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RSA.java
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package com.thealgorithms.ciphers;
import java.math.BigInteger;
import java.security.SecureRandom;
/**
* RSA is an asymmetric cryptographic algorithm used for secure data encryption and decryption.
* It relies on a pair of keys: a public key (used for encryption) and a private key
* (used for decryption). The algorithm is based on the difficulty of factoring large prime numbers.
*
* This implementation includes key generation, encryption, and decryption methods that can handle both
* text-based messages and BigInteger inputs. For more details on RSA:
* <a href="https://en.wikipedia.org/wiki/RSA_(cryptosystem)">RSA Cryptosystem - Wikipedia</a>.
*
* Example Usage:
* <pre>
* RSA rsa = new RSA(1024);
* String encryptedMessage = rsa.encrypt("Hello RSA!");
* String decryptedMessage = rsa.decrypt(encryptedMessage);
* System.out.println(decryptedMessage); // Output: Hello RSA!
* </pre>
*
* Note: The key size directly affects the security and performance of the RSA algorithm.
* Larger keys are more secure but slower to compute.
*
* @author Nguyen Duy Tiep
* @version 23-Oct-17
*/
public class RSA {
private BigInteger modulus;
private BigInteger privateKey;
private BigInteger publicKey;
/**
* Constructor that generates RSA keys with the specified number of bits.
*
* @param bits The bit length of the keys to be generated. Common sizes include 512, 1024, 2048, etc.
*/
public RSA(int bits) {
generateKeys(bits);
}
/**
* Encrypts a text message using the RSA public key.
*
* @param message The plaintext message to be encrypted.
* @throws IllegalArgumentException If the message is empty.
* @return The encrypted message represented as a String.
*/
public synchronized String encrypt(String message) {
if (message.isEmpty()) {
throw new IllegalArgumentException("Message is empty");
}
return (new BigInteger(message.getBytes())).modPow(publicKey, modulus).toString();
}
/**
* Encrypts a BigInteger message using the RSA public key.
*
* @param message The plaintext message as a BigInteger.
* @return The encrypted message as a BigInteger.
*/
public synchronized BigInteger encrypt(BigInteger message) {
return message.modPow(publicKey, modulus);
}
/**
* Decrypts an encrypted message (as String) using the RSA private key.
*
* @param encryptedMessage The encrypted message to be decrypted, represented as a String.
* @throws IllegalArgumentException If the message is empty.
* @return The decrypted plaintext message as a String.
*/
public synchronized String decrypt(String encryptedMessage) {
if (encryptedMessage.isEmpty()) {
throw new IllegalArgumentException("Message is empty");
}
return new String((new BigInteger(encryptedMessage)).modPow(privateKey, modulus).toByteArray());
}
/**
* Decrypts an encrypted BigInteger message using the RSA private key.
*
* @param encryptedMessage The encrypted message as a BigInteger.
* @return The decrypted plaintext message as a BigInteger.
*/
public synchronized BigInteger decrypt(BigInteger encryptedMessage) {
return encryptedMessage.modPow(privateKey, modulus);
}
/**
* Generates a new RSA key pair (public and private keys) with the specified bit length.
* Steps:
* 1. Generate two large prime numbers p and q.
* 2. Compute the modulus n = p * q.
* 3. Compute Euler's totient function: φ(n) = (p-1) * (q-1).
* 4. Choose a public key e (starting from 3) that is coprime with φ(n).
* 5. Compute the private key d as the modular inverse of e mod φ(n).
* The public key is (e, n) and the private key is (d, n).
*
* @param bits The bit length of the keys to be generated.
*/
public final synchronized void generateKeys(int bits) {
SecureRandom random = new SecureRandom();
BigInteger p = new BigInteger(bits / 2, 100, random);
BigInteger q = new BigInteger(bits / 2, 100, random);
modulus = p.multiply(q);
BigInteger phi = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
publicKey = BigInteger.valueOf(3L);
while (phi.gcd(publicKey).intValue() > 1) {
publicKey = publicKey.add(BigInteger.TWO);
}
privateKey = publicKey.modInverse(phi);
}
}