test: ConvertCircuit strategy using incorrect rate

crates/core/component/shielded-pool/src/convert.rs

@@ -296,4 +296,39 @@ mod tests {
             assert!(check_circuit_satisfaction(public, private).is_ok());
         }
     }
+
+    fn nonzero_u128() -> impl Strategy<Value = u128> {
+        prop::num::u128::ANY.prop_filter("nonzero", |x| *x != 0)
+    }
+
+    fn nonzero_u64() -> impl Strategy<Value = u64> {
+        prop::num::u64::ANY.prop_filter("nonzero", |x| *x != 0)
+    }
+
+    prop_compose! {
+        // The circuit should be unsatisfiable if the rate used by the prover is incorrect.
+        // We generate a random rate, filtering out non-zero denominators to avoid division by zero.
+        // This is the "true" rate.
+        // Next, we add a (u64) random value to the true rate, and the prover generates the balance
+        // using this incorrect rate.
+        fn arb_invalid_convert_statement_wrong_rate(balance_blinding: Fr)(amount in any::<u64>(), from_asset_id64 in any::<u64>(), to_asset_id64 in any::<u64>(), rate_num in nonzero_u64(), rate_denom in nonzero_u128(), random_rate_num in nonzero_u64()) -> (ConvertProofPublic, ConvertProofPrivate) {
+            let rate = U128x128::ratio(u128::from(rate_num), rate_denom).expect("the bounds will make this not overflow");
+            let incorrect_rate = rate.checked_add(&U128x128::ratio(random_rate_num, 1u64).expect("should not overflow")).expect("should not overflow");
+            let from = asset::Id(Fq::from(from_asset_id64));
+            let to = asset::Id(Fq::from(to_asset_id64));
+            let amount = Amount::from(amount);
+            let balance = Balance::from(Value { asset_id: to, amount: incorrect_rate.apply_to_amount(&amount).expect("the bounds will make this not overflow")}) - Value {asset_id: from, amount};
+            let public = ConvertProofPublic { from, to, rate, balance_commitment: balance.commit(balance_blinding) };
+            let private = ConvertProofPrivate { amount, balance_blinding };
+            (public, private)
+        }
+    }
+
+    proptest! {
+        #[test]
+        fn convert_proof_invalid_convert_statement_wrong_rate((public, private) in arb_invalid_convert_statement_wrong_rate(Fr::from(1u64))) {
+            assert!(check_satisfaction(&public, &private).is_err());
+            assert!(check_circuit_satisfaction(public, private).is_err());
+        }
+    }
 }