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一种计算旋转对称布尔函数的汉明重量和非线性度的新方法

张习勇 祁应红 高光普 李玉娟

张习勇, 祁应红, 高光普, 李玉娟. 一种计算旋转对称布尔函数的汉明重量和非线性度的新方法[J]. 电子与信息学报, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
引用本文: 张习勇, 祁应红, 高光普, 李玉娟. 一种计算旋转对称布尔函数的汉明重量和非线性度的新方法[J]. 电子与信息学报, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
张习勇, 祁应红, 高光普, 李玉娟. A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions[J]. Journal of Electronics & Information Technology, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164
Citation: 张习勇, 祁应红, 高光普, 李玉娟. A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions[J]. Journal of Electronics & Information Technology, 2015, 37(11): 2691-2696. doi: 10.11999/JEIT 150164

一种计算旋转对称布尔函数的汉明重量和非线性度的新方法

doi: 10.11999/JEIT 150164
基金项目: 

国家自然科学基金(61402522, 60803154, 61572027);数学工程与先进计算国家重点实验室课题;信息保障技术重点实验室开放基金(KJ-13-108)

A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions

Funds: 

The National Natural Science Foundation of China (61402522, 60803154, 61572027)

  • 摘要: 旋转对称布尔函数是一类重要的密码学函数,研究其重量和非线性度等密码学性质具有很好的理论价值。区别于已有的计算方法,该文利用特定的正规基把这些布尔函数的问题转化为有限域上的指数和问题,得到了4 ?? n和n=2s 时一些二次旋转对称布尔函数的重量和非线性度的新结果。使用所提的方法,可以计算几乎全部的二次旋转对称布尔函数的重量和非线性度。所提的新方法对于研究一般的旋转对称布尔函数具有一定的参考意义。
  • Pieprzyk J and Qu C X. Fast hashing and rotation-symmetric functions[J]. Journal of Universal Computer Science, 1999, 5(1): 20-31.
    Cusick T W and P. Fast evaluation, weights and nonlinearity of rotation-symmetric functions[J]. Discrete Mathematics, 2002, 258(1): 289-301.
    Ciungu L C. Cryptographic Boolean functions: Thus-Morse sequences, weight and nonlinearity[D]. [Ph.D. dissertation], University at Buffalo, 2010.
    Zhang X, Guo H, Feng R, et al.. Proof of a conjecture about rotation symmetric functions[J]. Discrete Mathematics, 2011, 311(14): 1281-1289.
    Wang B, Zhang X, and Chen W. The hamming weight and nonlinearity of a type of rotation symmetric Boolean function [J]. Acta Mathematica Sinica, Chinese Series, 2012, 55(4): 613-626.
    Cusick T W. Finding Hamming weights without looking at truth tables[J]. Cryptography and Communications, 2013, 5(1): 7-18.
    Brown A and Cusick T W. Equivalence classes for cubic rotation symmetric functions[J]. Cryptography and Communications, 2013, 5(2): 85-118.
    KV L, Sethumadhavan M, and Cusick T W. Counting rotation symmetric functions using Polyas theorem[J]. Discrete Applied Mathematics, 2014, 169: 162-167.
    Cusick T W and Cheon Y. Affine equivalence for cubic rotation symmetric Boolean functions with n=pq variables[J]. Discrete Mathematics, 2014, 327: 51-61.
    Cusick T W and Cheon Y. Affine equivalence of quartic homogeneous rotation symmetric Boolean functions[J]. Information Sciences, 2014, 259: 192-211.
    Kim H, Park S M, and Hahn S G. On the weight and nonlinearity of homogeneous rotation symmetric Boolean functions of degree 2[J]. Discrete Applied Mathematics, 2009, 157(2): 428-432.
    Liu H. On the weight and nonlinearity of quadratic rotation symmetric function with two MRS functions[J]. General Mathematics Notes, 2013, 16(1): 12-19.
    P and Maitra S. Rotation symmetric Boolean functions-count and cryptographic properties[J]. Discrete Applied Mathematics, 2008, 156(10): 1567-1580.
    Hou X D. Explicit evaluation of certain exponential sums of binary quadratic functions[J]. Finite Fields and Their Applications, 2007, 13(4): 843-868.
    Weinberger M J and Lempel A. Factorization of symmetric circulant matrices in finite fields[J]. Discrete Applied Mathematics, 1990, 28(3): 271-285.
    Zhang X, Cao X, and Feng R. A method of evaluation of exponential sum of binary quadratic functions[J]. Finite Fields and Their Applications, 2012, 18(6): 1089-1103.
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出版历程
  • 收稿日期:  2015-01-29
  • 修回日期:  2015-06-11
  • 刊出日期:  2015-11-19

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