Designs, Codes and Cryptography

, Volume 86, Issue 4, pp 939–953 | Cite as

Fast construction of binary ring FCSRs for hardware stream ciphers

  • Zhiqiang LinEmail author
  • Dingyi Pei
  • Dongdai Lin
  • Xiaolei Zhang


Stream ciphers based on linear feedback shift registers have been subject to algebraic attacks. To avoid these kinds of attacks, feedback with carry shift registers (FCSRs) have been proposed as an alternative. They are suitable for hardware implementations. FCSRs have been implemented using ring representation, in order to circumvent some weaknesses in the traditional representations. In this paper, we explore the simplest case of FCSRs, called binary FCSRs, which are common in applications. We give a fast algorithm to construct binary ring FCSRs for hardware stream ciphers.


Stream cipher l-Sequences 2-Adic ring FCSRs Transition matrix 

Mathematics Subject Classification

14G50 94A55 



This work is supported by the National Natural Science Foundations of China under Grant Nos. 11371106, 11271003 and 61309028, the Guangdong Province Natural Science Foundation of major basic research and Cultivation project under Grant No. 2015A030308016, the Project of Ordinary University Innovation Team Construction of Guangdong Province under Grant No. 2015KCXTD014, the Basic Research Major Projects of Department of education of Guangdong Province under Grant No. 2014KZDXM044 and the Collaborative Innovation Major Projects of Bureau of Education of Guangzhou City under Grant No. 1201610005.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Zhiqiang Lin
    • 1
    • 2
    Email author
  • Dingyi Pei
    • 1
    • 2
  • Dongdai Lin
    • 3
  • Xiaolei Zhang
    • 1
    • 2
  1. 1.College of Mathematics and Information ScienceGuangzhou UniversityGuangzhouChina
  2. 2.Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education InstitutesGuangzhou UniversityGuangzhouChina
  3. 3.The State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of SciencesBeijingChina

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