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Parallel Processing for Prime Factorization with Spatial Amplitude Modulation in Optics

  • Kouichi Nitta
  • Takashi Kamigiku
  • Takeshi Nakajima
  • Osamu Matoba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7715)

Abstract

An optical method for prime factorization is modified. The procedure in the original method is similar to that with quantum computing. In this repot, some differences between the quantum solution and the method are discussed. And, improvement for our method is proposed based on the discussion.

Keywords

Prime factorization Spatial parallel processing Amplitude modulation 

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References

  1. 1.
    Oltean, M.: Solving the Hamiltonian path problem with a light-based computer. Natural Computing 7, 57–70 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Haist, T., Osten, W.: An Optical Solution for the Traveling Salesman Problem. Opt. Express 15, 10473–10482 (2007)CrossRefGoogle Scholar
  3. 3.
    Shaked, N.T., Messika, S., Dolev, S., Rosen, J.: Optical solution for bounded NP-complete problems. Appl. Opt. 46, 711–724 (2007)CrossRefGoogle Scholar
  4. 4.
    Shamir, A.: Factoring Large Numbers with the TWINKLE Device (Extended Abstract). In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 2–12. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Nitta, K., Matoba, O., Yoshimura, T.: Parallel processing for multiplication modulo by means of phase modulation. Appl. Opt. 47, 611–616 (2008)CrossRefGoogle Scholar
  6. 6.
    Nitta, K., Katsuta, N., Matoba, O.: An Optical Parallel System for Prime Factorization. Jpn. J. Appl. Phy. 48, 09LA02-1–09LA02-5 (2009)Google Scholar
  7. 7.
    Nitta, K., Katsuta, N., Matoba, O.: Improvement of a system for prime factorization based on optical interferometer. In: Dolev, S., Oltean, M. (eds.) OSC 2009. LNCS, vol. 5882, pp. 124–129. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Nitta, K., Matoba, O.: An optical system for prime factorization based on parallel processing. In: Dolev, S., Oltean, M. (eds.) OSC 2010. LNCS, vol. 6748, pp. 10–15. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Shor, P.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proc. 35th Ann. Symp. on Foundations of Comput. Sci., vol. 1898, pp. 124–134 (1994)Google Scholar
  10. 10.
    Kamigiku, T., Nitta, K., Matoba, O.: Improvement of modulation patterns in a method for parallel modulo exponentiation with optical amplitude modulation. Technical Digest of Moc 2011, H-80 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kouichi Nitta
    • 1
  • Takashi Kamigiku
    • 1
  • Takeshi Nakajima
    • 1
  • Osamu Matoba
    • 1
  1. 1.Department of Systems Science, Graduate of System InformaticsKobe UniversityKobeJapan

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