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Open Access

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

Longfei Liu( ), Xiaoyuan Yang, Xiaoni Du, Bin Wei
Key Laboratory of Network & Information Security of APF, Engineering College of APF, Xi’an 710086, China.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China.
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Abstract

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.

Keywords

stream cipherpseudorandom sequencegeneralized cyclotomylinear complexity

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Tsinghua Science and Technology
Volume 21 Issue 3,
June 2016
Pages 295-301
DOI: 10.1109/TST.2016.7488740
Cite this article:
Liu L, Yang X, Du X, et al. On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr. Tsinghua Science and Technology, 2016, 21(3): 295-301. https://doi.org/10.1109/TST.2016.7488740

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Received: 15 January 2016
Accepted: 07 March 2016
Published: 13 June 2016
© The author(s) 2016
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