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A New Lattice Sieving Algorithm Base on Angular Locality-Sensitive Hashing

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Information Security and Cryptology (Inscrypt 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10726))

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Abstract

Currently, the space requirement of sieving algorithms to solve the shortest vector problem (SVP) grows as \(2^{0.2075n+o(n)}\), where n is the lattice dimension. In high dimensions, the memory requirement makes them uncompetitive with enumeration algorithms. Shi Bai et al. presents a filtered triple sieving algorithm that breaks the bottleneck with memory \( 2^{0.1887n+o(n)}\) and time \( 2^{0.481n+o(n)}\).

Benefiting from the angular locality-sensitive hashing (LSH) method, our proposed algorithm runs in time \(2^{0.4098n+o(n)}\) with the same space complexity \(2^{0.1887n+o(n)}\) as the filtered triple sieving algorithm. Our experiment demonstrates that the proposed algorithm achieves the desired results. Furthermore, we use the proposed algorithm to solve the closest vector problem (CVP) with the lowest space complexity as far as we know in the literature.

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Notes

  1. 1.

    The average probability that a distant (non-reducing) vector \(\varvec{w}\) collides with \(\varvec{v}\) in at least one of the t hash tables [20].

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Authors and Affiliations

  1. College of Information Engineering, Shenzhen University, Shenzhen, 518060, China

    Ping Wang

  2. College of Computer Science and Software, Shenzhen University, Shenzhen, 518060, China

    Dongdong Shang

Authors
  1. Ping Wang
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  2. Dongdong Shang
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Correspondence to Ping Wang .

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Editors and Affiliations

  1. Xidian University, Xi’an, China

    Xiaofeng Chen

  2. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  3. Columbia University, New York, New York, USA

    Moti Yung

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Wang, P., Shang, D. (2018). A New Lattice Sieving Algorithm Base on Angular Locality-Sensitive Hashing. In: Chen, X., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2017. Lecture Notes in Computer Science(), vol 10726. Springer, Cham. https://doi.org/10.1007/978-3-319-75160-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-75160-3_6

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  • Online ISBN: 978-3-319-75160-3

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