As for the problem that ElGamal digital signature scheme’s security is constantly being challenged and is becoming more and more serious, an improved ElGamal digital signature algorithm was 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 proposed scheme improved this demerit by adding a random number to the original 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. Its time complexity is better than the original one but the issue is about the time complexity which is still high. So in order to improve the time complexity another improved ElGamal digital signature algorithm is proposed. The scheme presented in this paper after analysis showed that the security level is kept high by using two random numbers and the time complexity is reduced.
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