Linear Complexity of n-Periodic Cyclotomic Sequences over 𝔽p

Qiuyan WANG  Yang YAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.5   pp.785-791
Publication Date: 2020/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2137
Type of Manuscript: LETTER
Category: Information Theory
Legendre sequences,  cyclotomic sequences,  linear complexity,  Gauss periods,  

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Periodic sequences, used as keys in cryptosystems, plays an important role in cryptography. Such periodic sequences should possess high linear complexity to resist B-M algorithm. Sequences constructed by cyclotomic cosets have been widely studied in the past few years. In this paper, the linear complexity of n-periodic cyclotomic sequences of order 2 and 4 over 𝔽p has been calculated, where n and p are two distinct odd primes. The conclusions reveal that the presented sequences have high linear complexity in many cases, which indicates that the sequences can resist the linear attack.