ElGamal Encryption & Decryption

What is ElGamal Encryption?

ElGamal is an asymmetric key encryption algorithm based on the Diffie-Hellman key exchange, developed by Taher Elgamal in 1985. It provides semantic security, meaning that encrypting the same message twice produces different ciphertexts, making it resistant to chosen-plaintext attacks.

How ElGamal Works

ElGamal vs Other Asymmetric Algorithms

Code Examples

Security.addProvider(new BouncyCastleProvider());
KeyPairGenerator kpg = KeyPairGenerator.getInstance("ElGamal", "BC");
kpg.initialize(1024);
KeyPair kp = kpg.generateKeyPair();

Cipher cipher = Cipher.getInstance("ElGamal/None/NoPadding", "BC");
cipher.init(Cipher.ENCRYPT_MODE, kp.getPublic());
byte[] ciphertext = cipher.doFinal(plaintext);

from Crypto.PublicKey import ElGamal
from Crypto.Random import get_random_bytes

# Generate key pair
key = ElGamal.generate(2048, get_random_bytes)
public_key = key.publickey()

# ElGamal is typically used with hybrid encryption
# combining with symmetric ciphers like AES

Use Cases and Best Practices

• Hybrid Encryption: Use ElGamal to encrypt symmetric keys (AES), then encrypt the actual data with AES. This combines ElGamal's security with AES's speed.
• Digital Signatures: ElGamal can be adapted for digital signatures (ElGamal signature scheme), though DSA (derived from ElGamal) is more commonly used.
• Key Exchange: ElGamal is closely related to Diffie-Hellman and can be used for secure key exchange protocols.
• Key Size: For standard ElGamal, use at least 2048-bit keys. For EC-ElGamal, 256-bit curves provide equivalent security.