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A Generalization and a Variant of Two Threshold Cryptosystems Based on Factoring

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Information Security (ISC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4779))

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Abstract

At Asiacrypt 2002, Katz and Yung presented two threshold cryptosystems based on factoring, a threshold version of Goldwasser-Micali’s probabilistic encryption assuming that \(p=q=3\bmod 4\), and a threshold Rabin signature scheme assuming that \(p=3 \bmod 8\) and \(q=7 \bmod 8\). In this paper, we show a generalized condition on p and q to obtain a threshold version of Goldwasser-Micali, and a threshold Rabin-type signature scheme due to Kurosawa and Ogata [7] for \(p=q=3 \bmod 4\) and

$$ {p+1 \over 4}={q+1 \over 4} \bmod \gcd(p-1,q-1). $$

Note that our set of (p,q) is disjoint from that of Katz-Yung threshold Rabin signature scheme.

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References

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Authors and Affiliations

  1. Department of Computer Science, University College London, UK

    Yvo Desmedt

  2. Department of Computer and Information Sciences, Ibaraki University, Japan

    Kaoru Kurosawa

Authors
  1. Yvo Desmedt
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  2. Kaoru Kurosawa
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Editor information

Juan A. Garay Arjen K. Lenstra Masahiro Mambo René Peralta

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Desmedt, Y., Kurosawa, K. (2007). A Generalization and a Variant of Two Threshold Cryptosystems Based on Factoring. In: Garay, J.A., Lenstra, A.K., Mambo, M., Peralta, R. (eds) Information Security. ISC 2007. Lecture Notes in Computer Science, vol 4779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75496-1_23

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  • DOI: https://doi.org/10.1007/978-3-540-75496-1_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75495-4

  • Online ISBN: 978-3-540-75496-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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