Journal of Cryptology

, Volume 20, Issue 4, pp 493–514 | Cite as

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

  • Eu-Jin GohEmail author
  • Stanislaw JareckiEmail author
  • Jonathan KatzEmail author
  • Nan WangEmail author


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.


Signature Scheme Random Oracle Discrete Logarithm Discrete Logarithm Problem Random Oracle Model 
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Copyright information

© International Association for Cryptologic Research 2007

Authors and Affiliations

  1. 1.Computer Science Department, Stanford UniversityStanford, CA 94305USA
  2. 2.School of Information and Computer Science, University of California at IrvineIrvine, CA 92697USA
  3. 3.Department of Computer Science, University of MarylandCollege Park, MD 20742USA

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