山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (5): 106-113.doi: 10.6040/j.issn.1671-9352.0.2015.295
孙天锋,胡斌
SUN Tian-feng, HU Bin
摘要： 研究最大代数免疫阶弹性函数的构造问题,提出了一种易于编程实现的弹性化思想。将择多函数作为初始函数,利用弹性化方法将其转化为弹性函数,给出了此函数具有最大代数免疫阶的充要条件,并简要讨论了该函数的非线性度及代数次数。
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| [1] COURTOIS N, PIEPRZYK J. Algebraic attacks on stream ciphers with linear feedback[C] //Proceedings of the 22nd International Conference on Theory and Applications of Cryptographic Techniques. LNCS, Berlin: Springer-Verlag, 2003:345-359. [2] CARLET C. On Bent and highly nonlinear balanced/resilient functions and their algebraic immunities[C] //Applied Algebra, Algebraic Algorithms and Error-Correcting Codes(AAECC). Berlin: Springer-Verlag, 2006:1-28. [3] ZHANG Weiguo, PASALIC E. Generalized maiorana mcFarland construction of resilient Boolean functions with high nonlinearity and good algebraic properties [J]. IEEE Transactions on Information Theory, 2014, 60(10):6681-6695. [4] 杜蛟,温巧燕,张劼,等. 素数元旋转对称弹性布尔函数的构造与计数[J].通信学报,2013,34(3):6-13. DU Jiao, WEN Qiaoyan, ZHANG Jie, et al. Construction and count of resilient rotation symmetric Boolean functions with prime number variables[J]. Journal on Communications, 2013, 34(3):6-13. [5] 杜蛟,温巧燕,张劼,等. 5元1阶弹性函数的代数免疫阶[J].通信学报, 2011,32(4):17-24. DU Jiao, WEN Qiaoyan, ZHANG Jie, et al. On the algebraic immunity for 1st-resilience Boolean functions with five variables[J]. Journal on Communications, 2011, 32(4):17-24. [6] 李旭,赵亚群. 偶变元1阶弹性最优代数免疫布尔函数的构造[J].信息工程大学学报,2011,12(6):641-645. LI Xu, ZHAO Yaqun. Construction of 1st-resilience Boolean functions with optimal algebraic immunity on even number of variables [J]. Journal of Information Engineering University, 2011, 12(6):641-645. [7] 董新峰,宋云芬,张文政,等. 具有高代数免疫阶的弹性布尔函数构造[J].计算机工程,2011,37(6):124-126. DONG Xinfeng, SONG Yunfen, ZHANG Wenzheng, et al. Construction of resilient Boolean function with high algebraic immunity order [J]. Computer Engineering, 2011, 37(6):124-126. [8] XIAO Guozheng, MASSEY J L. A spectral characterization of correlation immune combining functions[J]. IEEE Transactions on Information Theory, 1988, 34(3):569-571. [9] 张文英, 武传坤, 于静之. 密码学中布尔函数的零化子[J].电子学报, 2006, 34(1):51-54. ZHANG Wenying, WU Chuankun, YU Jingzhi. On the annihilators of cryptographic Boolean functions[J]. Acta Electronica Sinica, 2006, 34(1):51-54. [10] DALAI D K, MAITRA S. Reducing the number of homogeneous linear equations in finding annihilators [C] //Proceedings of the 4th International Conference on Sequences and Their Applications(SETA 2006). LNCS, Berlin: Springer-Verlag, 2006:376-390. [11] SARKAR S, MAITRA S. Construction of rotation symmetric Boolean functions with optimal algebraic immunity[J]. Computacióny Sistemas, 2009, 12(3):267-284. [12] DALAI D K, MAITRA S, SARKAR S. Basic theory in construction of Boolean functions with maximum possible annihilator immunity[J]. Design Codes and Cryptography, 2006, 40(1):41-58. |
| [1] | 柳扬. 布尔函数代数免疫阶的计算[J]. J4, 2010, 45(3): 55-60. |
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