diff --git a/src/field/crypto_bigint_const_monty.rs b/src/field/crypto_bigint_const_monty.rs
index 118f79b..e5002ee 100644
--- a/src/field/crypto_bigint_const_monty.rs
+++ b/src/field/crypto_bigint_const_monty.rs
@@ -9,7 +9,7 @@ use core::{
     str::FromStr,
 };
 use crypto_bigint::{
-    Limb,
+    Limb, NonZeroUint, Uint as CBUint,
     modular::{ConstMontyForm, ConstMontyParams as Params, Retrieve},
     subtle::{Choice, ConditionallySelectable, ConstantTimeEq},
 };
@@ -505,25 +505,28 @@ impl<Mod: Params<LIMBS>, const LIMBS: usize> Semiring for ConstMontyField<Mod, L
 impl<Mod: Params<LIMBS>, const LIMBS: usize> Ring for ConstMontyField<Mod, LIMBS> {}
 
 impl<Mod: Params<LIMBS>, const LIMBS: usize> Field for ConstMontyField<Mod, LIMBS> {
-    type Inner = ConstMontyForm<Mod, LIMBS>;
+    type Inner = Uint<LIMBS>;
 
     #[inline(always)]
     fn inner(&self) -> &Self::Inner {
-        &self.0
+        Uint::new_ref(self.0.as_montgomery())
     }
 }
 
 impl<Mod: Params<LIMBS>, const LIMBS: usize> ConstPrimeField for ConstMontyField<Mod, LIMBS> {
-    const MODULUS: Self::Inner = ConstMontyForm::<Mod, LIMBS>::new(Mod::PARAMS.modulus().as_ref());
+    const MODULUS: Self::Inner = *Uint::new_ref(Mod::PARAMS.modulus().as_ref());
     const MODULUS_MINUS_ONE_DIV_TWO: Self::Inner = {
-        let m_minus_one = ConstMontyForm::sub(&Self::MODULUS, &ConstMontyForm::ONE);
-        m_minus_one.div_by_2()
+        let m_minus_one = CBUint::wrapping_sub(Self::MODULUS.inner(), &CBUint::ONE);
+        let two = CBUint::<LIMBS>::wrapping_add(&CBUint::ONE, &CBUint::ONE);
+        Uint::new(CBUint::wrapping_div(
+            &m_minus_one,
+            &NonZeroUint::new_unwrap(two),
+        ))
     };
 
     #[inline(always)]
     fn new_unchecked(inner: Self::Inner) -> Self {
-        // Inner value is a ConstMontyForm so it's guaranteed to be valid
-        Self(inner)
+        Self(ConstMontyForm::from_montgomery(inner.into_inner()))
     }
 }
 
@@ -1295,6 +1298,14 @@ mod prop_tests {
     );
     type F = ConstMontyField<ModP, { U256::LIMBS }>;
 
+    #[test]
+    fn modulus_minus_one_div_two_correct() {
+        assert_eq!(
+            F::MODULUS_MINUS_ONE_DIV_TWO,
+            Uint::from_be_hex("006E54A6C50F6671DB743AAEC4CCBC3E82926C650F53AAF3D7C27DB237D18F93")
+        )
+    }
+
     fn any_f() -> impl Strategy<Value = F> {
         any::<u64>().prop_map(F::from)
     }
diff --git a/src/semiring/crypto_bigint_uint.rs b/src/semiring/crypto_bigint_uint.rs
index 4f3aa5c..482027f 100644
--- a/src/semiring/crypto_bigint_uint.rs
+++ b/src/semiring/crypto_bigint_uint.rs
@@ -6,7 +6,7 @@ use core::{
     hash::{Hash, Hasher},
     iter::{Product, Sum},
     ops::{
-        Add, AddAssign, Mul, MulAssign, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
+        Add, AddAssign, Div, Mul, MulAssign, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
         SubAssign,
     },
     str::FromStr,
@@ -269,6 +269,24 @@ impl_basic_op!(Add, add);
 impl_basic_op!(Sub, sub);
 impl_basic_op!(Mul, mul);
 
+impl<const LIMBS: usize> Div for Uint<LIMBS> {
+    type Output = Self;
+
+    #[inline(always)]
+    fn div(self, rhs: Self) -> Self::Output {
+        self.div(&rhs)
+    }
+}
+
+impl<'a, const LIMBS: usize> Div<&'a Self> for Uint<LIMBS> {
+    type Output = Self;
+
+    fn div(self, rhs: &'a Self) -> Self::Output {
+        let non_zero = crypto_bigint::NonZero::new(rhs.0).expect("division by zero");
+        Self(self.0.div(&non_zero))
+    }
+}
+
 impl<const LIMBS: usize> Rem for Uint<LIMBS> {
     type Output = Self;