单圈T函数可以作为LFSR(linear feedback shift register)的代替组件用来设计序列密码,这样的序列密码算法在软件上具有很好的运行效率.研究了单圈T函数输出序列的线性复杂度等密码学性质.给出了当n为一般情况时,单圈T函数输出序列的线性复杂度,以及相应的极小多项式.
The single-cycle T-functions can be used as substitute for LFSR (linear feedback shift register) in stream ciphers, and such stream ciphers are very efficient in software. We have studied some cryptographic properties of single-cycle T-functions. We present the linear complexity and the minimal polynomial of the output sequences of single-cycle T-functions when n is an arbitrary positive integer.
[1] Klimov A, Shamir A. A new class of invertible mappings //Kaliski B S, et al. Workshop on Cryptographic Hardware and Embeded Systems'2002. Berlin: Springer-Verlag, 2003: 470-483.
[2] Klimov A, Shamir A. Cryptographic applications of T-functions // Matsui M, Zuccherato R. Ninth Workshop on Selected Areas in Cryptography-SAC'2003. Berlin: Springer-Verlag, 2004: 248-261.
[3] Klimov A, Shamir A. New cryptographic primitives based on multiword T-functions // Roy B, Meier W. Workshop on Fast Software Encryption-FSE'2004. Berlin: Springer-Verlag, 2004: 1-15.
[4] Hong J, Lee D H, Yeom Y, et al. A new class of single cycle T-functions // Gilbert H, Handschuh H. Workshop on Fast Software Encryption-FSE'2005. Berlin: Springer-Verlag, 2005: 68-82.
[5] Molland H, Helleseth T. A linear weakness in the Klimov-Shamir T-function // Proceedings of the 2005 IEEE Int Symposium on Information Theory. IEEE, 2005: 1106-1110.
[6] Kolokotronis N. Cryptographic properties of stream ciphers based on T-functions // Proceedings of the 2006 IEEE Int Symposium on Information Theory. IEEE, 2006: 1604-1608.
[7] Zhang W Y, Wu C K. The algebraic normal form, linear complexity and k-error linear complexity of single-cycle T-function // Gong G, et al. Workshop on Sequences and Their Applications-SETA'2006. Berlin: Springer-Verlag, 2006: 391-401.
[8] Zhao L, Wen Q Y. Linear complexity and stability of output sequences of single cycle T-function[J]. Journal of Beijing University of Posts and Telecommunications, 2008, 31(4):62-65(in Chinese). 赵璐,温巧燕. 单圈T-函数输出序列的线性复杂度及稳定性[J]. 北京邮电大学学报,2008,31(4):62-65.
[9] Ding C S, Xiao G Z, Shan W J. The stability theory of stream ciphers[M]. Berlin Heidelberg: Springer-Verlag, 1991.
[10] Massey J, Costello D, Justesen J. Polynomial weights and code constructions[J]. IEEE Trans IT, 1973, 19(1):101-110.