环Z/(2e-1)上本原序列的密码性质分析

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.

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

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.