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On lattice-based algebraic feedback shift registers synthesis for multisequences

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Li-Ping Wang

  2. Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing, 100093, China

    Li-Ping Wang

  3. University of Chinese Academy of Sciences, Beijing, China

    Li-Ping Wang

  4. Department of Mathematics, University of California, Irvine, USA

    Daqing Wan

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  1. Li-Ping Wang
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  2. Daqing Wan
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Correspondence to Li-Ping Wang.

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This article is part of the Topical Collection on Sequences and Their Applications.

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Wang, LP., Wan, D. On lattice-based algebraic feedback shift registers synthesis for multisequences. Cryptogr. Commun. 10, 455–465 (2018). https://doi.org/10.1007/s12095-017-0230-0

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