From 9c696b523de502a966af283afcd7f7bceb5479d7 Mon Sep 17 00:00:00 2001
From: Barry Brown <profbbrown@gmail.com>
Date: Thu, 13 Jun 2024 06:49:14 +0000
Subject: [PATCH 1/3] Remove assumption of 26 as modulus

---
 src/core/Utils.mjs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/core/Utils.mjs b/src/core/Utils.mjs
index a9c381d7..707720cc 100755
--- a/src/core/Utils.mjs
+++ b/src/core/Utils.mjs
@@ -1275,7 +1275,7 @@ class Utils {
     static modInv(x, y) {
         x %= y;
         for (let i = 1; i < y; i++) {
-            if ((x * i) % 26 === 1) {
+            if ((x * i) % y === 1) {
                 return i;
             }
         }

From 8530c47cb8c92dc0ab3a9b93469c1c0a56e13465 Mon Sep 17 00:00:00 2001
From: Barry Brown <profbbrown@gmail.com>
Date: Thu, 13 Jun 2024 17:19:11 +0000
Subject: [PATCH 2/3] modInv uses Extended Euclidean Algorithm

---
 src/core/Utils.mjs | 27 +++++++++++++++++----------
 1 file changed, 17 insertions(+), 10 deletions(-)

diff --git a/src/core/Utils.mjs b/src/core/Utils.mjs
index 707720cc..08eadbf1 100755
--- a/src/core/Utils.mjs
+++ b/src/core/Utils.mjs
@@ -1266,19 +1266,26 @@ class Utils {
 
     /**
      * Finds the modular inverse of two values.
+     * Uses the Extended Euclidean Algorithm.
      *
-     * @author Matt C [matt@artemisbot.uk]
-     * @param {number} x
-     * @param {number} y
-     * @returns {number}
+     * @author Barry B [profbbrown@gmail.com]
+     * @param {number} a
+     * @param {number} n
+     * @returns {number|null}
      */
-    static modInv(x, y) {
-        x %= y;
-        for (let i = 1; i < y; i++) {
-            if ((x * i) % y === 1) {
-                return i;
-            }
+    static modInv(a, n) {
+        let t = 0, newT = 1, r = n, newR = a;
+
+        while (newR !== 0) {
+            const q = Math.floor(r / newR);
+            [t, newT] = [newT, t - q * newT];
+            [r, newR] = [newR, r - q * newR];
         }
+
+        if (r > 1) return null;
+        if (t < 0) t = t + n;
+
+        return t;
     }
 
 

From bc559888e6bfa29091992b6058048caa6358fc01 Mon Sep 17 00:00:00 2001
From: Barry Brown <profbbrown@gmail.com>
Date: Thu, 13 Jun 2024 20:57:17 +0000
Subject: [PATCH 3/3] Returns undefined if not invertible

---
 src/core/Utils.mjs | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/core/Utils.mjs b/src/core/Utils.mjs
index 08eadbf1..851044c3 100755
--- a/src/core/Utils.mjs
+++ b/src/core/Utils.mjs
@@ -1265,13 +1265,14 @@ class Utils {
 
 
     /**
-     * Finds the modular inverse of two values.
+     * Calculates the modular multiplicative inverse of a (mod n).
      * Uses the Extended Euclidean Algorithm.
+     * https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
      *
      * @author Barry B [profbbrown@gmail.com]
      * @param {number} a
      * @param {number} n
-     * @returns {number|null}
+     * @returns {number|undefined} The inverse of a (mod n), or undefined
      */
     static modInv(a, n) {
         let t = 0, newT = 1, r = n, newR = a;
@@ -1282,7 +1283,7 @@ class Utils {
             [r, newR] = [newR, r - q * newR];
         }
 
-        if (r > 1) return null;
+        if (r > 1) return undefined;
         if (t < 0) t = t + n;
 
         return t;