多重周期二元序列的联合k错2-adic复杂度  

Joint k-Error 2-Adic Complexity for Binary Periodic Multi-Sequences

作　　者：董丽华[1] 胡予濮[1] 曾勇[1] 

机构地区：[1]西安电子科技大学计算机网络与信息安全国家教育部重点实验室,西安710071

出　　处：《计算机学报》2009年第6期1134-1139,共6页Chinese Journal of Computers

基　　金：国家"九七三"重点基础研究发展规划项目基金(2007CB311201);国家自然科学基金(60473029;60673072);国家自然青年科学基金(60503010)资助~~

摘　　要：具有较强密码学性质的序列应该具有较大的2-adic复杂度,以抗击已知的带进位操作反馈移位寄存器综合算法,同时改变较少的几项也不应引起序列的2-adic复杂度的急剧减小,即k错2-adic复杂度也应尽可能地大.近来,向量化流密码的设计逐渐成为国内外密码学界关注的一个重要方向.对这种类型的流密码的安全性分析需要研究多重序列-有限多个序列的并行流的复杂度.目前对多重序列的复杂度研究多集中于线性复杂度.基于此,文中首先给出了多重二元序列的联合k错2-adic复杂度的定义.随后,借助数论中的中国剩余定理等相关理论给出了联合k错2-adic复杂度的下界,并讨论了具有最大联合2-adic复杂度以及较大联合k错2-adic复杂度的N周期序列的存在性及具有此种性质的序列的数目下界.以此种周期序列作为密钥流序列可以有效抵抗穷举攻击.Cryptographically strong sequences should have a large 2-adic complexity to thwart the known feedback with carry shift register synthesis algorithms. At the same time the change of a few terms should not cause a significant decrease of the 2-adic complexity, that is, the k-error 2-adic complexity should also be large. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multi-sequences. This paper introduces joint k-error 2-adic complexity measures for multi-sequences. Several results on the existence and lower bounds on the number of multi-sequences with maximal joint 2-adic complexity and large joint k-error 2-adic complexity are proved. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.

关 键 词：密码学 流密码 FCSR 联合2-adic复杂度 k错2-adic复杂度 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]