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Fast algorithm for finding a small root of a quadratic modular equation

  • Public-Key Cryptography
  • Conference paper
  • First Online:
Information Security (ISW 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1396))

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Abstract

The security of some cryptosystems is based on the difficulty of solving a quadratic modular equation. This paper shows a new algorithm for finding the small root of the quadratic modular equation. While previous algorithms for finding the small root of the modular equation are based on the LLL algorithm, the new algorithm is based on the continued fraction. Using the new algorithm, we can find the root less than n 1/4, where n is the modulus. The new algorithm is more efficient than previous algorithms even if the modulus is large.

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Author information

Authors and Affiliations

  1. Kobe University, 1-1 Rokkodai Nada Kobe, 657, Japan

    Hidenori Kuwakado & Hatsukazu Tanaka

Authors
  1. Hidenori Kuwakado
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  2. Hatsukazu Tanaka
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Editor information

Eiji Okamoto George Davida Masahiro Mambo

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© 1998 Springer-Verlag Berlin Heidelberg

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Kuwakado, H., Tanaka, H. (1998). Fast algorithm for finding a small root of a quadratic modular equation. In: Okamoto, E., Davida, G., Mambo, M. (eds) Information Security. ISW 1997. Lecture Notes in Computer Science, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030410

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  • DOI: https://doi.org/10.1007/BFb0030410

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64382-1

  • Online ISBN: 978-3-540-69767-1

  • eBook Packages: Springer Book Archive

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