No exponential quantum speedup for $\mathrm{SIS}^\infty$ anymore
Quantum Physics
2026-03-06 v3 Computational Complexity
Cryptography and Security
Data Structures and Algorithms
Abstract
In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for the average-case -Short Integer Solution () problem, in a parameter range outside the normal range of cryptographic interest, but still with no known efficient classical algorithm. This was particularly exciting since is a simple problem without structure, and their algorithmic techniques were different from those used in prior exponential quantum speedups. We present efficient classical algorithms for all of the and (more general) Constrained Integer Solution problems studied in their paper, showing there is no exponential quantum speedup anymore.
Cite
@article{arxiv.2510.07515,
title = {No exponential quantum speedup for $\mathrm{SIS}^\infty$ anymore},
author = {Robin Kothari and Ryan O'Donnell and Kewen Wu},
journal= {arXiv preprint arXiv:2510.07515},
year = {2026}
}