Step 4

src/NovaVerifierContract.sol

@@ -7,6 +7,7 @@ import "src/blocks/PolyEvalInstance.sol";
 import "src/verifier/Step1.sol";
 import "src/verifier/Step2.sol";
 import "src/verifier/Step3.sol";
+import "src/verifier/Step4.sol";
 import "src/NovaVerifierAbstractions.sol";
 
 contract NovaVerifierContract {
@@ -94,6 +95,12 @@ contract NovaVerifierContract {
             return false;
         }
 
+        // check the required multiset relationship
+        if (!Step4Lib.verify(proof)) {
+            console.log("[Step4] false");
+            return false;
+        }
+
         return true;
     }
 

src/verifier/Step4.sol

@@ -0,0 +1,36 @@
+// SPDX-License-Identifier: Apache-2.0
+pragma solidity ^0.8.0;
+
+import "@std/Test.sol";
+import "src/blocks/pasta/Pallas.sol";
+import "src/blocks/pasta/Vesta.sol";
+import "src/NovaVerifierAbstractions.sol";
+
+library Step4Lib {
+    function verify(Abstractions.CompressedSnark calldata proof) public view returns (bool) {
+        if (!verifyInner(proof.r_W_snark_primary, Vesta.P_MOD)) {
+            return false;
+        } else if (!verifyInner(proof.f_W_snark_secondary, Pallas.P_MOD)) {
+            return false;
+        }
+        return true;
+    }
+
+    function verifyInner(Abstractions.RelaxedR1CSSNARK calldata proof, uint256 modulus) private view returns (bool) {
+        // row
+        uint256 left = mulmod(proof.claims_product_arr[0], proof.claims_product_arr[2], modulus);
+        uint256 right = mulmod(proof.claims_product_arr[1], proof.claims_product_arr[3], modulus);
+        if (left != right) {
+            return false;
+        }
+
+        // col
+        left = mulmod(proof.claims_product_arr[4], proof.claims_product_arr[6], modulus);
+        right = mulmod(proof.claims_product_arr[5], proof.claims_product_arr[7], modulus);
+        if (left != right) {
+            return false;
+        }
+
+        return true;
+    }
+}