From d69172b5bf4de89ab168ff75153bee5d67546e9f Mon Sep 17 00:00:00 2001
From: QuantumSoham <quantumsc03@gmail.com>
Date: Mon, 28 Apr 2025 22:42:03 +0530
Subject: [PATCH] feat: add RSA encryption and decryption algorithm

---
 Ciphers/RSAAlgorithm.js           | 106 ++++++++++++++++++++++++++++++
 Ciphers/test/RSAAlgorithm.test.js |  14 ++++
 2 files changed, 120 insertions(+)
 create mode 100644 Ciphers/RSAAlgorithm.js
 create mode 100644 Ciphers/test/RSAAlgorithm.test.js

diff --git a/Ciphers/RSAAlgorithm.js b/Ciphers/RSAAlgorithm.js
new file mode 100644
index 0000000000..347e2531a1
--- /dev/null
+++ b/Ciphers/RSAAlgorithm.js
@@ -0,0 +1,106 @@
+// RSAAlgorithm.js
+
+/**
+ * Generates the greatest common divisor of two numbers.
+ * @param {number} a - First number.
+ * @param {number} b - Second number.
+ * @returns {number} - The GCD of a and b.
+ */
+export function gcd(a, b) {
+  if (b === 0) {
+    return a
+  }
+  return gcd(b, a % b)
+}
+
+/**
+ * Calculates modular inverse using Extended Euclidean Algorithm.
+ * @param {number} e - The number to find inverse for.
+ * @param {number} phi - The modulus.
+ * @returns {number} - The modular inverse of e mod phi.
+ */
+export function modInverse(e, phi) {
+  let [m0, x0, x1] = [phi, 0, 1]
+
+  if (phi === 1) {
+    return 0
+  }
+
+  while (e > 1) {
+    let q = Math.floor(e / phi)
+    ;[e, phi] = [phi, e % phi]
+    ;[x0, x1] = [x1 - q * x0, x0]
+  }
+
+  if (x1 < 0) {
+    x1 += m0
+  }
+
+  return x1
+}
+
+/**
+ * Performs modular exponentiation.
+ * @param {number} base - Base number.
+ * @param {number} exponent - Exponent.
+ * @param {number} modulus - Modulus.
+ * @returns {number} - (base^exponent) % modulus.
+ */
+export function modPow(base, exponent, modulus) {
+  if (modulus === 1) return 0
+  let result = 1
+  base = base % modulus
+
+  while (exponent > 0) {
+    if (exponent % 2 === 1) {
+      result = (result * base) % modulus
+    }
+    exponent = Math.floor(exponent / 2)
+    base = (base * base) % modulus
+  }
+
+  return result
+}
+
+/**
+ * Generates RSA keys.
+ * @param {number} p - A prime number.
+ * @param {number} q - A prime number.
+ * @returns {{publicKey: {e: number, n: number}, privateKey: {d: number, n: number}}}
+ */
+export function generateKeys(p, q) {
+  const n = p * q
+  const phi = (p - 1) * (q - 1)
+
+  let e = 2
+  while (e < phi && gcd(e, phi) !== 1) {
+    e++
+  }
+
+  const d = modInverse(e, phi)
+
+  return {
+    publicKey: { e, n },
+    privateKey: { d, n }
+  }
+}
+
+/**
+ * Encrypts a message with a public key.
+ * @param {number} message - The message to encrypt (as a number).
+ * @param {{e: number, n: number}} publicKey - The public key.
+ * @returns {number} - The encrypted message.
+ */
+export function encrypt(message, publicKey) {
+  return modPow(message, publicKey.e, publicKey.n)
+}
+
+/**
+ * Decrypts a cipher with a private key.
+ * @param {number} cipher - The encrypted message (cipher).
+ * @param {{d: number, n: number}} privateKey - The private key.
+ * @returns {number} - The decrypted message.
+ */
+export function decrypt(cipher, privateKey) {
+  return modPow(cipher, privateKey.d, privateKey.n)
+}
diff --git a/Ciphers/test/RSAAlgorithm.test.js b/Ciphers/test/RSAAlgorithm.test.js
new file mode 100644
index 0000000000..ac1d0e540f
--- /dev/null
+++ b/Ciphers/test/RSAAlgorithm.test.js
@@ -0,0 +1,14 @@
+// RSAAlgorithm.test.js
+import { describe, it, expect } from 'vitest'
+import { generateKeys, encrypt, decrypt } from '../RSAAlgorithm.js'
+
+describe('RSA Algorithm', () => {
+  it('should encrypt and decrypt correctly', () => {
+    const { publicKey, privateKey } = generateKeys(61, 53) // two primes
+    const message = 65
+    const cipher = encrypt(message, publicKey)
+    const decrypted = decrypt(cipher, privateKey)
+
+    expect(decrypted).toBe(message)
+  })
+})