The method of constructing the digital signature scheme based on the difficulty of the discrete logarithmic problem on the ring Zn

Abstract

Developing digital signature schemes to meet the needs of transactions and activities in society is always a matter of concern. However, the security of these schemes must always be guaranteed. In this paper, we propose a method to build a general signature scheme based on the discrete logarithmic problem on Zn rings. From the proposed method, it is possible to create a new signature schema family similar to the ElGamal signature family. However, when making the selection of the appropriate parameters, the proposed new method signature schemas have a higher degree of security than the ElGamal family schemas. Based on the general signature scheme, we have proposed three new signature schemes. The safety of these schemas is ensured by the difficulty of solving two problems simultaneously analyzing a large integer to prime factors (the numerical analysis problem) and the discrete logarithm problem on Zp (DLP). The proposed new schemas are suitable for practical applications requiring high security.