Journal of Cryptology

, Volume 16, Issue 4, pp 239-247

First online:

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

  • Antoine JouxAffiliated withDCSSI Crypto Lab, 51 Bd de Latour Maubourg, F-75700 Paris 07 SP Email author 
  • , Kim  NguyenAffiliated withInstitut für experimentelle Mathematik, Universität GH Essen, Ellernstrasse 29, 45326 Essen

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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