An implementation of ElGamal elliptic curves cryptosystems (original) (raw)

Concept of public key cryptography was first introduced by Difie and Hellman in 1976 which using discrete logarithm problem as base of dificulty. In 1985, T. ElGamal proposed public key cyptosystem scheme based on discrete logarithm problem. Elliptic curve cryptosystems were first proposed in 1985 independently by Neil Koblitz and Victor Miller. Elliptic curve cryptosystems are unique in using elliptic curve groups for arithmetic. This cryptosystem based on discrete logarithm problem in the group of points of an elliptic curve defined over a finite field. The discrete logarithm problem in an elliptic curve group appears to be much harder than the discrete logarithm problem in other groups. Hence elliptic curwes cyptosystem can match the security of other cryptosystems while wing smaller key. In this paper we will discuss a VLSI implementation of Elliptic Curves Cryptosystem for ElGamal encryption scheme.