Separating decision diffie-hellman from computational diffie-hellman in cryptographic groups

Abstract

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. © 2003 International Association for Cryptological Research.