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A Practical and Tightly Secure Signature Scheme Without Hash Function

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Topics in Cryptology – CT-RSA 2007 (CT-RSA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4377))

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Abstract

In 1999, two signature schemes based on the flexible RSA problem (a.k.a. strong RSA problem) were independently introduced: the Gennaro-Halevi-Rabin (GHR) signature scheme and the Cramer-Shoup (CS) signature scheme. Remarkably, these schemes meet the highest security notion in the standard model. They however differ in their implementation. The CS scheme and its subsequent variants and extensions proposed so far feature a loose security reduction, which, in turn, implies larger security parameters. The security of the GHR scheme and of its twinning-based variant are shown to be tightly based on the flexible RSA problem but additionally (i) either assumes the existence of division-intractable hash functions, or (ii) requires an injective mapping into the prime numbers in both the signing and verification algorithms.

In this paper, we revisit the GHR signature scheme and completely remove the extra assumption made on the hash functions without relying on injective prime mappings. As a result, we obtain a practical signature scheme (and an on-line/off-line variant thereof) whose security is solely and tightly related to the strong RSA assumption.

The work described in this paper has been supported in part by the European Commission through the IST Programme under Contract IST-2002-507932 ECRYPT.

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Author information

Authors and Affiliations

  1. Gemalto, Security Labs, Avenue du Jujubier, 13705, La Ciotat Cedex, France

    Benoît Chevallier-Mames

  2. Thomson R&D France, Technology Group, Corporate Research, Security Laboratory, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné, France

    Marc Joye

Authors
  1. Benoît Chevallier-Mames
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  2. Marc Joye
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Editors and Affiliations

  1. Information Sharing Platform Laboratories, NTT Corporation, Japan

    Masayuki Abe

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Chevallier-Mames, B., Joye, M. (2006). A Practical and Tightly Secure Signature Scheme Without Hash Function. In: Abe, M. (eds) Topics in Cryptology – CT-RSA 2007. CT-RSA 2007. Lecture Notes in Computer Science, vol 4377. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11967668_22

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  • DOI: https://doi.org/10.1007/11967668_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69327-7

  • Online ISBN: 978-3-540-69328-4

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