A Three-Level Sieve Algorithm for the Shortest Vector Problem

Conference paper

DOI: 10.1007/978-3-662-43414-7_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8282)
Cite this paper as:
Zhang F., Pan Y., Hu G. (2014) A Three-Level Sieve Algorithm for the Shortest Vector Problem. In: Lange T., Lauter K., Lisoněk P. (eds) Selected Areas in Cryptography -- SAC 2013. SAC 2013. Lecture Notes in Computer Science, vol 8282. Springer, Berlin, Heidelberg

Abstract

In AsiaCCS 2011, Wang et al. proposed a two-level heuristic sieve algorithm for the shortest vector problem in lattices, which improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we present a three-level sieve algorithm in this paper, which is shown to have better time complexity. More precisely, the time complexity of our algorithm is \(2^{0.3778n+o(n)}\) polynomial-time operations and the corresponding space complexity is \(2^{0.2833n+o(n)}\) polynomially many bits.

Keywords

Lattice Shortest vector problem Sieve algorithm Sphere covering 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Key Laboratory of Mathematics Mechanization, Academy of Mathematics & NCMISChinese Academy of SciencesBeijingChina

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