Efficient Signature Schemes with Tight Reductions to the Diffie-Hellman Problems

  • Authors:
  • Eu-Jin Goh;Stanislaw Jarecki;Jonathan Katz;Nan Wang

  • Affiliations:
  • Computer Science Department, Stanford University, Stanford, CA 94305, USA;School of Information and Computer Science, University of California at Irvine, Irvine, CA 92697, USA;Department of Computer Science, University of Maryland, College Park, MD 20742, USA;Department of Computer Science, University of Maryland, College Park, MD 20742, USA

  • Venue:
  • Journal of Cryptology
  • Year:
  • 2007

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Abstract

We propose and analyze two efficient signature schemes whose security is tightly related to the Diffie-Hellman problems in the random oracle model. The security of our first scheme relies on the hardness of the computational Diffie-Hellman problem; the security of our second scheme - which is more efficient than the first-is based on the hardness of the decisional Diffie-Hellman problem, a stronger assumption. Given the current state of the art, it is as difficult to solve the Diffie-Hellman problems as it is to solve the discrete logarithm problem in many groups of cryptographic interest. Thus, the signature schemes shown here can currently offer substantially better efficiency (for a given level of provable security) than existing schemes based on the discrete logarithm assumption. The techniques we introduce can also be applied in a wide variety of settings to yield more efficient cryptographic schemes (based on various number-theoretic assumptions) with tight security reductions.