The Unique Distribution of Zeros in Compressing Sequences Derived from Primitive Sequences over z/（p^e）  

作　　者：ZHENG Qunxiong QI Wenfeng 

机构地区：[1]Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China [2]State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Chinese Journal of Electronics》2010年第1期159-164,共6页电子学报（英文版）

摘　　要：Let Z/（p^e） be the integer residue ring with odd prime p and integer e ≥ 3. Any sequence a over Z/（p^e） has a unique p-adic expansion a = a0 ＋a1 .p ＋... 3e -1 .Pc- 1, where ai can be regarded as a sequence over Z/（p） for 0 ≤ i ≤ e - 1. Let f（x） be a strongly primitive polynomial over Z/（pe） and let a, b be two primitive sequences generated by f（x） over Z/（pe）. Assume ∮（x0,...,Xe-1） =xe-1 ＋ η（x0,..., Xe-2）, where the degree of xe-2 in η/（x0, ...xe-2） is less than p-1. It is shown that if ∮（ao（t）,...,ae-l（t）） = 0 if and only if ∮（bo（t）,...,be-l（t）） = 0 for all nonnegative integer t with α（t）≠ 0, where a is an m-sequence determined by if（x） and a0, then a = b. In particular, when η（x0,..., Xe-2） = 0, it is just the former result on the unique distribution of zeros in the highest level sequences.

关 键 词：Stream cipher Integer residue ring Linear recurring sequence Compressing map Primitive sequence o-Uniformity 

分 类 号：O157.4[理学—数学] O174.52[理学—基础数学]