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It's been a while since I've read this paper, and I remember having a lot of trouble with this derivation. I'm sure there is an easy way to see it, but I don't see it, so I'll just brute force through with the algabra. First, some context: When the simulator is given a random element as the last term in the tuple the simulator will either abort (and ...


The previous comments skip an important fact. I think that a PE for all circuits and A FE for all circuits are equivalent in the sense that you can build the second from the first one (the opposite direction is trivial). A key for a circuit C with output size of n bits can be implemwnted as n PE keys in which the i-th key is relative to the circuit that ...

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