Paper 1997/008

Factoring via Strong Lattice Reduction Algorithms

Harald Ritter and Carsten Roessner

Abstract

We address to the problem to factor a large composite number by lattice reduction algorithms. Schnorr has shown that under a reasonable number theoretic assumptions this problem can be reduced to a simultaneous diophantine approximation problem. The latter in turn can be solved by finding sufficiently many l_1--short vectors in a suitably defined lattice. Using lattice basis reduction algorithms Schnorr and Euchner applied Schnorrs reduction technique to 40--bit long integers. Their implementation needed several hours to compute a 5% fraction of the solution, i.e., 6 out of 125 congruences which are necessary to factorize the composite. In this report we describe a more efficient implementation using stronger lattice basis reduction techniques incorporating ideas of Schnorr, Hoerner and Ritter. For 60--bit long integers our algorithm yields a complete factorization in less than 3 hours.

Metadata
Available format(s)
PS
Publication info
Published elsewhere. Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive.
Contact author(s)
roessner @ cs uni-frankfurt de
History
1997-06-13: received
Short URL
https://ia.cr/1997/008
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:1997/008,
      author = {Harald Ritter and Carsten Roessner},
      title = {Factoring via Strong Lattice Reduction Algorithms},
      howpublished = {Cryptology ePrint Archive, Paper 1997/008},
      year = {1997},
      note = {\url{https://eprint.iacr.org/1997/008}},
      url = {https://eprint.iacr.org/1997/008}
}
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