Paper 2005/051 Original: eprint.iacr.org/2005/051 ↗
A Note on Shor's Quantum Algorithm for Prime Factorization
Abstract
It's well known that Shor[1] proposed a polynomial time algorithm for prime factorization by using quantum computers. For a given number $n$, he gave an algorithm for finding the order $r$ of an element $x$ (mod $n$) instead of giving an algorithm for factoring $n$ directly. The indirect algorithm is feasible because factorization can be reduced to finding the order of an element by using randomization[2]. But a point should be stressed that the order of the number must be even. Actually, the restriction can be removed in a particular case. In this paper, we show that factoring RSA modulus (a product of two primes) only needs to find the order of $2$, whether it is even or not.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2005-02-21: last updated
- 2005-02-21: published
- Short URL
- https://ia.cr/2005/051
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2005/051,
author = {Zhengjun Cao},
title = {A Note on Shor's Quantum Algorithm for Prime Factorization},
howpublished = {Cryptology {ePrint} Archive, Paper 2005/051},
year = {2005},
url = {https://eprint.iacr.org/2005/051}
}