**On Factoring Arbitrary Integers with Known Bits**

*Mathias Herrmann and 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.

**Category / Keywords: **foundations / factoring

**Publication Info: **Full Version of the Workshop "Kryptologie in Theorie und Praxis" paper

**Date: **received 18 Sep 2007

**Contact author: **herrmann at rbg informatik tu-darmstadt de

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20070919:213103 (All versions of this report)

**Short URL: **ia.cr/2007/374

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