Paper 2024/629
Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms
, University of OxfordAbstract
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
-
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},
note = {\url{https://eprint.iacr.org/2024/629}},
url = {https://eprint.iacr.org/2024/629}
}
