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Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 1023–1038 | Cite as

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

  • Weihua Liu
  • Andrew Klapper
  • Zhixiong Chen
Article
  • 112 Downloads

Abstract

Register synthesis for multi-sequences has significance for the security of word-oriented stream ciphers. Feedback with carry shift registers (FCSRs) are promising alternatives to linear feedback shift registers for the design of stream ciphers. In this paper, we solve the FCSR synthesis problem for multi-sequences by two rational approximation algorithms using lattice theory. One is based on the lattice reduction greedy algorithm proposed by Nguyen and Stehlé (ACM Trans Algorithms (TALG) 5(4):46, 2009). The other is based on the LLL algorithm which is a polynomial time lattice reduction algorithm. Both of these rational approximation algorithms can find the smallest common FCSR for a given multi-sequence but with different numbers of known terms. When the number of sequences within the multi-sequence is less than or equal to 3, the former is suggested because it has better time complexity and fewer terms are needed. Otherwise, the latter will have better time complexity.

Keywords

Multi-sequences Lattice basis reduction algorithm FCSR synthesis problem 

Mathematics Subject Classification

94A55 

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. CNS-1420227. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. Zhixiong Chen was partially supported by the National Natural Science Foundation of China under Grant No. 61373140 and China Scholarship Council.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceThe William Paterson University of New JerseyWayneUSA
  2. 2.Department of Computer ScienceUniversity of KentuckyLexingtonUSA
  3. 3.Provincal Key Laboratory of Applied MathematicsPutian UniversityPutianChina

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