Cryptology ePrint Archive: Report 1997/008

Factoring via Strong Lattice Reduction Algorithms

Harald Ritter, 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.

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Publication Info: Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive.

Date: received June 13th, 1997.

Contact author: roessnercs uni-frankfurt de

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