Abstract
The proposed by Meier and Staffelbach Self-Shrinking Generator (SSG) which has efficient hardware implementation only with a single Linear Feedback Shift Register is suitable for low-cost and fast stream cipher applications. In this paper we generalize the idea of the SSG for arbitrary Galois Field . The proposed variant of the SSG is called the -ary Generalized Self-Shrinking Generator (pGSSG). We suggest a method for transformation of a non-binary self-shrunken pGSSG sequence into balanced binary sequence. We prove that the keystreams of the pGSSG have large period and good statistical properties. The analysis of the experimental results shows that the pGSSG sequences have good randomness properties. We examine the complexity of exhaustive search and entropy attacks of the pGSSG. We show that the pGSSG is more secure than SSG and Modified SSG against these attacks. We prove that the complexity of the used pGSSG attacks increases with increasing the prime . Previously mentioned properties give the reason to say that the pGSSG satisfy the basic security requirements for a stream chipper and can be useful as a part of modern stream ciphers.
Highlights
The binary Pseudorandom Sequences (PRSs) with maximum period and good statistical and correlation properties have established themselves as foundation for generation of many signals used in modern communication and information systems
It is proved that the p-ary Generalized Self-Shrinking Generator (pGSSG) has large period and good statistical properties
The experimental results analysis shows that the sequence generated by pGSSG is well balanced, uniform, scalable, uncompressible and unpredictable
Summary
The binary Pseudorandom Sequences (PRSs) with maximum period and good statistical and correlation properties have established themselves as foundation for generation of many signals used in modern communication and information systems. In order to ensure practical stability of a chosen crypto-algorithm it is necessary to break the linearity in the generated linear sequence It could be done by applying a nonlinear function over a part of the generated bits for additional allocation [5, 12]. Self-shrinking generator [11] is a keystream generator used as a stream cipher It is based on the shrinking principle [4, 14] and has remarkably low hardware requirements. An attack on SSG requiring very small keystream data (2.41n) is the binary decision diagram (BDD) cryptanalysis proposed by Krause in [19] with time complexity O(20.656n) and equivalent memory complexity O(20.656n). In this paper a p-ary generalized self-shrinking generator which produces nonbinary sequences is proposed. The security of the pGSSG against the exhaustive search and entropy attacks are analysed
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