Solving Linear Equations Modulo Divisors: On Factoring Given Any Bits

@inproceedings{Herrmann2008SolvingLE,
title={Solving Linear Equations Modulo Divisors: On Factoring Given Any Bits},
author={Mathias Herrmann and Alexander May},
booktitle={ASIACRYPT},
year={2008}
}

We study the problem of finding solutions to linear equations modulo an unknown divisor p of a known composite integer N . An important application of this problem is factorization of N with given bits of p. It is well-known that this problem is polynomial-time solvable if at most half of the bits of p are unknown and if the unknown bits are located in one consecutive block. We introduce an heuristic algorithm that extends factoring with known bits to an arbitrary number n of blocks… CONTINUE READING