New Blind Signature Protocols Based on Finite Subgroups with Two-Dimensional Cyclicity

Abstract

In this paper, we propose two new blind digital signature protocols based on the difficulty of the discrete logarithm problem (DLP) modulo a composite number n = p · q. These are the first protocols of such type that are based on the computational difficulty of the DLP modulo a composite number. The use of the last difficult problem provides increased security of the signature protocols due to reducing the probability of the potential breaking the protocols, which is connected with potential appearance of the breakthrough solutions of the following two computationally difficult problems: (1) finding discrete logarithm modulo prime and (2) factoring composite number n containing two unknown prime divisors. The designed protocols are based on using finite groups possessing two-dimensional cyclicity. When selecting parameters providing 80-bit security, the signature size in the proposed blind protocols is equal to 240 bits.