Dept. of Information-Communications Engineering, University of Electro-Communications The Institute of Electronics, Information and Communication Engineers
Noboru KUNIHIRO
Dept. of Information-Communications Engineering, University of Electro-Communications The Institute of Electronics, Information and Communication Engineers
Naoki KANAYAMA
Dent. of Risk Engineering. Faculty of Systems and Information Engineering, University of Tsukuba The Institute of Electronics, Information and Communication Engineers
Kazuo OHTA
Dept. of Information-Communications Engineering, University of Electro-Communications The Institute of Electronics, Information and Communication Engineers
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.
