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seen Jan 6 at 7:38

comment garbled circuit vs fully homomorphic encryption
I saw this paper, but it's about combining GC, FHE and ABE to achieve FE. Still uncertain if it answers my questions.
comment Why is proof-by-reduction needed (for Elgamal proof of security, for example)?
why don't they have the same distribution? they're both uniform distributions over the same group.
comment Why are protocols often proven secure under the random oracle model instead of a hash assumption?
I was veering more towards the proof technique in the random oracles. It is not by simply replacing the random oracle with a perfect random function we can arrive at the same proof in the standard model. But what seems troubling to me is the fact that security proof in the random oracle allows the simulator to see the oracle queries made by the adversary. Is there any justification for this? Or is this simply that we cannot do without this assumption?
comment The security proof for Key Policy Attribute Based Encryption
I re-phrased the question by quoting the proof from paper. I used different notations in my original question, which probably cause misunderstanding.
comment The security proof for Key Policy Attribute Based Encryption
I'm not sure if that is the case, because what being played here is the Decisional BHD game between the challenger and the simulator. The simulator gets inputs from the challenger (gγ,gλ,gβ,h) and tries to outputs b=0 or b=1 depending if h=gγλβ. In order to do that, the simulator plays a game with the ABE adversary in the selective set model. Now for this being the game, and for the fact that *PolyUnSat*(T,A,gγ) was used by the simulator to generate the key for all T such that T(A)=0, I don't think that the simulator knows what γ is.