Black-Box Models of Computation
Several abstract models of computation have been proposed in the literature to capture the notion of “generic groups” or their extensions [BS84, Nec94, Sho97, Mau05]. The black-box model we are going to describe in the sequel is a generalization of the model introduced by Maurer in [Mau05], which in turn can be seen as a generalization of the model of [Sho97]. While Maurer's model captures only the case where a generic algorithm operates on elements of a single algebraic structure, like a group or a ring, we extend this model in order to be able to describe settings where more than one algebraic structure is considered, as in pairing-based cryptography [DBS04], for instance.
KeywordsRandom Oracle Discrete Logarithm Discrete Logarithm Problem Random String Simulation Game
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