diff --git a/packages/circuits/helpers/substring-match.circom b/packages/circuits/helpers/substring-match.circom
index b1143b6a..cb2e31cb 100644
--- a/packages/circuits/helpers/substring-match.circom
+++ b/packages/circuits/helpers/substring-match.circom
@@ -2,6 +2,7 @@ pragma circom 2.1.6;
 
 include "circomlib/circuits/comparators.circom";
 include "circomlib/circuits/mux1.circom";
+include "../utils/hash.circom";
 
 /// @title SubstringMatch
 /// @notice This template verifies if a given substring exists within a larger string at a specified index
@@ -15,9 +16,21 @@ include "circomlib/circuits/mux1.circom";
 /// @output isValid A signal that is 1 if the substring matches at the given index, 0 otherwise
 template SubstringMatch(maxLength, maxSubstringLength) {
     signal input in[maxLength];
-    signal input startIndex;
     signal input revealedString[maxSubstringLength];
-    signal input r;
+    signal input startIndex;
+
+    // Derive r from the inputs
+    signal r;
+    component rHasher;
+    rHasher = PoseidonModular(maxLength + maxSubstringLength + 1);
+    rHasher.in[0] <== startIndex;
+    for (var i = 0; i < maxSubstringLength; i++) {
+        rHasher.in[i + 1] <== revealedString[i];
+    }
+    for (var i = 0; i < maxLength; i++) {
+        rHasher.in[i + maxSubstringLength + 1] <== in[i];
+    }
+    r <== rHasher.out;
 
     // Check if each character in the revealed string is non-zero
     signal isNonZero[maxSubstringLength];
diff --git a/packages/circuits/tests/substring-match.test.ts b/packages/circuits/tests/substring-match.test.ts
index 7ee83e9e..ad9174c9 100644
--- a/packages/circuits/tests/substring-match.test.ts
+++ b/packages/circuits/tests/substring-match.test.ts
@@ -24,8 +24,7 @@ describe('SubstringMatch', () => {
     const input = {
       in: padArray([104, 101, 108, 108, 111, 32, 119, 111, 114, 108, 100], 32), // "hello world"
       startIndex: 6,
-      revealedString: padArray([119, 111, 114, 108, 100], 16), // "world"
-      r: 69, // A prime number for the random linear combination
+      revealedString: padArray([119, 111, 114, 108, 100], 16), // "world" 
     };
 
     const witness = await circuit.calculateWitness(input);
@@ -41,7 +40,6 @@ describe('SubstringMatch', () => {
       in: padArray([104, 101, 108, 108, 111, 32, 119, 111, 114, 108, 100], 32), // "hello world"
       startIndex: 6,
       revealedString: padArray([119, 111, 114, 108, 107], 16), // "worlk" (last character different)
-      r: 69,
     };
 
     const witness = await circuit.calculateWitness(input);
@@ -57,7 +55,6 @@ describe('SubstringMatch', () => {
       in: padArray([104, 101, 108, 108, 111, 32, 119, 111, 114, 108, 100], 32), // "hello world"
       startIndex: 0,
       revealedString: padArray([104, 101, 108, 108, 111], 16), // "hello"
-      r: 69,
     };
 
     const witness = await circuit.calculateWitness(input);
@@ -73,7 +70,6 @@ describe('SubstringMatch', () => {
       in: padArray([104, 101, 108, 108, 111, 32, 119, 111, 114, 108, 100], 32), // "hello world"
       startIndex: 7,
       revealedString: padArray([111, 114, 108, 100], 16), // "orld"
-      r: 69,
     };
 
     const witness = await circuit.calculateWitness(input);
@@ -89,7 +85,6 @@ describe('SubstringMatch', () => {
       in: padArray([104, 101, 108, 108, 111, 32, 119, 111, 114, 108, 100], 32), // "hello world"
       startIndex: 32, // Out of bounds (valid indices are 0-31)
       revealedString: padArray([100], 16), // "d"
-      r: 69,
     };
 
     const witness = await circuit.calculateWitness(input);