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On the construction of odd-variable boolean functions with optimal algebraic immunity

On the construction of odd-variable boolean functions with optimal algebraic immunity
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摘要 Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity. Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.
作者 ZHANG Jie WEN Qiao-yan
机构地区 School of Science State Key Laboratory of Networking and Switching Technology
出处 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2013年第3期73-77,共5页 中国邮电高校学报（英文版）
基金 supported by the National Natural Science Foundation of China (61102093, 61170270, 61121061) The Fundamental Research for the Central Universities (BUPT 2012RC0710)
关键词 algebraic immunity Boolean functions algebraic attacks ANNIHILATORS algebraic immunity, Boolean functions, algebraic attacks, annihilators
分类号 TN918.1 [电子电信—通信与信息系统]
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  • 1LIAO QunYing1, LIU Feng2 & FENG KeQin2 1 College of Mathematics and Software Sciences, Sichuan Normal University, Chengdu 610066, China 2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.On (2~m + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2^(m-1)[J].Science China Mathematics,2009,52(1):17-28. 被引量：4
  • 2LI Na QI WenFeng.Boolean functions of an odd number of variables with maximum algebraic immunity[J].Science in China(Series F),2007,50(3):307-317. 被引量：8
  • 3Deepak Kumar Dalai,Subhamoy Maitra,Sumanta Sarkar.Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity[J].Designs Codes and Cryptography.2006(1)
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The Journal of China Universities of Posts and Telecommunications
2013年 第3期

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