|
|
- 2016
最大代数免疫阶弹性函数的构造
|
Abstract:
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。
Abstract: The construction of resilient functions with maximum algebraic immunity was studied by a new method of flexibility, which can be carried out by software implementation easily. By means of flexibility, any majority function can be transformed into resilient function. A sufficient and necessary condition on which the resilient function has maximum algebraic immunity was obtained. Moreover, the cryptographic properties of the resilient function, such as nonlinearity and algebraic degree were studied
| [1] | 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. |
| [2] | XIAO Guozheng, MASSEY J L. A spectral characterization of correlation immune combining functions[J]. IEEE Transactions on Information Theory, 1988, 34(3):569-571. |
| [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] | 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. |
| [8] | 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. |
| [9] | SARKAR S, MAITRA S. Construction of rotation symmetric Boolean functions with optimal algebraic immunity[J]. Computacióny Sistemas, 2009, 12(3):267-284. |
| [10] | 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. |
| [11] | 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. |
| [12] | 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. |
