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On the Improvement of Fermat Factorization

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Network and System Security (NSS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7645))

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Abstract

Given an integer N = pq, which is a product of two primes, it is difficult to determine the prime factors p and q efficiently. However, for the suitable size of a number N, Fermat’s algorithm is one of the most simple method for solving it. In this paper, a method called EPF for estimating the prime factors of a composite number is proposed. We use the technique of continued fractions to output two integers, p E  + q E and p E ·q E , which are close to p + q and p·q, respectively. Furthermore, we show that EPF can be adopted to reduce the loop count in Fermat’s algorithm before factoring a composite number. The effect depends on the size of the prime factor. We believe that there are still other applications as well wherein EPF can be used.

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Author information

Authors and Affiliations

  1. Institute of Information Science, Academia Sinica, Taipei, Taiwan

    Mu-En Wu

  2. Department of Computer Science, National Chengchi University, Taipei, Taiwan

    Raylin Tso

  3. Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan

    Hung-Min Sun

Authors
  1. Mu-En Wu
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  2. Raylin Tso
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  3. Hung-Min Sun
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Editor information

Editors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, 350108, Fuzhou, Fujian, China

    Li Xu

  2. Department of Computer Science, CERIAS and Cyber Center, Purdue University, 47907-2107, West Lafayette, IN, USA

    Elisa Bertino

  3. School of Computer Science and Software Engineering, University of Wollongong, 2522, Wollongong, NSW, Australia

    Yi Mu

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Wu, ME., Tso, R., Sun, HM. (2012). On the Improvement of Fermat Factorization. In: Xu, L., Bertino, E., Mu, Y. (eds) Network and System Security. NSS 2012. Lecture Notes in Computer Science, vol 7645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34601-9_29

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  • DOI: https://doi.org/10.1007/978-3-642-34601-9_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34600-2

  • Online ISBN: 978-3-642-34601-9

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