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As @xagawa mentioned in his comment, it depends on what you mean by "controled". In the case of using a programmable random oracle, yes, the reduction (in particular the simulation of the challenger of the real game) decides about what to return as answer to an oracle query. Thereby, the reduction has to guarantee that the "programmed" answers are ...


Firstly, I should clarify: I am just referring to the standard definition of a random oracle. There are other scenario's (better discussed in DrL's answer), but these tend to be explicitly referred to. That is, if you have a standard 'random oracle', this answer should hold. On the other hand, if you have a different type of oracle, this won't hold. A ...

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