diff --git a/src/core/config/Categories.json b/src/core/config/Categories.json
index aac00ca1ca..e0b8e8dd40 100644
--- a/src/core/config/Categories.json
+++ b/src/core/config/Categories.json
@@ -222,6 +222,7 @@
             "Subtract",
             "Multiply",
             "Divide",
+            "Extended GCD",
             "Mean",
             "Median",
             "Standard Deviation",
diff --git a/src/core/lib/BigIntUtils.mjs b/src/core/lib/BigIntUtils.mjs
new file mode 100644
index 0000000000..dce23f2670
--- /dev/null
+++ b/src/core/lib/BigIntUtils.mjs
@@ -0,0 +1,53 @@
+/**
+ * @author p-leriche [philip.leriche@cantab.net]
+ * @copyright Crown Copyright 2025
+ * @license Apache-2.0
+ */
+
+import OperationError from "../errors/OperationError.mjs";
+
+/**
+ * Number theory utilities used by cryptographic operations.
+ *
+ * Currently provides:
+ *   - parseBigInt
+ *   - Extended Euclidean Algorithm
+ *
+ * Additional algorithms may be added as required.
+ */
+
+/**
+ * parseBigInt helper operation
+ */
+export function parseBigInt(value, param) {
+    const v = (value ?? "").trim();
+    if (/^0x[0-9a-f]+$/i.test(v)) return BigInt(v);
+    if (/^[+-]?[0-9]+$/.test(v)) return BigInt(v);
+    throw new OperationError(param + " must be decimal or hex (0x...)");
+}
+
+/**
+ * Extended Euclidean Algorithm
+ *
+ * Returns [g, x, y] such that:
+ *   a*x + b*y = g = gcd(a, b)
+ *
+ *   (Uses an iterative algorithm to avoid possible stack overflow)
+ */
+export function egcd(a, b) {
+    let oldR = a, r = b;
+    let oldS = 1n, s = 0n;
+    let oldT = 0n, t = 1n;
+
+    while (r !== 0n) {
+        const quotient = oldR / r;
+
+        [oldR, r] = [r, oldR - quotient * r];
+        [oldS, s] = [s, oldS - quotient * s];
+        [oldT, t] = [t, oldT - quotient * t];
+    }
+
+    // oldR is the gcd
+    // oldS and oldT are the Bézout coefficients
+    return [oldR, oldS, oldT];
+}
diff --git a/src/core/operations/ExtendedGCD.mjs b/src/core/operations/ExtendedGCD.mjs
new file mode 100644
index 0000000000..88069c7459
--- /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;
diff --git a/tests/operations/tests/ExtendedGCD.mjs b/tests/operations/tests/ExtendedGCD.mjs
new file mode 100644
index 0000000000..aeefe5e4d2
--- /dev/null
+++ b/tests/operations/tests/ExtendedGCD.mjs
@@ -0,0 +1,126 @@
+/**
+ * Extended GCD tests.
+ *
+ * @author p-leriche [philip.leriche@cantab.net]
+ *
+ * @copyright Crown Copyright 2025
+ * @license Apache-2.0
+ */
+import TestRegister from "../../lib/TestRegister.mjs";
+
+TestRegister.addTests([
+    {
+        name: "Extended GCD: coprime numbers (3, 11)",
+        input: "",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 1\n\n" +
+            "Béut coefficients:\n" +
+            "  x = 4\n" +
+            "  y = -1\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (3) ×(4) + (11) ×(-1) = 1",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["3", "11"],
+            },
+        ],
+    },
+    {
+        name: "Extended GCD: non-coprime numbers (240, 46)",
+        input: "",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 2\n\n" +
+            "Béut coefficients:\n" +
+            "  x = -9\n" +
+            "  y = 47\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (240) ×(-9) + (46) ×(47) = 2",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["240", "46"],
+            },
+        ],
+    },
+    {
+        name: "Extended GCD: with zero (17, 0)",
+        input: "",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 17\n\n" +
+            "Béut coefficients:\n" +
+            "  x = 1\n" +
+            "  y = 0\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (17) ×(1) + (0) ×(0) = 17",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["17", "0"],
+            },
+        ],
+    },
+    {
+        name: "Extended GCD: hexadecimal input (0xFF, 0x11)",
+        input: "",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 17\n\n" +
+            "Béut coefficients:\n" +
+            "  x = 1\n" +
+            "  y = -15\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (255) ×(1) + (17) ×(-15) = 17",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["0xFF", "0x11"],
+            },
+        ],
+    },
+    {
+        name: "Extended GCD: using input field for value a",
+        input: "42",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 7\n\n" +
+            "Béut coefficients:\n" +
+            "  x = -2\n" +
+            "  y = 3\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (42) ×(-2) + (35) ×(3) = 7",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["", "35"],
+            },
+        ],
+    },
+    {
+        name: "Extended GCD: large numbers",
+        input: "",
+        expectedOutput: "Extended Euclidean Algorithm Results:\n" +
+            "=====================================\n\n" +
+            "gcd(a, b) = 1\n\n" +
+            "Béut coefficients:\n" +
+            "  x = -80538738812075595\n" +
+            "  y = 10000000000000000\n\n" +
+            "Verification:\n" +
+            "  a·x + b·y = gcd(a, b)\n" +
+            "  (123456789012345678901234567890) ×(-80538738812075595) + (994064509324197316) ×(10000000000000000) = 1",
+        recipeConfig: [
+            {
+                op: "Extended GCD",
+                args: ["123456789012345678901234567890", "994064509324197316"],
+            },
+        ],
+    },
+]);