Tighter Reductions for Forward-Secure Signature Schemes

  • Michel Abdalla
  • Fabrice Ben Hamouda
  • David Pointcheval
Conference paper

DOI: 10.1007/978-3-642-36362-7_19

Volume 7778 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Abdalla M., Ben Hamouda F., Pointcheval D. (2013) Tighter Reductions for Forward-Secure Signature Schemes. In: Kurosawa K., Hanaoka G. (eds) Public-Key Cryptography – PKC 2013. Lecture Notes in Computer Science, vol 7778. Springer, Berlin, Heidelberg

Abstract

In this paper, we revisit the security of factoring-based signature schemes built via the Fiat-Shamir transform and show that they can admit tighter reductions to certain decisional complexity assumptions such as the quadratic-residuosity, the high-residuosity, and the φ-hiding assumptions. We do so by proving that the underlying identification schemes used in these schemes are a particular case of the lossy identification notion recently introduced by Abdalla et al. at Eurocrypt 2012. Next, we show how to extend these results to the forward-security setting based on ideas from the Itkis-Reyzin forward-secure signature scheme. Unlike the original Itkis-Reyzin scheme, our construction can be instantiated under different decisional complexity assumptions and has a much tighter security reduction. Finally, we show that the tighter security reductions provided by our proof methodology can result in concrete efficiency gains in practice, both in the standard and forward-security setting, as long as the use of stronger security assumptions is deemed acceptable. All of our results hold in the random oracle model.

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Michel Abdalla
    • 1
  • Fabrice Ben Hamouda
    • 1
  • David Pointcheval
    • 1
  1. 1.Departement d’InformatiqueÉcole normale supérieureParisFrance