Cryptology ePrint Archive: Report 2015/522

Speeding-up lattice sieving without increasing the memory, using sub-quadratic nearest neighbor search

Anja Becker, Nicolas Gama, Antoine Joux

Abstract: We give a simple heuristic sieving algorithm for the $m$-dimensional exact shortest vector problem (SVP) which runs in time $2^{0.3112m +o(m)}$. Unlike previous time-memory trade-offs, we do not increase the memory, which stays at its bare minimum $2^{0.2075m +o(m)}$. To achieve this complexity, we borrow a recent tool from coding theory, known as nearest neighbor search for binary code words. We simplify its analysis, and show that it can be adapted to solve this variant of the fixed-radius nearest neighbor search problem: Given a list of exponentially many unit vectors of $\mR^m$, and an angle $\gamma\pi$, find all pairs of vectors whose angle $\leq\gamma\pi$. The complexity is sub-quadratic which leads to the improvement for lattice sieves.

Category / Keywords: public-key cryptography / Nearest neighbor search, lattice, sieve

Date: received 31 May 2015, last revised 24 Aug 2015

Contact author: anja becker at epfl ch

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Version: 20150824:143217 (All versions of this report)

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