On Factoring Arbitrary Integers with Known Bits

Mathias Herrmann; Alexander May

Paper 2007/374 Original: eprint.iacr.org/2007/374 ↗

On Factoring Arbitrary Integers with Known Bits

Mathias Herrmann

Alexander May

Abstract

We study the {\em factoring with known bits problem}, where we are given a composite integer $N=p_1p_2\dots p_r$ and oracle access to the bits of the prime factors $p_i$, $i=1, \dots, r$. Our goal is to find the full factorization of $N$ in polynomial time with a minimal number of calls to the oracle. We present a rigorous algorithm that efficiently factors $N$ given $(1-\frac{1}{r}H_r)\log N$ bits, where $H_r$ denotes the $r^{th}$ harmonic number.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2007-09-19: last updated; 2007-09-19: published
Short URL: https://ia.cr/2007/374
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2007/374,
      author = {Mathias Herrmann and Alexander May},
      title = {On Factoring Arbitrary Integers with Known Bits},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/374},
      year = {2007},
      url = {https://eprint.iacr.org/2007/374}
}