On the linear complexity of binary threshold sequences derived from Fermat quotients

被引：51
|
作者：
Chen, Zhixiong [1 ,2 ]
Du, Xiaoni [3 ]
机构：
[1] Putian Univ, Dept Math, Putian 351100, Fujian, Peoples R China
[2] Chinese Acad Sci, Grad Sch, State Key Lab Informat Secur, Beijing 100049, Peoples R China
[3] Northwest Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Gansu, Peoples R China
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2013年 / 67卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Fermat quotients; Finite fields; Binary sequences; Linear complexity; Cryptography; SUMS;
D O I：
10.1007/s10623-012-9608-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We determine the linear complexity of a family of p (2)-periodic binary threshold sequences derived from Fermat quotients modulo an odd prime p, where p satisfies . The linear complexity equals p (2) - p or p (2) - 1, depending whether or 3 (mod 4). Our research extends the results from previous work on the linear complexity of the corresponding binary threshold sequences when 2 is a primitive root modulo p (2). Moreover, we present a partial result on their linear complexities for primes p with . However such so called Wieferich primes are very rare.
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页码：317 / 323
页数：7
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