Linear Complexity over Fq of Generalized Cyclotomic Quaternary Sequences with Period 2p

Minglong QI  Shengwu XIONG  Jingling YUAN  Wenbi RAO  Luo ZHONG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.7   pp.1569-1575
Publication Date: 2015/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.1569
Type of Manuscript: LETTER
Category: Cryptography and Information Security
linear complexity,  generalized cyclotomic sequences,  quaternary sequences,  stream cipher,  generating polynomial,  

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Let r be an odd prime, such that r≥5 and rp, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field Frm. Let G(x) be the generating polynomial of the considered quaternary sequences over Fq[x] with q=rm. By explicitly computing the number of zeros of the generating polynomial G(x) over Frm, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to $ rac{1}{2}(3p-1) $ which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.