整数剩余类环上本原序列在Garner分解下最高权位的保熵性

The Highest-level Entropy-preservation of Primitive Sequences by Garner Decomposition over Integer Residue Rings

整数剩余类环上压缩导出序列简称环上导出序列,是一类重要的非线性序列.目前国际4G移动通信三大标准之一的ZUC算法所采用的序列源就是一类环上导出序列.环上导出序列的非线性来源于压缩映射,特别的,如果该压缩映射是保熵的,即压缩后序列和原始序列一一对应,这时压缩后序列含有原始序列的所有信息,这使得保熵压缩映射成为环上导出序列研究的核心问题.本文基于序列的Garner分解提出了一种新的压缩方式,即将整数剩余类环上本原序列压缩到其Garner分解下的最高权位序列,并对部分情形给出了保熵性的证明.本文结论可以给出范围更广的合数环上的压缩导出序列,为环上导出序列在密码学中的进一步应用提供更多素材.同时,通过选取合适的参数,根据本文结论可以得到拥有理想的周期特性、复杂的非线性结构以及易于软硬件实现的非线性序列.

The compression-derived sequences over integer residual rings is an important class of nonlinear sequences.For example,the ZUC algorithm,one of the three international standards for 4G mobile communication,adopts compression-derived sequences over Z/(231 ?? 1).The nonlinearity of the sequences over integer residual rings is derived from the compression mapping,and mainly from the compression mapping with entropy-preservation.Note that the highest-level sequences exist in primitive sequences by Garner decomposition over integer residual rings.Based on this objective,this study proposes a new compression method by Garner decomposition of sequences,and gives the proof of entropy-preservation for some cases.The results in this study show that,more nonlinear sequences with ideal periodic characteristics,complex nonlinear structures and a convenient implementation can be obtained by choosing suitable parameters.