Journal of Cryptology

, Volume 16, Issue 4, pp 239–247

Separating Decision Diffie–Hellman from Computational Diffie–Hellman in Cryptographic Groups


DOI: 10.1007/s00145-003-0052-4

Cite this article as:
Joux, A. & Nguyen, K. J Cryptol (2003) 16: 239. doi:10.1007/s00145-003-0052-4


In many cases the security of a cryptographic scheme based on computational Diffie–Hellman does in fact rely on the hardness of the decision Diffie–Hellman problem. In this paper we construct concrete examples of groups where the stronger hypothesis, hardness of the decision Diffie–Hellman problem, no longer holds, while the weaker hypothesis, hardness of computational Diffie–Hellman, is equivalent to the hardness of the discrete logarithm problem and still seems to be a reasonable hypothesis.

Discrete logarithm Diffie–Hellman Elliptic curve Weil pairing 

Copyright information

© International Association for Cryptological Research 2003

Authors and Affiliations

  1. 1.DCSSI Crypto Lab, 51 Bd de Latour Maubourg, F-75700 Paris 07 SPFrance
  2. 2.Institut für experimentelle Mathematik, Universität GH Essen, Ellernstrasse 29, 45326 EssenGermany

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