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arXiv · 2609.21612

Faster SVP in Polynomial Space

Yansong Feng·Yiming Gao·Jiaqi Liu
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Abstract

Kannan's algorithm, as analyzed by Hanrot and Stehlé in 2007, solves the exact Euclidean shortest vector problem in polynomial space and $n^{\frac{n}{2e}+o(n)}$ time. In the classical setting with polynomial space, we obtain the first improvement on this bound via a randomized algorithm that runs in $n^{\frac{n}{4e}+o(n)}$ time. The main idea is to represent a fixed shortest vector in many ways as a difference of samples, thereby enabling the low-space collision search of Lyu and Zhu (SODA 2023) to replace exhaustive enumeration in the original analysis.

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Yansong Feng, Yiming Gao, Jiaqi Liu. 2026-09-18. Faster SVP in Polynomial Space. https://arxiv.org/abs/2609.21612

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