Paper 2004/339 Original: eprint.iacr.org/2004/339 ↗
Divisors in Residue Classes, Constructively
Abstract
Let $r,s,n$ be integers satisfying $0 \leq r < s < n$, $s \geq n^{\alpha}$, $\alpha > 1/4$, and $\gcd(r,s)=1$. Lenstra showed that the number of integer divisors of $n$ equivalent to $r \pmod s$ is upper bounded by $O((\alpha-1/4)^{-2})$. We re-examine this problem; showing how to explicitly construct all such divisors and incidentally improve this bound to $O((\alpha-1/4)^{-3/2})$.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2004-12-07: last updated
- 2004-12-07: published
- Short URL
- https://ia.cr/2004/339
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/339,
author = {Don Coppersmith and Nick Howgrave-Graham and S. V. Nagaraj},
title = {Divisors in Residue Classes, Constructively},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/339},
year = {2004},
url = {https://eprint.iacr.org/2004/339}
}