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May 31, 2018 at 5:30 comment added Yehuda Lindell The efficiency and inefficiency is an orthogonal issue. I explained why its not the hidden bits model, since the trapdoor is used in a different way. Regarding inefficiency, indeed, the hidden bits model is extremely inefficient in practice since all you can do is open bits and to get a reasonable NIZK from this you need an incredibly massive CRS.
May 30, 2018 at 15:13 vote accept Ginswich
May 30, 2018 at 15:13 comment added Ginswich I see. So, the inefficiency of the hidden-bits model is due to this need of revealing the chosen bits and the associated process (I'm following Proof of Theorem 1 in Katz's lecture notes, based on your response). In Groth-Sahai, there is no need to reveal these bits, and the trapdoor is used for simulation purposes (I'm almost guessing here, but that is another question...) Thanks, Professor!
May 30, 2018 at 14:35 history answered Yehuda Lindell CC BY-SA 4.0