Construction of even-variable rotation symmetric Boolean functions with maximum algebraic immunity  

作　　者：FU ShaoJing LI Chao MATSUURA Kanta QU LongJiang 

机构地区：[1]Department of Mathematics and System Science,National University of Defense Technology [2]Institute of Industrial Science,University of Tokyo,Tokyo 153-8505,Japan [3]State Key Laboratory of Information Security,Graduate University of Chinese Academy of Sciences

出　　处：《Science China(Information Sciences)》2013年第3期56-64,共9页中国科学（信息科学）（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 61070215,60803156);the open research fund of State Key Laboratory of Information Security (Grant No. 01-07);Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX2009B001)

摘　　要：Rotation symmetric Boolean functions （RSBFs） have been used as components of different cryp- tosysterns. In this paper, we investigate n-variable （n even and n ≥ 12） RSBFs to achieve maximum algebraic immunity （AI）, and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI. We also prove that our construction provides high algebraic degree in some case.Rotation symmetric Boolean functions （RSBFs） have been used as components of different cryp- tosysterns. In this paper, we investigate n-variable （n even and n ≥ 12） RSBFs to achieve maximum algebraic immunity （AI）, and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI. We also prove that our construction provides high algebraic degree in some case.

关 键 词：Boolean function rotation symmetry algebraic immunity NONLINEARITY 

分 类 号：O174[理学—数学]