English

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 \ell_\infty-Short Integer Solution (SIS\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 SIS\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 SIS\mathrm{SIS}^\infty 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}
}
R2 v1 2026-07-01T06:25:11.298Z