diff --git a/src/params.nr b/src/params.nr
index 01854ab..f5beb50 100644
--- a/src/params.nr
+++ b/src/params.nr
@@ -39,6 +39,17 @@ impl<let N: u32, let MOD_BITS: u32> BigNumParams<N, MOD_BITS> {
     }
 }
 
+impl<let N: u32, let MOD_BITS: u32> std::cmp::Eq for BigNumParams<N, MOD_BITS> {
+    fn eq(self, other: Self) -> bool {
+        (self.has_multiplicative_inverse == other.has_multiplicative_inverse)
+            & (self.modulus == other.modulus)
+            & (self.modulus_u60 == other.modulus_u60)
+            & (self.modulus_u60_x4 == other.modulus_u60_x4)
+            & (self.double_modulus == other.double_modulus)
+            & (self.redc_param == other.redc_param)
+    }
+}
+
 fn get_double_modulus<let N: u32>(modulus: [Field; N]) -> [Field; N] {
     let TWO_POW_120: Field = 0x1000000000000000000000000000000;
     let m: U60Repr<N, 2> = U60Repr::from(modulus);
diff --git a/src/runtime_bignum.nr b/src/runtime_bignum.nr
index 3e64566..0325ca5 100644
--- a/src/runtime_bignum.nr
+++ b/src/runtime_bignum.nr
@@ -201,6 +201,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     }
 
     unconstrained fn __eq(self, other: Self) -> bool {
+        assert(self.params == other.params);
         __eq(self.limbs, other.limbs)
     }
 
@@ -218,6 +219,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __add(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         let limbs = unsafe { __add(params, self.limbs, other.limbs) };
         Self { params, limbs }
     }
@@ -225,6 +227,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __sub(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         let limbs = unsafe { __sub(params, self.limbs, other.limbs) };
         Self { params, limbs }
     }
@@ -232,6 +235,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __mul(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         let limbs = unsafe { __mul::<_, MOD_BITS>(params, self.limbs, other.limbs) };
         Self { params, limbs }
     }
@@ -239,6 +243,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __div(self, divisor: Self) -> Self {
         let params = self.params;
+        assert(params == divisor.params);
         let limbs = unsafe { __div::<_, MOD_BITS>(params, self.limbs, divisor.limbs) };
         Self { params, limbs }
     }
@@ -246,6 +251,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __udiv_mod(self, divisor: Self) -> (Self, Self) {
         let params = self.params;
+        assert(params == divisor.params);
         let (q, r) = unsafe { __udiv_mod(self.limbs, divisor.limbs) };
         (Self { limbs: q, params }, Self { limbs: r, params })
     }
@@ -261,6 +267,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
     // UNCONSTRAINED! (Hence `__` prefix).
     fn __pow(self, exponent: Self) -> Self {
         let params = self.params;
+        assert(params == exponent.params);
         let limbs = unsafe { __pow::<_, MOD_BITS>(params, self.limbs, exponent.limbs) };
         Self { limbs, params }
     }
@@ -348,6 +355,7 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
 
     fn assert_is_not_equal(self, other: Self) {
         let params = self.params;
+        assert(params == other.params);
         assert_is_not_equal(params, self.limbs, other.limbs);
     }
 
@@ -358,22 +366,26 @@ impl<let N: u32, let MOD_BITS: u32> RuntimeBigNumTrait<N, MOD_BITS> for RuntimeB
 
     fn udiv_mod(self, divisor: Self) -> (Self, Self) {
         let params = self.params;
+        assert(params == divisor.params);
         let (q, r) = udiv_mod::<_, MOD_BITS>(params, self.limbs, divisor.limbs);
         (Self { limbs: q, params }, Self { limbs: r, params })
     }
 
     fn udiv(self, divisor: Self) -> Self {
         let params = self.params;
+        assert(params == divisor.params);
         Self { limbs: udiv::<_, MOD_BITS>(params, self.limbs, divisor.limbs), params }
     }
 
     fn umod(self, divisor: Self) -> Self {
         let params = self.params;
+        assert(params == divisor.params);
         Self { limbs: umod::<_, MOD_BITS>(params, self.limbs, divisor.limbs), params }
     }
 
     fn conditional_select(lhs: Self, rhs: Self, predicate: bool) -> Self {
         let params = lhs.params;
+        assert(params == rhs.params);
         Self { limbs: conditional_select(lhs.limbs, rhs.limbs, predicate), params }
     }
 }
@@ -383,6 +395,7 @@ impl<let N: u32, let MOD_BITS: u32> std::ops::Add for RuntimeBigNum<N, MOD_BITS>
     //       via evaluate_quadratic_expression
     fn add(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         Self { limbs: add::<_, MOD_BITS>(params, self.limbs, other.limbs), params }
     }
 }
@@ -392,6 +405,7 @@ impl<let N: u32, let MOD_BITS: u32> std::ops::Sub for RuntimeBigNum<N, MOD_BITS>
     //       via evaluate_quadratic_expression
     fn sub(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         Self { limbs: sub::<_, MOD_BITS>(params, self.limbs, other.limbs), params }
     }
 }
@@ -403,6 +417,7 @@ impl<let N: u32, let MOD_BITS: u32> std::ops::Mul for RuntimeBigNum<N, MOD_BITS>
     //      will create much fewer constraints than calling `mul` and `add` directly
     fn mul(self, other: Self) -> Self {
         let params = self.params;
+        assert(params == other.params);
         Self { limbs: mul::<_, MOD_BITS>(params, self.limbs, other.limbs), params }
     }
 }
@@ -411,6 +426,7 @@ impl<let N: u32, let MOD_BITS: u32> std::ops::Div for RuntimeBigNum<N, MOD_BITS>
     // Note: this method is expensive! Witness computation is extremely expensive as it requires modular exponentiation
     fn div(self, divisor: Self) -> Self {
         let params = self.params;
+        assert(params == divisor.params);
         Self { limbs: div::<_, MOD_BITS>(params, self.limbs, divisor.limbs), params }
     }
 }
@@ -418,6 +434,7 @@ impl<let N: u32, let MOD_BITS: u32> std::ops::Div for RuntimeBigNum<N, MOD_BITS>
 impl<let N: u32, let MOD_BITS: u32> std::cmp::Eq for RuntimeBigNum<N, MOD_BITS> {
     fn eq(self, other: Self) -> bool {
         let params = self.params;
+        assert(params == other.params);
         eq::<_, MOD_BITS>(params, self.limbs, other.limbs)
     }
 }