Linearity properties of binary FCSR sequences

Authors:
Tian Tian;Wen-Feng Qi
Affiliations:
Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, People's Republic of China;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, People's Republic of China and State Key Laboratory of Information Security, Institute of Soft ...
Venue:
Designs, Codes and Cryptography
Year:
2009

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Abstract

Maximal length FCSR sequences, or l-sequences, are an important type of nonlinear sequences used for building stream ciphers. This paper studies the linearity properties of l-sequences. Although it is widely accepted that l-sequences have high linear complexities close to their half periods, it is shown that for most of the l-sequences, linear relations with large statistical advantage exist.