Abstract
In this paper we propose an algorithm of factoring any integer N which has k different prime factors with the same bit-length, when about (1/k+2+ε/k-1)log2N high-order bits of each prime factor are given. For a fixed ε, the running time of our algorithm is heuristic polynomial in (log2N). Our factoring algorithm is based on a lattice-based algorithm of solving any k-variate polynomial equation over Z, which might be an independent interest.
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