Score:2

Upper bound for the Gap Diffie–Hellman (in the generic group model)

sa flag

Does it exist an upper bound for the advantage of solving the Gap Diffie-Hellman problem (possibly expressed in terms of the order of the group, number of queries to the oracle, time, etc.)?

Score:1
ru flag

Well, there's the obvious upper bound of $O(|G|^{1/2})$ group operations from eschewing oracle calls and simply using the generic group functionality to do Pollard $\lambda$ like attacks.

More germanely, gap Diffie-Hellman questions arise most commonly in the area of pairing-based cryptography and here cryptographers have introduced a different model to the generic group plus decisional oracle. Instead they talk about the semi-generic group model (see Jager and Rupp ASIACRYPT 2010 for example) where they assume generic "input groups" to the pairing and augment this with a bilinear map to a third group.

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