Iftach Haitner

The question whether or not parallel repetition reduces the soundness error is a fundamental question in the theory of protocols. While parallel repetition reduces (at an exponential rate) the error in interactive proofs and (at a weak exponential rate) in special cases of interactive arguments (e.g., 3-message protocols - Bellare, ... more >>>

Kai-Min Chung, Feng-Hao Liu

Following Hastad, Pass, Pietrzak, and Wikstrom (2008), we study parallel repetition theorems for public-coin interactive arguments and their generalization. We obtain the following results:

1. We show that the reduction of Hastad et al. actually gives a tight direct product theorem for public-coin interactive arguments. That is, $n$-fold parallel repetition ... more >>>

Yael Tauman Kalai, Ran Raz, Ron Rothblum

We construct a 1-round delegation scheme (i.e., argument-system) for every language computable in time t=t(n), where the running time of the prover is poly(t) and the running time of the verifier is n*polylog(t). In particular, for every language in P we obtain a delegation scheme with almost linear time verification. ... more >>>

Noga Amit, Guy Rothblum

We study the following question: what cryptographic assumptions are needed for obtaining constant-round computationally-sound argument systems? We focus on argument systems with almost-linear verification time for subclasses of $\mathbf{P}$, such as depth-bounded computations.

Kilian's celebrated work [STOC 1992] provides such 4-message arguments for $\mathbf{P}$ (actually, for $\mathbf{NP}$) using collision-resistant hash ...
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