## Cryptology ePrint Archive: Report 2018/079

Progressive lattice sieving

Thijs Laarhoven and Artur Mariano

Abstract: Most algorithms for hard lattice problems are based on the principle of rank reduction: to solve a problem in a $d$-dimensional lattice, one first solves one or more problem instances in a sublattice of rank $d - 1$, and then uses this information to find a solution to the original problem. Existing lattice sieving methods, however, tackle lattice problems such as the shortest vector problem (SVP) directly, and work with the full-rank lattice from the start. Lattice sieving further seems to benefit less from starting with reduced bases than other methods, and finding an approximate solution almost takes as long as finding an exact solution. These properties currently set sieving apart from other methods.

In this work we consider a progressive approach to lattice sieving, where we gradually introduce new basis vectors only when the sieve has stabilized on the previous basis vectors. This leads to improved (heuristic) guarantees on finding approximate shortest vectors, a bigger practical impact of the quality of the basis on the run-time, better memory management, a smoother and more predictable behavior of the algorithm, and significantly faster convergence - compared to traditional approaches, we save between a factor $20$ to $40$ in the time complexity for SVP.

Category / Keywords: foundations / lattice-based cryptography, lattice sieving, shortest vector problem (SVP), nearest neighbor searching

Original Publication (in the same form): PQCrypto 2018

Date: received 18 Jan 2018, last revised 13 Feb 2018

Contact author: mail at thijs com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2018/079

[ Cryptology ePrint archive ]