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Separating Decision Diffie-Hellman from Diffie-Hellman in cryptographic groups
Authors: Antoine Joux, Kim NguyenAbstract:
In many cases, the security of a cryptographic scheme based on Diffie–Hellman does in fact rely on the hardness of the
Diffie–Hellman Decision problem. In this paper, we show that the
hardness of Decision Diffie–Hellman is a much stronger hypothesis than the hardness of the regular Diffie–Hellman problem. Indeed, we
describe a reasonably looking cryptographic group where Decision
Diffie–Hellman is easy while Diffie–Hellman is equivalent to a –
presumably hard – Discrete Logarithm Problem. This shows that care
should be taken when dealing with Decision Diffie–Hellman, since its
security cannot be taken for granted.
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