Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (4): 651-661.doi: 10.21629/JSEE.2019.04.03

• Electronics Technology • Previous Articles     Next Articles

Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Wenjuan JIA1(), Juntao GAO2,*(), Peng ZHANG1()   

  1. 1 School of Telecommunications Engineering, Xidian University, Xi'an 710071, China
    2 The State Key Laboratory of Integrated Services Network, Xidian University, Xi'an 710071, China
  • Received:2018-07-30 Online:2019-08-01 Published:2019-08-29
  • Contact: Juntao GAO E-mail:18368910175@163.com;jtgao@mail.xidian.edu.cn;297966738@qq.com
  • About author:JIA Wenjuan was born in 1994. She received her B.S. degree from Northwest Normal University. She is a Ph.D candidate in cryptography from Xidian University. Her research interests include Latticebased cryptography, stream cipher and pseudorandom sequence. E-mail:18368910175@163.com|GAO Juntao was born in 1979. He received his D.E.degree incryptography from Xidian University. He is now an associate professor. His research interests include block chain, stream cipher and pseudorandom sequence. E-mail:jtgao@mail.xidian.edu.cn|ZHANG Peng was born in 1992. He received his B.S. degree from Henan University and his M.S. degree in cryptography from Xidian University. His research interests include compressive sensing and cryptography. E-mail:297966738@qq.com
  • Supported by:
    the National Key Research and Development Program of China(2016YFB0800601);the Natural Science Foundation of China(61303217);the Natural Science Foundation of China(61502372);the Fundamental Research Funds for the Central Universities(JB140115);the Natural Science Foundation of Shaanxi Province(2013JQ8002);the Natural Science Foundation of Shaanxi Province(2014JQ8313);This work was supported by the National Key Research and Development Program of China (2016YFB0800601), the Natural Science Foundation of China (61303217; 61502372), the Fundamental Research Funds for the Central Universities (JB140115), and the Natural Science Foundation of Shaanxi Province (2013JQ8002; 2014JQ8313)

Abstract:

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets. This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr. Its linear complexity, minimal polynomial, and autocorrelation are investigated. The results show that these sequences have a large linear complexity when 2 ∈D1, which means they can resist the Berlekamp-Massey attack. Furthermore, the autocorrelation values are close to 0 with a probability of approximately 1-1/r. Therefore, when r is a big prime, the new sequence has a good autocorrelation.

Key words: generalized cyclotomic sequence, linear complexity, minimal polynomial, autocorrelation value