diff --git a/crates/proof-of-sql/src/base/scalar/test_scalar_test.rs b/crates/proof-of-sql/src/base/scalar/test_scalar_test.rs
index 439e833a6..249ec30b3 100644
--- a/crates/proof-of-sql/src/base/scalar/test_scalar_test.rs
+++ b/crates/proof-of-sql/src/base/scalar/test_scalar_test.rs
@@ -1,6 +1,13 @@
+use core::str::FromStr;
+
 use crate::base::scalar::{test_scalar::TestScalar, Scalar};
+use bnum::types::U256;
 use num_traits::Inv;
 
+use super::ScalarExt;
+
+const MAX_TEST_SCALAR_SIGNED_VALUE_AS_STRING: &str = "3618502788666131106986593281521497120428558179689953803000975469142727125494";
+
 #[test]
 fn we_can_get_test_scalar_constants_from_z_p() {
     assert_eq!(TestScalar::from(0), TestScalar::ZERO);
@@ -10,3 +17,51 @@ fn we_can_get_test_scalar_constants_from_z_p() {
     assert_eq!(-TestScalar::TWO.inv().unwrap(), TestScalar::MAX_SIGNED);
     assert_eq!(TestScalar::from(10), TestScalar::TEN);
 }
+
+#[test]
+fn we_can_convert_u256_to_test_scalar_with_wrapping(){
+    // ARRANGE
+    let u256_value = U256::TWO;
+
+    // ACT
+    let test_scalar = TestScalar::from_wrapping(u256_value);
+
+    // ASSERT
+    assert_eq!(test_scalar, TestScalar::TWO);
+}
+
+#[test]
+fn we_can_convert_u256_to_test_scalar_with_wrapping_of_large_value(){
+    // ARRANGE
+    let u256_value = U256::from_str(MAX_TEST_SCALAR_SIGNED_VALUE_AS_STRING).unwrap() * U256::TWO + U256::ONE;
+
+    // ACT
+    let test_scalar = TestScalar::from_wrapping(u256_value);
+
+    // ASSERT
+    assert_eq!(test_scalar, TestScalar::ZERO);
+}
+
+#[test]
+fn we_can_convert_test_scalar_to_u256_with_wrapping(){
+    // ARRANGE
+    let test_scalar = TestScalar::TWO;
+
+    // ACT
+    let u256_value = test_scalar.into_u256_wrapping();
+
+    // ASSERT
+    assert_eq!(u256_value, U256::TWO);
+}
+
+#[test]
+fn we_can_convert_test_scalar_to_256_with_wrapping_of_negative_value(){
+    // ARRANGE
+    let test_scalar = -TestScalar::ONE;
+
+    // ACT
+    let u256: bnum::BUint<4> = test_scalar.into_u256_wrapping();
+
+    // ASSERT
+    assert_eq!(u256, U256::from_str(MAX_TEST_SCALAR_SIGNED_VALUE_AS_STRING).unwrap() * U256::TWO);
+}
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