计算机科学 ›› 2015, Vol. 42 ›› Issue (3): 153-157.doi: 10.11896/j.issn.1002-137X.2015.03.032
黄景廉,王 卓,李 娟
HUANG Jing-lian, WANG Zhuo and LI Juan
摘要： 以布尔函数的导数和自定义的e-导数为研究工具,研究了一类特定Hamming重量的H布尔函数的代数次数、代数免疫性、相关免疫性之间的关联问题。得出H布尔函数的组成部分e-导数的代数次数决定了H布尔函数的代数次数；H布尔函数的e-导数与H布尔函数的代数免疫阶的大小紧密关联；H布尔函数的e-导数可将H布尔函数的代数免疫性、零化子、相关免疫性、代数次数联系到一起等。同时,导出了公式法和级联法两类求解H布尔函数最低代数次数零化子的不同方法。
| [1] Xiao G,Massey J.A Spectral Characterization of Correlation-Immune Combining Functions[J].IEEE Trans.on Inform.Theo-ry,1988,34(3):569-571 [2] Preneel B,Leekwijck W,Linden L,et al.Propagation Characteri-stics of Boolean Functions[M]∥Advances in Cryptology-EUROCRYPT’90,1991,473:161-173 [3] Pan S,Fu X,Zhang W.Construction of 1-ResilientBoolean Functions with Optimal Algebraic Immunity and Good Nonlinearity[J].Journal of Computer Science and Technology,2011,26(2):269-275 [4] Zheng Y,Zhang X.Plateaued functions:Information and Communication Security Second International Conference[C]∥ICICS’99.Sydney,Australia,1999,LNCS,1726:284-300 [5] Meier W,Pasalic E,Carle C.Algebraic attacks and decomposition of Boolean functions[C]∥Advances in Cryptology-EUROCRYPT 2004.Interlaken,Switzerland,2004,LNCS,3027:474-491 [6] 温巧燕,钮心忻,杨义先.现代密码学中的布尔函数[M].北京:科学出版社,2000 [7] Batten L M.Algebraic Attacks over GF(q)[C]∥Progress in Cryptology-INDOCRYPT 2004.Chennai,India,2005,LNCS,3348:84-91 [8] Armknecht F,Carlet C,Gaborit P,et al.Efficient Computationof Algebraic Immunity for Algebraic and Fast Algebraic Attacks[C]∥Advances in Cryptology-EUROCRYPT 2006St.Petersburg,Russia,2006,LNCS,4004:147-164 [9] Didier F,Tillich J.Computing the algebraic immunity efficiently[M]∥Fast Software Encryption 2006,2006,4047:359-374 [10] Zhang W,Wu C,Yu J.On the Annihilators of CryptographicBoolean Functions[J].Acta Electronica Sinica,2006,34(1):51-54 [11] Reed I S.A class of multiple-error-correcting codes and the decoding scheme[J].IRE Transactions on Information Theory,1954,4(4):38-49 [12] Akers S B.On a theory of Boolean functions[J].Journal of the Society for Industrial and Applied Mathematics,1959,7(4):487-498 [13] Li W,Wang Z,Huang J.The e-derivative of boolean functions and its application in the fault detection and cryptographic system[J].Kybernetes,2011,40(5/6):905-911 [14] 黄景廉,王卓.H布尔函数的相关免疫性与重量的关系[J].通信学报,2012,33(2):110-118 |
| No related articles found! |
|
||
首页