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

• URL: http://arxiv.org/abs/2510.07515v2
• Date: Wed, 29 Oct 2025 18:12:03 GMT
• Title: No exponential quantum speedup for $\mathrm{SIS}^\infty$ anymore
• Authors: Robin Kothari, Ryan O'Donnell, Kewen Wu,
• Abstract summary: We present an efficient quantum algorithm for the average-case $ell_infty cryptographic$-Short Solution ($mathrmSISinfty$) problem.
• Score: 2.8004615208539523
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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