>(instance, &config.is_ltu);
 
         let msb_is_equal = lhs_msb == rhs_msb;
         let msb_diff_inv = if msb_is_equal {
@@ -154,15 +154,15 @@ impl LtInput<'_> {
             lhs_msb as i64 - rhs_msb as i64
         };
         set_val!(instance, config.msb_is_equal, {
-            i64_to_ext::<E>(msb_is_equal as i64)
+            i64_to_base::<F>(msb_is_equal as i64)
         });
         set_val!(instance, config.msb_diff_inv, {
-            i64_to_ext::<E>(msb_diff_inv)
+            i64_to_base::<F>(msb_diff_inv)
         });
 
         // is_lt = a_s\cdot (1-b_s)+eq(a_s,b_s)\cdot ltu(a_{<s},b_{<s})$
         let is_lt = lhs_msb * (1 - rhs_msb) + msb_is_equal as u8 * is_ltu as u8;
-        set_val!(instance, config.is_lt, { i64_to_ext::<E>(is_lt as i64) });
+        set_val!(instance, config.is_lt, { i64_to_base::<F>(is_lt as i64) });
 
         assert!(is_lt == 0 || is_lt == 1);
         is_lt > 0
diff --git a/ceno_zkvm/src/uint.rs b/ceno_zkvm/src/uint.rs
index 23235eefc..16581124d 100644
--- a/ceno_zkvm/src/uint.rs
+++ b/ceno_zkvm/src/uint.rs
@@ -123,7 +123,7 @@ impl<const M: usize, const C: usize, E: ExtensionField> UInt<M, C, E> {
         }
     }
 
-    pub fn assign(&self, instance: &mut [MaybeUninit<E>], values: Vec<E>) {
+    pub fn assign(&self, instance: &mut [MaybeUninit<E::BaseField>], values: Vec<E::BaseField>) {
         assert!(
             values.len() == Self::NUM_CELLS,
             "assign input length mismatch. input_len={}, NUM_CELLS={}",
diff --git a/ceno_zkvm/src/utils.rs b/ceno_zkvm/src/utils.rs
index 610da0c58..116888944 100644
--- a/ceno_zkvm/src/utils.rs
+++ b/ceno_zkvm/src/utils.rs
@@ -11,13 +11,12 @@ pub fn ext_to_u64<E: ExtensionField>(x: &E) -> u64 {
     bases[0].to_canonical_u64()
 }
 
-pub fn i64_to_ext<E: ExtensionField>(x: i64) -> E {
-    let x0 = if x >= 0 {
-        E::BaseField::from(x as u64)
+pub fn i64_to_base<F: SmallField>(x: i64) -> F {
+    if x >= 0 {
+        F::from(x as u64)
     } else {
-        -E::BaseField::from((-x) as u64)
-    };
-    E::from_bases(&[x0, E::BaseField::ZERO])
+        -F::from((-x) as u64)
+    }
 }
 
 /// This is helper function to convert witness of u8 limb into u16 limb