On Doubly-Efficient Interactive Proof Systems
نویسنده
چکیده
An interactive proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier’s strategy can be implemented in almost-linear-time. Such proof systems, introduced by Goldwasser, Kalai, and Rothblum (JACM, 2015), make the benefits of interactive proof system available to real-life agents who are restricted to polynomial-time computation. We survey the main two constructions of doubly-efficient interactive proof system: the system for sets having (uniform) bounded-depth circuits (due to Goldwasser, Kalai and Rothblum (JACM, 2015)), and the system for sets that are recognized in polynomial-time and small space (due to Reingold, Rothblum, and Rothblum (STOC, 2016)). Our presentation of the first construction is quite complete (except for some technical details), but for the second construction we only provide an overview. In addition, we present simpler constructions of doubly-efficient interactive proof system for “locally characterizable” sets like t-no-CLIQUE (due to Goldreich and Rothblum (ECCC, 2017)).
منابع مشابه
Overview of the doubly-efficient interactive proof systems of RRR
We provide an overview of the doubly-efficient interactive proof systems of Reingold, Rothblum, and Rothblum (STOC, 2016). Recall that by their result, any set that is decidable in polynomial-time by an algorithm of space complexity s(n) ≤ n, has a constant-round interactive proof system in which the prover runs polynomial time and the verifier runs in time Õ(n).
متن کاملOn the doubly-efficient interactive proof systems of GKR
We present a somewhat simpler variant of the doubly-efficient interactive proof systems of Goldwasser, Kalai, and Rothblum (JACM, 2015). Recall that these proof systems apply to logspace uniform sets in NC (or, more generally, to inputs that are acceptable by log-space uniform bounded-depth circuits, where the number of rounds in the proof system is linearly related to the depth of the circuit)...
متن کاملSimple Doubly-Efficient Interactive Proof Systems for Locally-Characterizable Sets
A proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier’s strategy can be implemented in almost-linear-time. We present direct constructions of doubly-efficient interactive proof systems for problems in P that are believed to have relatively high complexity. Specifically, such constructions are presented for t-CLIQUE and...
متن کاملCertifying Trapdoor Permutations, Revisited
The modeling of trapdoor permutations has evolved over the years. Indeed, finding an appropriate abstraction that bridges between the existing candidate constructions and the needs of applications has proved to be challenging. In particular, the notions of certifying permutations (Bellare and Yung, 96), enhanced and doubly enhanced trapdoor permutations (Goldreich, 04, 08, 11, Goldreich and Rot...
متن کاملGuiding Program Development Systems by a Connection Based Proof Strategy
We present an automated proof method for constructive logic based on Wallen’s matrix characterization for intuitionistic validity. The proof search strategy extends Bibel’s connection method for classical predicate logic. It generates a matrix proof which will then be transformed into a proof within a standard sequent calculus. Thus we can use an efficient proof method to guide the development ...
متن کامل