Chapter

Selected Areas in Cryptography -- SAC 2013

Volume 8282 of the series Lecture Notes in Computer Science pp 29-47

Date:

A Three-Level Sieve Algorithm for the Shortest Vector Problem

  • Feng ZhangAffiliated withKey Laboratory of Mathematics Mechanization, Academy of Mathematics & NCMIS, Chinese Academy of Sciences Email author 
  • , Yanbin PanAffiliated withKey Laboratory of Mathematics Mechanization, Academy of Mathematics & NCMIS, Chinese Academy of Sciences Email author 
  • , Gengran HuAffiliated withKey Laboratory of Mathematics Mechanization, Academy of Mathematics & NCMIS, Chinese Academy of Sciences

* Final gross prices may vary according to local VAT.

Get Access

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