Paper 2026/2622
Faster Matrix Multiplication Leads to Faster Lattice Sieving
Abstract
Let $\omega$ denote the matrix multiplication exponent. Very recently, OpenAI showed that $\omega\le9/4$. We demonstrate that, for any fixed $\eta>0$, if $\omega\le9/4-\eta$, then there is a constant $\delta=\delta(\eta)>0$ such that heuristic lattice sieving can be improved to $(3/2-\delta)^{n/2+o(n)}$ time under the spherical heuristic used in the BDGL analysis. With known matrix multiplication algorithms, our method already yields subquadratic search within BDGL buckets.
Metadata
- Available format(s)
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PDF
- Category
- Foundations
- Publication info
- Preprint.
- Contact author(s)
-
qw1234567 @ mail ustc edu cn
hghu2005 @ ustc edu cn - History
- 2026-10-26: approved
- 2026-10-24: received
- See all versions
- Short URL
- https://ia.cr/2026/2622
- License
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CC BY
BibTeX
@misc{cryptoeprint:2026/2622,
author = {Yiming Gao and Honggang Hu},
title = {Faster Matrix Multiplication Leads to Faster Lattice Sieving},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2622},
year = {2026},
url = {https://eprint.iacr.org/2026/2622}
}
