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The Search Successive Minima Problem Is Equivalent to Its Optimization Version

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Book cover Information Security Applications (WISA 2017)

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Abstract

The shortest vector problem (SVP) and the shortest independent vectors problem (SIVP) are two famous problems in lattices, which are usually used to evaluate the hardness of some computational problems related to lattices. It is well known that the search-SVP is equivalent to its optimization version. However, it seems very difficult to prove the equivalence between search-SIVP and optimization-SIVP. In this paper, we revisit the Successive Minima Problem (SMP), which is proved the equivalence relation with SIVP. Naturally we will consider its optimization version as to find all successive minima of a given lattice, and finally we will prove that it is equivalent to its search version.

This work was supported in part by the NNSF of China (No. 61572490, and No. 11471314), the National Center for Mathematics and Interdisciplinary Sciences, CAS, and Science and Technology on Communication Security Laboratory (No. 9140C110301150C11051).

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Acknowledgement

We very thank the anonymous referees for their valuable suggestions on how to improve the presentation of this paper.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Haoyu Li & Yanbin Pan

  2. Science and Technology on Communication Security Laboratory, Chengdu, 610041, China

    Haoyu Li & Yanbin Pan

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Haoyu Li

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  1. Haoyu Li
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  2. Yanbin Pan
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Correspondence to Yanbin Pan .

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Editors and Affiliations

  1. KAIST, Daejeon, Korea (Republic of)

    Brent ByungHoon Kang

  2. Georgia Institute of Technology, Atlanta, Georgia, USA

    Taesoo Kim

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Li, H., Pan, Y. (2018). The Search Successive Minima Problem Is Equivalent to Its Optimization Version. In: Kang, B., Kim, T. (eds) Information Security Applications. WISA 2017. Lecture Notes in Computer Science(), vol 10763. Springer, Cham. https://doi.org/10.1007/978-3-319-93563-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-93563-8_4

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