GF(3)上一类广义自缩序列的伪随机性

Pseudo- Randomness of New Generalized Self- shrinking Sequence on GF(3)

在GF(3)上构造了一类广义自缩序列的新模型,经过分析和计算,证明了新型广义自缩序列的最小周期为:2×3n-1,并对新序列的1长1-游程的个数进行精确的统计,计算出0-游程,1-游程,2-游程的分布非常均衡。研究得出此类新序列不但保持了GF(2)上第四类广义自缩序列良好的伪随机性,而且在此基础上得出一些新的密码学指标,相比之下各项指标都有很大的提高,并与GF(3)上其它广义自缩序列相比具有更好的密码学特性。

New model of a generalized self-shrinking sequence is constructed, based on this new model, the analysis and calculation indicates that the minimum cycle of this new-type generalized self-shrinking sequence is 2×3^n-1. Accurate statistics is also done on the number of new sequences 1 long 1-pattern, and calculation shows that the 0-pattern, 1-pattern, 2-pattern are in very balanced distribution. Research indicates that such new sequences over GF （2） on the fourth class of generalized self shrinking sequences have fairly good pseudo-randomness, some new indicators of cryptography are drawn, and all are relatively improved. The new self-shrinking sequence on GF（ 3 ） keeps very good pseudo-randomness, and as compared with other self-shrinking sequences, has much better crypto properties.