Lattice Enumeration with Discrete Pruning: Improvements, Cost Estimation and Optimal Parameters

Lattice enumeration is a linear-space algorithm for solving the shortest lattice vector problem (SVP). Extreme pruning practical technique accelerating enumeration, which has mature theoretical analysis and implementation. However, these works have yet to be applied discrete pruning. In this paper, we improve pruned (DP enumeration) provide solution proposed by Léo Ducas Damien Stehlé regarding cost estimation of We first rectify randomness assumption more precisely describe point distribution DP enumeration. Then, propose series improvements, including new polynomial-time binary search cell radius, refined cell-decoding rerandomization reprocessing strategy, all aiming lift efficiency build precise cost-estimation model Based on simulation, good accuracy in experiments. This simulator enables us an optimization method calculating optimal parameters minimize running time. The experimental results asymptotic both show that could outperform extreme pruning, means our optimized might become most efficient polynomial-space SVP solver date. An open-source implementation with its also provided.