ElGamal encryption

In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985.^[1] ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. The Digital Signature Algorithm (DSA) is a variant of the ElGamal signature scheme, which should not be confused with ElGamal encryption.

ElGamal encryption can be defined over any cyclic group ${\displaystyle G}$, like multiplicative group of integers modulo n if and only if n is 1, 2, 4, p^k or 2p^k, where p is an odd prime and k > 0. Its security depends upon the difficulty of the Decisional Diffie Hellman Problem in ${\displaystyle G}$.