Hybrid Damgård Is CCA1-Secure under the DDH Assumption

  • Authors:
  • Yvo Desmedt;Helger Lipmaa;Duong Hieu Phan

  • Affiliations:
  • University College London, UK;Cybernetica AS, Estonia;University of Paris 8, France

  • Venue:
  • CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
  • Year:
  • 2008

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Abstract

In 1991, Damgård proposed a simple public-key cryptosystem that he proved CCA1-secure under the Diffie-Hellman Knowledge assumption. Only in 2006, Gjøsteen proved its CCA1-security under a more standard but still new and strong assumption. The known CCA2-secure public-key cryptosystems are considerably more complicated. We propose a hybrid variant of Damgård's public-key cryptosystem and show that it is CCA1-secure if the used symmetric cryptosystem is CPA-secure, the used MAC is unforgeable, the used key-derivation function is secure, and the underlying group is a DDH group. The new cryptosystem is the most efficient known CCA1-secure hybrid cryptosystem based on standard assumptions.