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LUO Bingyu, ZHANG Jingwei, ZHAO Chang’an. Linear Complexity of A Family of Binary p2q2-periodic Sequences From Euler Quotients[J]. Chinese Journal of Electronics. doi: 10.1049/cje.2020.00.125
 Citation: LUO Bingyu, ZHANG Jingwei, ZHAO Chang’an. Linear Complexity of A Family of Binary p2q2-periodic Sequences From Euler Quotients[J]. Chinese Journal of Electronics.

# Linear Complexity of A Family of Binary p2q2-periodic Sequences From Euler Quotients

##### doi: 10.1049/cje.2020.00.125
Funds:  This work was supported by Guangdong Major Project of Basic and Applied Basic Research(2019B030302008), the National Natural Science Foundation of China (61972428), the Open Fund of State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093) (2020-ZD-02). The work of Jingwei Zhang was partially supported by Guangdong Basic and Applied Basic Research Foundation(2019A1515011797)
• Author Bio:

received the B.E. degree in mathematics from Sun Yatsen University. He is a Ph.D. candidate of Sun Yat-sen University. His research interests include sequences design and number theory. (Email: luoby@mail2.sysu.edu.cn)

received the Ph.D. degree in electronics engeneering from Sun Yat-sen University. She currently works in School of Information Science, Guangdong University of Finance and Economics in Guangdong. Her research interests include sequences design and coding theory. (Email: jingweizhang@gdufe.edu.cn)

(corresponding author) received the Bachelor’s degree in electronical engineering in 2001, the Master’s degree in applied mathematics in 2005, the Ph.D. degree in information science and technology in 2008 respectively from Sun Yat-sen University, Guangzhou, China. He presently works in school of mathmatics in Sun Yat-sen University. His research interest lies in elliptic curve cryptography, sequences designs and coding theory

• Accepted Date: 2021-08-21
• Available Online: 2022-01-05
• A family of binary sequences derived from Euler quotients $\psi(\cdot)$ with RSA modulus $pq$ is introduced. Here two primes $p$ and $q$ are distinct and satisfy $\gcd(pq, (p-1)(q-1))=1$. The linear complexities and minimal polynomials of the proposed sequences are determined. Besides, this kind of sequences is shown not to have correlation of order $four$, although there exists the following relation $\psi(t)-\psi(t+p^2q)-\psi(t+q^2p)+\psi(t+(p+q)pq)=$$0 \pmod {pq}$ for any integer $t$ by the properties of Euler quotients.
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