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arXiv · 2510.07515

No exponential quantum speedup for $\mathrm{SIS}^\infty$ anymore

Robin Kothari·Ryan O'Donnell·Kewen Wu
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Abstract

In 2021, Chen, Liu, and Zhandry presented an efficient quantum algorithm for the average-case $\ell_\infty$-Short Integer Solution ($\mathrm{SIS}^\infty$) 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 $\mathrm{SIS}^\infty$ 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 $\mathrm{SIS}^\infty$ and (more general) Constrained Integer Solution problems studied in their paper, showing there is no exponential quantum speedup anymore.

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Robin Kothari, Ryan O'Donnell, Kewen Wu. 2025-10-08. No exponential quantum speedup for $\mathrm{SIS}^\infty$ anymore. https://arxiv.org/abs/2510.07515

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