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We present a general parallel-repetition theorem with an efficient reduction. As a corollary of this theorem we establish that parallel repetition reduces the soundness error at an exponential rate in any public-coin argument, and more generally, any argument where the verifier’s messages, but not necessarily its decision to accept or reject, can be efficiently simulated with noticeable probability.
We study efficient parallel repetition theorems for several classes of interactive arguments and obtain the following results: 1 We show a tight parallel repetition theorem for public-coin interactive arguments by giving a tight analysis for a reduction algorithm of Håstad et al. [HPPW08]. That is, n-fold parallel repetition decreases the soundness error from δ to δ...
We consider weakly-verifiable puzzles which are challenge-response puzzles such that the responder may not be able to verify for itself whether it answered the challenge correctly. We consider k-wise direct product of such puzzles, where now the responder has to solve k puzzles chosen independently in parallel. Canetti et al have earlier shown that such direct product puzzles have a hardness which...
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