On the nonlinearity of maximum-length NFSR feedbacks
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Linear Feedback Shift Registers (LFSRs) are the main building block of many classical stream ciphers; however due to their inherent linearity, most of the LFSR-based designs do not offer the desired security levels. In the last decade, using Nonlinear Feedback Shift Registers (NFSRs) in stream ciphers became very popular. However, the theory of NFSRs is not well-understood, and there is no efficient method that constructs a cryptographically strong feedback function and also, given a feedback function it is hard to predict the period. In this paper, we study the maximum-length NFSRs, focusing on the nonlinearity of their feedback functions. First, we provide some upper bounds on the nonlinearity of the maximum-length feedback functions, and then we study the feedback functions having nonlinearity 2 in detail. We also show some techniques to improve the nonlinearity of a given feedback function using cross-joining.
KeywordsNonlinearity NFSR Stream ciphers Cryptography
Mathematics Subject Classifications (2010)94A55 94A60 68P25
The author would like to thank Çağdaş Çalık for his valuable comments. The author would also like to thank the anonymous reviewers for their suggestions to improve the quality of the paper.
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