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A Simulated Annealing Algorithm for SVP Challenge Through y-Sparse Representations of Short Lattice Vectors

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Abstract

In this paper, we propose a novel simulated annealing algorithm for the shortest vector problem through y-sparse representations of short lattice vectors. A Markov analysis proves that the algorithm guarantees to converge to the shortest vector at a probability 1, under certain conditions to ensure strong ergodicity of its inhomogeneous Markov chain. After that, we propose a polynomial-time approximation version of our algorithm, and the experimental results under benchmarks in SVP challenge [27] show that the simulated annealing one outperforms the famous Kannan’s algorithm in two aspects: it runs exponentially faster and it succeeds in searching the shortest vectors in lattices of higher dimensions. Therefore, our newly-proposed algorithm is a fast and efficient SVP solver and paves a completely new road for SVP algorithms.

D. Ding—National Natural Science Foundation of China (Grant No. 61133013) and 973 Program (Grant No. 2013CB834205).

G. Zhu—National Development Foundation for Cryptological Research (No. MMJJ201401003).

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Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Dan Ding

  2. Data Communication Science and Technology Research Institute, Beijing, 100191, China

    Guizhen Zhu

Authors
  1. Dan Ding
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  2. Guizhen Zhu
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Correspondence to Dan Ding .

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Editors and Affiliations

  1. Google, New York, New York, USA

    Moti Yung

  2. Beijing Institute of Technology, Beijing, China

    Liehuang Zhu

  3. Institute for Infocomm Research, Singapore

    Yanjiang Yang

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Ding, D., Zhu, G. (2015). A Simulated Annealing Algorithm for SVP Challenge Through y-Sparse Representations of Short Lattice Vectors. In: Yung, M., Zhu, L., Yang, Y. (eds) Trusted Systems. INTRUST 2014. Lecture Notes in Computer Science(), vol 9473. Springer, Cham. https://doi.org/10.1007/978-3-319-27998-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-27998-5_4

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  • Online ISBN: 978-3-319-27998-5

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