Divisors in Residue Classes, Constructively

Don Coppersmith; Nick Howgrave-Graham; S.  V.  Nagaraj

Paper 2004/339

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

Metadata

Available format(s): PS
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: lattice divisors LLL
Contact author(s): nhowgravegraham @ ntru com
History: 2004-12-07: received
Short URL: https://ia.cr/2004/339
License: 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},
      url = {https://eprint.iacr.org/2004/339}
}