Block Korkin-Zolotarev algorithm generalization and their practical implementation (Russian)

TL;DR

This paper introduces a practical GPU-accelerated algorithm for block Korkin-Zolotarev lattice reduction, combining QR-decomposition and shortest vector enumeration, validated through empirical tests on random lattices.

Contribution

It presents a novel practical implementation of block Korkin-Zolotarev reduction using GPU acceleration and specific numerical methods.

Findings

Effective GPU implementation of the reduction algorithm

Successful empirical validation on random lattices

Potential for improved lattice reduction performance

Abstract

We propose a practical algorithm for block Korkin-Zolotarev reduction, a concept introduced by Schnorr, using CPU arbitrary length Householder QR-decomposition for orthogonalization and double precision OpenCL GPU Finke-Post shortest vector enumeration. Empirical tests was used on random lattices in the sense of Goldstein and Mayer.