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I want to prove security of my system by reduction to the security of an underlying non-interactive proof system for proving knowledge. I know a game that captures the desired security property of my system, and I want to reduce to an adversary's inability to produce a non-interactive proof without a witness (since possession of the witness suffices to win the aforementioned game), which games capture suitable properties of non-interactive proof systems?

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  • $\begingroup$ Are you assuming that your underlying non-interactive proof system is zero-knowledge (NIZK)? If yes, then I think it would not be possible to do the reduction since this would mean that there exists a simulator which can produce the proof without having the witness! $\endgroup$ – Hamidreza Jul 9 at 8:42
  • $\begingroup$ @Hamidreza Any suggestion as to what reduction should be used in such cases? $\endgroup$ – user2768 Jul 9 at 13:28
  • $\begingroup$ Sorry, I don't understand what you mean?! my understanding is that in NIZK proofs, we assume the existence of a simulator which can simulate the proof without having the witness (i.e., by having the simulation trapdoor). This equivalently means that the lack of witness is not sufficient to claim an adversary's inability to produce the proof! $\endgroup$ – Hamidreza Jul 9 at 15:44
  • $\begingroup$ @Hamidreza I understand your point, a simulator...can simulate the proof without having the witness. I'm trying to understand what the OP could do. If they can't reduce to [the] adversary's inability to produce a non-interactive proof without a witness (because of the simulator), then what can they reduce to? $\endgroup$ – user2768 Jul 10 at 9:49

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