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On the Nonlinearity of Maximum-length NFSR Feedbacks

Published

Author(s)

Meltem Sonmez Turan

Abstract

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 with maximum period 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.
Citation
Cryptography and Communication
Volume
4
Issue
3-4

Keywords

Nonlinearity , NFSR , Stream Ciphers , Cryptography

Citation

Sonmez, M. (2012), On the Nonlinearity of Maximum-length NFSR Feedbacks, Cryptography and Communication, [online], https://doi.org/10.1007/s12095-012-0067-5 (Accessed December 6, 2023)
Created August 14, 2012, Updated November 10, 2018