ElGamal Digital Signature Algorithm of Adding a Random Number

Abstract

As f or the problem that ElGamal digital signature scheme’s security is constantly being challenged and increasingly becomes increasingly serious , an improved ElGamal digital signature algorithm is proposed. As the original ElGamal algorithm has its own security disadvantages that only one random number is used, in order to improve its security, the scheme presented in this paper improved this demerit by adding a random number to the orig i nal one and increasing difficulty of deciphering key. The security of the improved signature scheme is the same with the ElGamal signature scheme which is based on the difficult computable nature of discrete logarithm over finite fields. Then issues about how to increase the complexity between the random number and the key by adding a random number is discussed. Last, we analyzed the improved signature scheme from the following two aspects: security complexity and time complexity. The analysis showed that the safety of the improved signature scheme was higher than that of the original one, and the improved one has a smaller time complexity.