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Factorization of Square-Free Integers with High Bits Known

  • Bagus Santoso
  • Noboru Kunihiro
  • Naoki Kanayama
  • Kazuo Ohta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4341)

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 \((\frac{1}{k+2}+\frac{\epsilon}{k(k-1)})\log N\) high-order bits of each prime factor are given. For a fixed ε, the running time of our algorithm is heuristic polynomial in (logN). 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.

Keywords

Polynomial Time Prime Factor Triangular Matrix Chinese Remainder Theorem Independent Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bagus Santoso
    • 1
  • Noboru Kunihiro
    • 1
  • Naoki Kanayama
    • 2
  • Kazuo Ohta
    • 1
  1. 1.The University of Electro-CommunicationsChofu-shi, TokyoJapan
  2. 2.University of TsukubaIbarakiJapan

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