diff --git a/src/field.rs b/src/field.rs
index 37c94de..b6410a8 100644
--- a/src/field.rs
+++ b/src/field.rs
@@ -1,12 +1,16 @@
 //! This module defines our customized field trait.
 
+use ff::Field;
 use ff::PrimeField;
 use halo2curves::serde::SerdeObject;
+use rand_core::RngCore;
 use serde::Serialize;
 
 use crate::{fp2::GoldilocksExt2, Goldilocks, GoldilocksExt3};
 
 pub trait SmallField: PrimeField + Serialize + SerdeObject {
+    /// Base field
+    type BaseField;
     /// Extension degree of the Field
     const DEGREE: usize;
     /// Identifier string
@@ -16,12 +20,16 @@ pub trait SmallField: PrimeField + Serialize + SerdeObject {
     /// Convert a field elements to a u64 vector
     fn to_canonical_u64_vec(&self) -> Vec<u64>;
     /// Convert self to limbs of Goldilocks elements
-    fn to_limbs(&self) -> Vec<Goldilocks>;
+    fn to_limbs(&self) -> Vec<Self::BaseField>;
     /// Convert limbs into self
-    fn from_limbs(limbs: &[Goldilocks]) -> Self;
+    fn from_limbs(limbs: &[Self::BaseField]) -> Self;
+    /// Sample a random over the base field
+    fn sample_base(rng: impl RngCore) -> Self;
 }
 
 impl SmallField for Goldilocks {
+    type BaseField = Self;
+
     const DEGREE: usize = 1;
     const NAME: &'static str = "Goldilocks";
 
@@ -43,8 +51,14 @@ impl SmallField for Goldilocks {
     fn from_limbs(limbs: &[Goldilocks]) -> Self {
         limbs[0]
     }
+
+    fn sample_base(mut rng: impl RngCore) -> Self {
+        Self::random(&mut rng)
+    }
 }
 impl SmallField for GoldilocksExt2 {
+    type BaseField = Goldilocks;
+
     const DEGREE: usize = 2;
     const NAME: &'static str = "GoldilocksExt2";
 
@@ -71,8 +85,14 @@ impl SmallField for GoldilocksExt2 {
     fn from_limbs(limbs: &[Goldilocks]) -> Self {
         Self(limbs[..1].try_into().unwrap())
     }
+
+    fn sample_base(mut rng: impl RngCore) -> Self {
+        Self::BaseField::random(&mut rng).into()
+    }
 }
 impl SmallField for GoldilocksExt3 {
+    type BaseField = Goldilocks;
+
     const DEGREE: usize = 3;
     const NAME: &'static str = "GoldilocksExt3";
 
@@ -99,4 +119,8 @@ impl SmallField for GoldilocksExt3 {
     fn from_limbs(limbs: &[Goldilocks]) -> Self {
         Self(limbs[..2].try_into().unwrap())
     }
+
+    fn sample_base(mut rng: impl RngCore) -> Self {
+        Self::BaseField::random(&mut rng).into()
+    }
 }