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Paper: On Factoring Arbitrary Integers with Known Bits

Authors:
Mathias Herrmann
Alexander May
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URL: http://eprint.iacr.org/2007/374
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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.
BibTeX
@misc{eprint-2007-13654,
  title={On Factoring Arbitrary Integers with Known Bits},
  booktitle={IACR Eprint archive},
  keywords={foundations / factoring},
  url={http://eprint.iacr.org/2007/374},
  note={Full Version of the Workshop "Kryptologie in Theorie und Praxis" paper herrmann@rbg.informatik.tu-darmstadt.de 13774 received 18 Sep 2007},
  author={Mathias Herrmann and Alexander May},
  year=2007
}