Open AccessCorrelation measures of binary sequences derived from Euler quotients
Author(s) -
Huaning Liu,
Zhixiong Chen,
Chenhuang Wu
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022619
Subject(s) - mathematics , quotient , fermat's last theorem , pseudorandom number generator , binary number , euler's formula , pseudorandomness , cryptography , trace (psycholinguistics) , dirichlet distribution , discrete mathematics , pure mathematics , arithmetic , algorithm , mathematical analysis , linguistics , philosophy , boundary value problem
Fermat-Euler quotients arose from the study of the first case of Fermat's Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whose linear complexities and trace representations were calculated. In this work, we further study their correlation measures by introducing a new approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $ 4 $-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.