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 $G$ , 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 a certain problem in $G$ related to computing discrete logarithms.

^ Taher ElGamal (1985). "A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms" (PDF). IEEE Transactions on Information Theory. 31 (4): 469–472. CiteSeerX 10.1.1.476.4791. doi:10.1109/TIT.1985.1057074. S2CID 2973271. (conference version appeared in CRYPTO'84, pp. 10–18)

[1] Taher ElGamal (1985). "A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms" (PDF). IEEE Transactions on Information Theory. 31 (4): 469–472. CiteSeerX 10.1.1.476.4791. doi:10.1109/TIT.1985.1057074. S2CID 2973271. (conference version appeared in CRYPTO'84, pp. 10–18)

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