Some cryptanalysis of a p -ary generalized self-shrinking generator

Abstract

The binary Pseudo Random Sequences (PRSs) with maximum period and good statistical and correlation properties have been widely used in cryptography and modern communication and information systems. To achieve unconditional security of the PRSs applications they must have long period, balance property, run property, n-tuple distribution, two-level auto correlation, low-level cross correlation and large linear span. Because of that the architecture of a p-ary Generalized Self-Shrinking Generator (pGSSG) which produces non binary nonlinear PRSs is proposed in this paper. The security of the pGSSG against the exhaustive search and entropy attacks are investigated. It is shown that the pGSSG is more secure than Self-Shrinking Generator and Modified SSG (MSSG) against these attacks. It is proven that the complexity of the used pGSSG attack increases with increasing the prime p.