Paper 2026/1876

AH-BKZ: A Lattice Reduction Algorithm with Asynchronous Hybrid Processing

Abstract

Evaluating the hardness of the Shortest Vector Problem (SVP) is essential for selecting secure parameters in lattice-based cryptography. The fastest current SVP solvers are based on variants of G6K, but their large memory consumption remains a major bottleneck, making high-dimensional executions difficult. A common strategy for alleviating this memory bottleneck is strong basis reduction preprocessing before a sieve-based algorithm. This strategy can solve SVP instances in higher dimensions than standalone G6K under the same memory constraints, but the time required for basis reduction becomes a major issue. ProPnjBKZ, a fast basis reduction algorithm optimized by Wang et al., is currently used as a promising preprocessing method for solving high-dimensional SVP instances. In this paper, we identify that, in the ProPnjBKZ-based SVP-solving pipeline, memory resources can remain underutilized during the preprocessing phase, since ProPnjBKZ requires less memory than the subsequent high-dimensional sieving process. Based on this observation, we propose AH-BKZ, which exploits such unused computational resources by asynchronously running multiple SVP oracles, thereby accelerating basis reduction. Our experiments show that, compared with ProPnjBKZ-based preprocessing, AH-BKZ reduces the overall runtime by up to 23.1% and by 18.6% on average among successful runs for dimensions 124-148 under comparable peak memory constraints. Moreover, in a supplementary experiment conducted in a larger computational environment, AH-BKZ set new solving records for dimension 163 in the TU Darmstadt SVP Challenge and for dimension 164 in the Ideal Lattice Challenge.

Note: The submission version of a paper accepted at ICICS 2026.