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计算机工程 ›› 2010, Vol. 36 ›› Issue (1): 164-165,.doi: 10.3969/j.issn.1000-3428.2010.01.057

• 安全技术 • 上一篇    下一篇

GF(2)上周期为2pn序列的m(s)

赵 峰1,2，冯金磊2   

  1. (1.安徽工业大学管理科学与工程学院，马鞍山243002；2. 安徽工业大学计算机学院，马鞍山243002)
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:2010-01-05 发布日期:2010-01-05

m(s) of Sequences with Period 2pn over GF(2)

ZHAO Feng1,2, FENG Jin-lei2   

  1. (1. College of Management Science and Engineering, Anhui University of Technology, Ma’anshan 243002; 2. College of Computer, Anhui University of Technology, Ma’anshan 243002)
  • Received:1900-01-01 Revised:1900-01-01 Online:2010-01-05 Published:2010-01-05

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摘要： 给出多项式的若干引理，并对引理进行证明。在此基础上，给出GF(2)上周期序列线性复杂度的表达形式，应用该表达式得出周期N=2pn的二元序列线性复杂度和m(s)之间的关系，其中p是个奇素数，并且2是一个模p2的本源根。结合魏算法，给出2个实例进行证明，结果表明该结果的正确性。

关键词: 密码, 流密码, 线性复杂度, 最小多项式

Abstract: This paper gives some polynomial lemmas and proof of lemma. On basis of these lemmas, the expression of Linear Complexity(LC) of periodic sequences is gave. Application of the expression show the most important result of this article, a relationship between m(s) and the LC of a given sequence s with period N=2pn over GF(2). Where p is an odd prime, 2 is a primitive root module p. Combined with Wei algorithm, it gives two examples to prove the results. Result shows that the relationship is correct.

Key words: cipher, stream cipher, Linear Complexity(LC), minimum polynomial

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