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)


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.


Polynomial Time Prime Factor Triangular Matrix Chinese Remainder Theorem Independent Degree 
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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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