Cryptography and Communications

, Volume 10, Issue 3, pp 455–465 | Cite as

On lattice-based algebraic feedback shift registers synthesis for multisequences

  • Li-Ping Wang
  • Daqing Wan
Part of the following topical collections:
  1. Special Issue on Sequences and Their Applications


In this paper we show that algebraic feedback shift registers synthesis problems over residue class rings, some ramified extensions and some quadratic integer rings for multisequences are reduced to the successive minima problem in lattice theory. Therefore they can be solved by polynomial-time algorithms since the number of multiple sequences is fixed.


Feedback shift registers Register synthesis N-adic numbers Lattices 

Mathematics Subject Classification (2010)

14G50 11B37 11J13 



We gratefully thank Wen-Feng Qi, Daniele Micciancio and Weihua Liu for fruitful discussions. We also thank the anonymous reviewers for very helpful suggestions and comments. The research was partially supported by National Natural Science Foundation of China (No. 61170289) and 973 Program (2013CB834203).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communications Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina
  4. 4.Department of MathematicsUniversity of CaliforniaIrvineUSA

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