Public-key cryptosystem based on the discrete logarithm problem

Abstract

In 1985, T. ElGamal proposed a public-key cryptosystem and a signature scheme, in which the difficulty of breaking the system is based on the difficulty of computing a discrete logarithm in a finite group. For the same security level, the size of the ciphertext and the computational time of ElGamal's encryption are double those of the wellknown RSA scheme. In this paper, we propose a public-key cryptosystem based on the discrete logarithm, in which the size of the ciphertext and the computational time are the same as those of the RSA scheme, and the security level is the same as the ElGamal cryptosystem.