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The generic group model has recently been used to prove the security of certain asymmetric encryption and signature schemes. This paper presents results that show that there exist problems in that are provably hard in the generic group model but easy to solve whenever the random encoding function is replaced with a specific encoding function (or one drawn from a specific set of encoding functions). In particular we show that there exist cryptographic schemes that are provably hard in the generic group model but easy to break in practice.

Adapting the Weaknesses of the Random Oracle Model to the Generic Group Model