A Digital Signature Scheme on the Conic Curve over Zn Based on Two Hard Problems

Recently, Xiao et al. proposed a digital signature scheme (XWS scheme) based on the conic curve over Zn and claimed that the security relied on both of the factorization and the discrete logarithm. However, there is a flaw in the XWS scheme, where the modulus n can be factorized easily. This flaw shows that the XWS scheme is not a scheme whose security based on integer factorization problem. To address this issue, an improved digital signature scheme based on two hard problems simultaneously is proposed in this paper. Furthermore, the numeric simulation for the improved scheme is presented. Since the security of the improved scheme is indeed based on two hard problems, it not only maintains the merits of the XWS scheme, but also overcomes the vulnerability of the XWS scheme.