On the Linear Complexity of Legendre Sequences Over Fq

Qiuyan WANG  Dongdai LIN  Xuan GUANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A    No.7    pp.1627-1630
Publication Date: 2014/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.1627
Type of Manuscript: LETTER
Category: Cryptography and Information Security
legendre sequences,  linear complexity,  minimal polynomial,  

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In this paper, the linear complexity and minimal polynomials of Legendre sequences over Fq have been calculated, where q = pm and p is a prime number. Our results show that Legendre sequences have high linear complexity over Fq for a large part of prime power number q so that they can resist the linear attack method.