Enhance docs, add more tests in RSA (#5898)

src/main/java/com/thealgorithms/ciphers/RSA.java

@@ -4,7 +4,27 @@ import java.math.BigInteger;
 import java.security.SecureRandom;
 
 /**
- * @author Nguyen Duy Tiep on 23-Oct-17.
+ * 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 {
 
@@ -12,55 +32,88 @@ public class RSA {
     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);
     }
 
     /**
-     * @return encrypted message
+     * 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();
     }
 
     /**
-     * @return encrypted message as big integer
+     * 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);
     }
 
     /**
-     * @return plain message
+     * 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());
     }
 
     /**
-     * @return plain message as big integer
+     * 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);
     }
 
     /**
-     * Generate a new public and private key set.
+     * 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 r = new SecureRandom();
-        BigInteger p = new BigInteger(bits / 2, 100, r);
-        BigInteger q = new BigInteger(bits / 2, 100, r);
+        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 m = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
+        BigInteger phi = (p.subtract(BigInteger.ONE)).multiply(q.subtract(BigInteger.ONE));
 
         publicKey = BigInteger.valueOf(3L);
-
-        while (m.gcd(publicKey).intValue() > 1) {
+        while (phi.gcd(publicKey).intValue() > 1) {
             publicKey = publicKey.add(BigInteger.TWO);
         }
 
-        privateKey = publicKey.modInverse(m);
+        privateKey = publicKey.modInverse(phi);
     }
 }