Handbook of Applied Cryptography
Handbook of Applied Cryptography
Maximal-Period Sequences Generated by Feedback-Limited Nonlinear Shift Registers
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the (im)possibility of practical and secure nonlinear filters and combiners
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
On the distribution of de Bruijn sequences of given complexity
IEEE Transactions on Information Theory
The number of cross-join pairs in maximum length linear sequences
IEEE Transactions on Information Theory
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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.