ElGamal Public Key Cryptosystem

The ElGamal cryptosystem is an asymmetric encryption method that uses a pair of keys: a public key for encryption and a private key for decryption. It is based on the difficulty of solving certain mathematical problems, making it computationally secure. The system allows secure communication between parties without requiring a shared secret key in advance.

In the encryption process, a sender uses the receiver’s public key along with a randomly chosen number to convert the original message into ciphertext. The receiver then uses their private key to decrypt the ciphertext and retrieve the original message. This method ensures that even if someone intercepts the ciphertext, they cannot recover the original message without the private key.

ElGamal is widely used in secure communication systems and digital signatures because of its strong security features. Its security depends on the use of large numbers and randomness during encryption. The cryptosystem forms the basis for other cryptographic protocols, such as the Digital Signature Algorithm (DSA), and is an important tool for maintaining confidentiality and authenticity in modern communication.