Pump-BSKZ: A Novel Sieve Algorithm to Solve Shortest Vector Problem

To solve hard problems in lattices is a crucial topic in lattice-based cryptanalysis, where the Shortest Vector Problem (SVP) is one of the most famous lattice problems. Recently, there are two kinds of approaches to solve approximate SVP. The one is Block Korkine-Zolotarev (BKZ)-type lattice reduction algorithms combined with enumeration, which suffers from high time complexity. The other is sieving algorithms such as the General Sieve Kernel (G6K) algorithm, which requires exponential space cost. In order to solve the above problems, in this paper, we propose a novel sieve algorithm, named Pump-BSKZ, to solve the approximate SVP with low time complexity and limited space cost. Firstly, our Pump-BSKZ algorithm can reduce a random lattice basis to a basis with better quality. We design a Block wise Sieving Korbine-Zolotarev (BSKZ) algorithm and apply sieving as a subroutine for solving SVP in local blocks. Secondly, our Pump-BSKZ algorithm can solve SVP in lattice with higher dimension. Based on the reduced basis, we design an improved Pump-sieve algorithm to find a shortest vector in arbitrary n-dimensional lattices. Thirdly, we give the formal proof of correctness for our Pump-BSKZ algorithm, then analyze time and space complexity. Finally, experiments done on TU Darmstadt SVP challenge in dimensions 90-130 reveal that our algorithm outperforms both BKZ 2.0 algorithm and G6K algorithm on time and space cost.