Expected values for the rational complexity of finite binary 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:
2010

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Abstract

2-Adic complexity plays an important role in cryptology. It measures the difficulty of outputting a binary sequence using a feedback with carry shift register. This paper studies the 2-adic complexity of finite sequences by investigating the corresponding rational complexity whose logarithm to the base 2 is just equal to the 2-adic complexity. Experiments show that the logarithm to the base 2 of the expected values for rational complexity is a good approximation to the expected values for the 2-adic complexity. Both a nontrivial lower bound and a nontrivial upper bound on the expected values for the rational complexity of finite sequences are given in the paper. In particular, the lower bound is much better than the upper bound.