Remarks on some signature schemes based on factoring and discrete logarithms

Recently, He [Digital signature scheme based on factoring and discrete logarithms, Electronics Letters 37 (4) (2001) 220-222], Hwang et al. [Improved digital signature scheme based on factoring and discrete logarithms, Journal of Discrete Mathematical Sciences & Cryptography 5 (2) (2002) 151-155], and Wang et al. [Proceedings of the17th International Conference on Advanced Information Networking and Applications, 2003, pp. 557-560] proposed some digital signature schemes based on factoring and discrete logarithms. The major concept of these schemes is that it is very unlikely to efficiently solve factoring and discrete logarithm problems simultaneously. Therefore, the security of these schemes is higher than that of the schemes based on either factoring or discrete logarithms. In this paper, we point out that these schemes do not satisfy the claimed properties. We show that their security is based only on the difficulty of solving the discrete logarithm problem.