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On the complexity of composite numbers

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Algorithms and Computation (ISAAC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 650))

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References

  1. Adleman, L.M. and Huang, M.D.A., “Recognizing Primes in Random Polynomial Time,” Proc. of STOC, pp.462–469 (1987).

    Google Scholar 

  2. Aiello, W. and Håstad, J., “Statistical Zero-Knowledge Languages Can Be Recognized in Two Rounds,” JCSS, Vol. 42, No.3, pp. 327–345 (1991).

    Google Scholar 

  3. Babai, L. and Moran, S., “Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes,” JCSS, Vol. 36, No.2, pp. 254–276 (1988).

    Google Scholar 

  4. Bellare, M., Micali, S., and Ostrovsky, R., “Perfect Zero-Knowledge in Constant Rounds,” Proc. of STOC, pp.482–493 (1990).

    Google Scholar 

  5. Fortnow, L., The Complexity of Perfect Zero-Knowledge,” Proc. of STOC, pp.204–209 (1987).

    Google Scholar 

  6. Goldreich, O. and Krawczyk, H., “On the Composition of Zero-Knowledge Proof Systems,” Proc. of ICALP'90, LNCS 443, Springer-Verlag, Berlin, pp. 268–282 (1990).

    Google Scholar 

  7. Goldwasser, S., Micali, S., and Rackoff, C., “The Knowledge Complexity of Interactive Proof Systems,” SIAM J. Comput., Vol. 18, No.1, pp. 186–208 (1989).

    Article  Google Scholar 

  8. Goldreich, O., Micali, S., and Wigderson, A., “Proofs that Yield Nothing But Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems,” JACM, Vol. 38, No.1, pp. 691–729 (1991).

    Article  Google Scholar 

  9. Goldreich, O. and Oren, Y., “Definitions and Properties of Zero-Knowledge Proof Systems,” Tech. Rep. #610, Technion, Department of Computer Science (1990).

    Google Scholar 

  10. Rabin, M.O., “Probabilistic Algorithm for Primality Testing,” Journal of Number Theory, Vol. 12, pp. 128–138 (1980).

    Article  Google Scholar 

  11. Solovay, R. and Strassen, V., “A Fast Monte Calro Test for Primality,” SIAM J. Comput., Vol. 6, No.1, pp. 84–85 (1977).

    Article  Google Scholar 

  12. Tompa, M. and Woll, H., “Random Self-Reducibility and Zero-Knowledge Interactive Proofs of Possession of Information,” Proc. of FOCS, pp.472–482 (1987).

    Google Scholar 

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Authors and Affiliations

  1. Department of Information Processing, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259, Nagatsuta, Midori-ku, 227, Yokohama, Japan

    Toshiya Itoh & Kenji Horikawa

Authors
  1. Toshiya Itoh
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  2. Kenji Horikawa
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Editor information

Toshihide Ibaraki Yasuyoshi Inagaki Kazuo Iwama Takao Nishizeki Masafumi Yamashita

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© 1992 Springer-Verlag Berlin Heidelberg

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Itoh, T., Horikawa, K. (1992). On the complexity of composite numbers. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_76

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  • DOI: https://doi.org/10.1007/3-540-56279-6_76

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56279-5

  • Online ISBN: 978-3-540-47501-9

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