Factoring via Strong Lattice Reduction Algorithms

We address to the problem to factor a large composite number by lattice reduction algorithms Schnorr Sc 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 nding su ciently many short vectors in a suitably de ned lattice Using lattice basis reduction algorithms Schnorr and Euchner applied the reduction technique of Sc to bit long integers Their implementation needed several hours to compute a fraction of the solution i e out of congruences which are necessary to factorize the composite In this report we describe a more e cient implementation using stronger lattice basis reduction techniques incorporating ideas of SH and R For bit long integers our algorithm yields a complete factorization in less than hours