### Divisors in Residue Classes, Constructively

Don Coppersmith, Nick Howgrave-Graham, and S. V. Nagaraj

##### 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 $O((\alpha-1/4)^{-3/2})$.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
lattice divisors LLL
Contact author(s)
nhowgravegraham @ ntru com
History
Short URL
https://ia.cr/2004/339

CC BY

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},
note = {\url{https://eprint.iacr.org/2004/339}},
url = {https://eprint.iacr.org/2004/339}
}

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