Factorization of Square-Free Integers with High Bits Known

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 ( 1 k+2 + k(k-1) ) log N high-order bits of each prime factor are given. For a fixed , the running time of our algorithm is heuristic polynomial in (log N). Our factoring algorithm is based on a new lattice-based algorithm of solving any k-variate polynomial equation over Z, which might be an independent interest.

• Type: Journal
• Year: 2008
• Where: IEICET
• Authors: Bagus Santoso, Noboru Kunihiro, Naoki Kanayama, Kazuo Ohta
• Keywords: Algorithm, IEICET 2008, K-variate Polynomial Equation, Prime Factor