Further results on the nonlinearity of maximum-length NFSR feedbacks

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• 作者：Mingxing Wang ; Yupeng Jiang ; Dongdai Lin
• 关键词：Nonlinearity ; NFSR ; State graph ; Stream cipher
• 刊名：Cryptography and Communications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：8
• 期：1
• 页码：1-6
• 全文大小：129 KB
• 参考文献：1.Turan, M.S.: On the nonlinearity of maximum-length NFSR feedbacks. Crypto. Commun 4(3–4), 233–243 (2012)MathSciNet CrossRef MATH
  2.Golomb, S.W.: Shift Register Sequences. Aegean Park Press, New York.USA (1982)MATH
  3.de Bruijn, N. G.: A combinatorrial problem. Proc. K. Ned. Acad. Wet. Ser. A 49(7), 758–764 (1946)MathSciNet MATH
  4.Lidl, R., Niederreiter, H.: Finite fields, in encyclopedia of mathematics and its applications, vol.20, Reading, MA, USA: AddisonWesley, pp. 428–431 (1983)
  
• 作者单位：Mingxing Wang (1)
  Yupeng Jiang (1)
  Dongdai Lin (1)
  
  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China
  
• 刊物类别：Computer Science
• 刊物主题：Coding and Information Theory
  Mathematics of Computing
  
• 出版者：Springer New York
• ISSN：1936-2455

文摘

Turan gave bounds on the number of maximum-length feedback functions with nonlinearity 2 and t for even t<2 n−2 in the paper (Crypto. Commun. 4 (3-4), pp. 233-243 (2012)). In this correspondence, we give two further results. First, the exact number of maximum-length feedback functions with nonlinearity 2 is obtained. Second, an improved bound on the number of maximum-length feedback functions with nonlinearity t<2 n−2 is given.