环Z／（2^e-1）上本原序列的密码性质分析  

On the Cryptographic Properties of Primitive Sequences over Z/（2^e-1）

作　　者：郑群雄[1] 朱宣勇[1] 戚文峰[1] 

机构地区：[1]信息工程大学信息工程学院,河南郑州450002

出　　处：《信息工程大学学报》2012年第4期389-395,共7页Journal of Information Engineering University

基　　金：国家自然科学基金资助项目(61070178;61100202)

摘　　要：环Z/(2e-1)上的本原序列是最近被提出并研究的一类新型非线性序列源,其特殊形式环Z/(231-1)上的本原序列已应用于4G移动通信标准候选算法ZUC算法的设计中。文章研究了环Z/(2e-1)上本原序列的密码性质,指出该类序列源存在的潜在弱点以及可行的解决方案。结论表明,这类序列源具有诸多优良的密码性质,包括理想的周期性质、比特分位序列具有复杂的非线性、比特分位序列地位等价、模2保熵性以及良好的伪随机性。Recently, a class of nonlinear driving sequences, primitive sequences over integer resi-due ring Z/（2^e-1） , was proposed and studied. In particular, primitive sequences over Z/（2^31 - 1 ） had been chosen as the driving sequences of the ZUC algorithm, a new cryptographic algorithm that was proposed for inclusion in ‘4G＇ mobile standard called LTE （Long Term Evolution）. In this paper, the cryptographic properties of primitive sequences over Z/（2^e - 1 ） are studied. It is shown that such sequences have many desirable properties, including large period, complex nonlinearity of bit sequences, no weak bit sequences, distinctness of modulo 2 reductions and good statistical prop-erties.

关 键 词：序列密码 整数剩余类环 线性递归序列 本原序列 模压缩 

分 类 号：TN918.1[电子电信—通信与信息系统] O157.4[电子电信—信息与通信工程]