Paper 2024/629

Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms

Cédric Pilatte, University of Oxford
Abstract

In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of Shor's algorithm that requires far fewer quantum gates. His algorithm relies on a number-theoretic conjecture on the elements in $(\mathbb{Z}/N\mathbb{Z})^{\times}$ that can be written as short products of very small prime numbers. We prove a version of this conjecture using tools from analytic number theory such as zero-density estimates. As a result, we obtain an unconditional proof of correctness of this improved quantum algorithm and of subsequent variants.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
factoringquantumnumber theorylatticesGeneralized Riemann Hypothesis
Contact author(s)
cedric pilatte @ maths ox ac uk
History
2024-04-26: approved
2024-04-24: received
See all versions
Short URL
https://ia.cr/2024/629
License
Creative Commons Attribution-NonCommercial-ShareAlike
CC BY-NC-SA

BibTeX

@misc{cryptoeprint:2024/629,
      author = {Cédric Pilatte},
      title = {Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/629},
      year = {2024},
      url = {https://eprint.iacr.org/2024/629}
}
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