From e1c35c36fc5c0d8d1ecde9370d2b5afd35008110 Mon Sep 17 00:00:00 2001
From: Philip Le Riche <7701190+p-leriche@users.noreply.github.com>
Date: Wed, 25 Feb 2026 20:18:15 +0000
Subject: [PATCH] Add ExtendedGCD operation

---
 src/core/config/Categories.json     |   2 -
 src/core/operations/ExtendedGCD.mjs | 101 ++++++++++++++++++++++++++++
 2 files changed, 101 insertions(+), 2 deletions(-)
 create mode 100644 src/core/operations/ExtendedGCD.mjs

diff --git a/src/core/config/Categories.json b/src/core/config/Categories.json
index ab1dafb0..7a65c054 100644
--- a/src/core/config/Categories.json
+++ b/src/core/config/Categories.json
@@ -228,8 +228,6 @@
             "Subtract",
             "Multiply",
             "Divide",
-            "Modular Exponentiation",
-            "Modular Inverse",
             "Extended GCD",
             "Mean",
             "Median",
diff --git a/src/core/operations/ExtendedGCD.mjs b/src/core/operations/ExtendedGCD.mjs
new file mode 100644
index 00000000..88069c74
--- /dev/null
+++ b/src/core/operations/ExtendedGCD.mjs
@@ -0,0 +1,101 @@
+/**
+ * @author p-leriche [philip.leriche@cantab.net]
+ * @copyright Crown Copyright 2025
+ * @license Apache-2.0
+ */
+
+import Operation from "../Operation.mjs";
+import OperationError from "../errors/OperationError.mjs";
+import { parseBigInt, egcd } from "../lib/BigIntUtils.mjs";
+
+/* ---------- operation class ---------- */
+
+/**
+ * Extended GCD operation
+ */
+class ExtendedGCD extends Operation {
+    /**
+     * ExtendedGCD constructor
+     */
+    constructor() {
+        super();
+
+        this.name = "Extended GCD";
+        this.module = "Crypto";
+        this.description =
+            "Computes the Extended Euclidean Algorithm for integers <i>a</i> and <i>b</i>.<br><br>" +
+            "Finds integers <i>x</i> and <i>y</i> (Bezout coefficients) such that:<br>" +
+            "a*x + b*y = gcd(a, b)<br><br>" +
+            "This is fundamental to many number theory algorithms including modular inverse, " +
+            "solving linear Diophantine equations, and cryptographic operations.<br><br>" +
+            "<b>Input handling:</b> If either <i>a</i> or <i>b</i> is left blank, " +
+            "its value is taken from the Input field.";
+        this.infoURL = "https://wikipedia.org/wiki/Extended_Euclidean_algorithm";
+        this.inputType = "string";
+        this.outputType = "string";
+        this.args = [
+            {
+                name: "Value a",
+                type: "string",
+                value: ""
+            },
+            {
+                name: "Value b",
+                type: "string",
+                value: ""
+            }
+        ];
+    }
+
+    /**
+     * @param {string} input
+     * @param {Object[]} args
+     * @returns {string}
+     */
+    run(input, args) {
+        const [aStr, bStr] = args;
+
+        // Trim everything so "" and "   " count as empty
+        const aParam = aStr?.trim();
+        const bParam = bStr?.trim();
+        const inputVal = input?.trim();
+
+        let a, b;
+
+        if (aParam && bParam) {
+            // Case 1: both values given as parameters
+            a = aParam;
+            b = bParam;
+        } else if (!aParam && bParam) {
+            // Case 2: a missing - take from input
+            a = inputVal;
+            b = bParam;
+            if (!a) throw new OperationError("Value a must be defined");
+        } else if (aParam && !bParam) {
+            // Case 3: b missing - take from input
+            a = aParam;
+            b = inputVal;
+            if (!b) throw new OperationError("Value b must be defined");
+        } else if (!aParam && !bParam) {
+            // Case 4: both values missing
+            throw new OperationError("Values a and b must be defined");
+        }
+
+        const aBI = parseBigInt(a, "Value a");
+        const bBI = parseBigInt(b, "Value b");
+
+        const [g, x, y] = egcd(aBI, bBI);
+        const gcd = g < 0n ? -g : g;
+
+        // Format output string bearing in mind that crypto-grade numbers
+        // may greatly exceed the line length.
+        let output = "gcd: " + gcd.toString() + "\n\n";
+        output += "Bezout coefficients:\n";
+        output += "x = " + x.toString() + "\n";
+        output += "y = " + y.toString() + "\n\n";
+
+        return output;
+    }
+}
+
+export default ExtendedGCD;