On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr  

作　　者：Longfei Liu Xiaoyuan Yang Xiaoni Du Bin Wei 

机构地区：[1]Key Laboratory of Network & Information Security of APF,Engineering College of APF [2]College of Mathematics and Statistics,Northwest Normal University

出　　处：《Tsinghua Science and Technology》2016年第3期295-301,共7页清华大学学报（自然科学版（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos.61272492,61103231,61202492,61202395,61462077,and 61562077);the Program for New Century Excellent Talents in University (No.NCET-12-0620)

摘　　要：Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd（p-1, q-1 ）=gcd（p- 1, r-1）=gcd（q-1, r-1）=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF（2） is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd（p-1, q-1 ）=gcd（p- 1, r-1）=gcd（q-1, r-1）=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF（2） is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.

关 键 词：stream cipher pseudorandom sequence generalized cyclotomy linear complexity 

分 类 号：O156[理学—数学]