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*. Its security depends upon the difficulty of a certain problem in

related to computing discrete logarithms.

## . . . ElGamal encryption . . .

ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm.

The first party, Alice, generates a key pair as follows:

- Generate an efficient description of a cyclic group
- Choose an integer
- Compute
- The
**public key**consists of the values

## . . . ElGamal encryption . . .

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