# The real-life meaning of proving over a group that doesn't support the oracle?

If I proved a scheme's security under GDH assumption, in real-life, if this DDH oracle does exist, then it's good, but what about other side ? In real-life, if this DDH oracle doesn't exist, then what's the meaning of proving?

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An oracle gives an advantage to the attacker. So absence of the oracle shouldn't hurt security. (Though for some schemes, absence of the oracle means that the legitimate user can't be implemented efficiently. For example BLS requires uses cheap DDH to validate the signature.) –  CodesInChaos Dec 4 '13 at 12:31
@CodesInChaos : for example what? –  Alex Dec 4 '13 at 12:39
Presence or absence of the oracle is irrelevant for the security of the scheme. If the security of your scheme is equivalent to a certain reduction not existing, then if that reduction exists, your scheme will be broken because the legitimate user acts as the relevant oracle. –  K.G. Dec 4 '13 at 14:31
@CodesInChaos：cheap DDH　？can you show me an example ? –  Alex Dec 6 '13 at 4:10

when a scheme(e.g. protocol) is implemented over a group say $\mathbb{G}$ that does not admit a DDH oracle, if I prove the security of this scheme under GDH assumption,then if a successful adversary can be constructed, what does this mean ? –  Alex Dec 4 '13 at 12:48