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Journal of Information Science and Engineering, Vol. 27 No. 6, pp. 1931-1942 (November 2011)

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

Full Text () Retrieve PDF document (201111_09.pdf)

Received March 3, 2010; revised January 6, 2011; accepted April 27, 2011.
Communicated by Wen-Guey Tzeng.
* This work was supported by the National Nature Science Foundation of China (No. 61103191), and Key Lab of Fujian Province University Network Security and Cryptology (No. 2011003).