An enhanced elgamal scheme with respect to the Tiersma attack

Abstract

To enhance ElGamal's protection based on a discrete logarithm problem, He&Kiesler propose a protection based on discrete logarithm and factorization problems.Although Tiersma suggests that as long as the discrete logarithm problem can be solved,the He&Kiesler scheme can also be crypt-analyzed. This paper is to strengthen the He & Kielser scheme. In addition to the He & Kielser advantage, Tiersma's attack can be stopped. Given the solution of discrete logarithm, Tiersma focuses on obtaining the square of the private key and forging the digital signature of the user under attack to detour the factorization problem . In order to counteract this attack, an additional parameter is needed to result in a failure to find the private key. In our scheme, an attacker can hardly detour factorization problem. Thus, in addition to the He & Kiesler advantage, our method can be used to counteract the Tiersma attack.