IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Cryptography and Information Security
Factorization of Square-Free Integers with High Bits Known
Bagus SANTOSONoboru KUNIHIRONaoki KANAYAMAKazuo OHTA
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2008 Volume E91.A Issue 1 Pages 306-315

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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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© 2008 The Institute of Electronics, Information and Communication Engineers
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