Balanced 2p-variable rotation symmetric Boolean functions with optimal algebraic immunity, good nonlinearity, and good algebraic degree

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Li, Xiangxue^1,2  Zhou, Qifeng¹  Qian, Haifeng¹  Yu, Yu³  Tang, Shaohua⁴ 

[1] E China Normal Univ, Dept Comp Sci & Technol, Shanghai 200241, Peoples R China

[2] Xian Univ Posts & Telecommun, Natl Engn Lab Wireless Secur, Xian 710121, Peoples R China

[3] Tsinghua Univ, Inst Interdisciplinary Informat Sci, Beijing 100084, Peoples R China

[4] S China Univ Technol, Sch Comp Sci & Engn, Guangzhou 510006, Guangdong, Peoples R China

关键词: Boolean function;    Algebraic immunity;    Nonlinearity;    Degree;   

DOI  :  10.1016/j.jmaa.2013.02.009

来源: Elsevier

【 摘 要 】

In designing cryptographic Boolean functions, it is challenging to achieve at the same time the desirable features of algebraic immunity, balancedness, nonlinearity, and algebraic degree for necessary resistance against algebraic attack, correlation attack, Berlekamp-Massey attack, etc. This paper constructs balanced rotation symmetric Boolean functions on n variables where n = 2p and p is an odd prime. We prove the construction has an optimal algebraic immunity and is of high nonlinearity. We check that, at least for those primes p which are not of the form of a power of two plus one, the algebraic degree of the construction achieves in fact the upper bound n - 1. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free