Apr 28, 2025
diff --git a/Ciphers/RSAAlgorithm.js b/Ciphers/RSAAlgorithm.js
 // 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
 // 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)
  })
 })
Original file line number	Diff line number	Diff line change
		@@ -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)
		}
Original file line number	Diff line number	Diff line change
		@@ -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)
		})
		})