International Association
for Cryptologic Research

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.