JISE

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Journal of Information Science and Engineering, Vol. 27 No. 6, pp. 1931-1942

Construction of Odd-Variable Resilient Boolean Functions with Optimal Degree

SHAOJING FU, BING SUN⁺, CHAO LI⁺ AND LONGJIANG QU⁺
College of Computer
⁺College of Science
National University of Defense Technology
Changsha, 410073 P.R. China
Key Lab of Network Security and Cryptology
Fujian Normal University
Fuzhou, 350007 P.R. China

In this paper, we investigate the problem of obtaining new construction methods for resilient Boolean functions. Given n (n odd and n >= 35), we firstly provide degree optimized 1-resilient n-variable functions with currently best known nonlinearity. Then we extend our method to obtain m-resilient (m > 1) Boolean functions with degree n - m - 1, we show that these Boolean functions also achieve currently best known nonlinearity. Finally, the algebraic immunity and immunity against fast algebraic attack of the obtained Boolean functions are investigated.

Keywords: stream cipher, Boolean function, resiliency, nonlinearity, algebraic immunity

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