CryptoDB
A Note on Shor's Quantum Algorithm for Prime Factorization
Authors: | |
---|---|
Download: | |
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. |
BibTeX
@misc{eprint-2005-12388, title={A Note on Shor's Quantum Algorithm for Prime Factorization}, booktitle={IACR Eprint archive}, keywords={foundations / Shor's quantum algorithm, RSA modulus.}, url={http://eprint.iacr.org/2005/051}, note={ zjcamss@hotmail.com 12833 received 18 Feb 2005}, author={Zhengjun Cao}, year=2005 }