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Download Concurrent Zero Knowledge: (with Additional Background by by Alon Rosen PDF

By Alon Rosen

Zero-knowledge proofs are attention-grabbing and very important constructs. Their interesting nature is because of their doubtless contradictory definition; zero-knowledge proofs are convincing and but yield not anything past the validity of the statement being proved. Their applicability within the area of cryptography is vast.A primary query concerning zero-knowledge protocols is whether or not their safeguard is preserved while many situations of the protocol are finished at the same time. the sensible value of this question, within the days of intensive web verbal exchange, turns out transparent. this query is usually fascinating from a theoretical perspective - as well as being hard from an algorithmic viewpoint, the learn of zero-knowledge within the concurrent environment has contributed vastly to our realizing of the concurrent safety of cryptographic protocols.Protocols that stay zero-knowledge while many cases are finished simultaneously are known as concurrent zero-knowledge, and this ebook is dedicated to their examine. The ebook offers structures of concurrent zero-knowledge protocols, besides proofs of safeguard. It additionally indicates why "traditional" facts innovations (i.e., black-box simulation) are usually not compatible for setting up the concurrent zero-knowledge estate of "message-efficient" protocols. The e-book gains introductory and concluding chapters on zero-knowledge by way of Oded Goldreich.

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Extra info for Concurrent Zero Knowledge: (with Additional Background by Oded Goldreich)

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M0k , M1k ). Reveal σ1 , . . , σk . Reveal Mσ11 , Mσ22 , . . , Mσkk . The verifier accepts if and only if for all j, the message Mσj is “valid”. By the hiding property of the commitment used in (v1), we are guaranteed that when sending (p1), the prover P has “no idea” about the values of σ1 , . . , σk , and so the soundness of the original protocol is preserved. To see that the resulting protocol is ZK, consider the following simulation technique. Start by obtaining the (v1) message from the verifier V ∗ .

We say that P, V is black-box concurrent zero-knowledge, if for every polynomial q(·), there exists a probabilistic polynomial-time algorithm Sq , so that for every concurrent adversary circuit V ∗ that runs at most q(|x|) concurrent sessions, Sq (x) runs in time polynomial in q(|x|) and |x|, and satisfies that the ensembles {viewPV ∗ (x)}x∈L ∗ and {SqV (x)}x∈L are computationally indistinguishable. 7 Conventions Used in Construction of Simulators Deviation Gap and Expected Polynomial-Time Simulators.

Intuitively, since in an actual execution of the protocol, the prover does not know the value of σ, the protocol constitutes a proof system for Hamiltonicity (with soundness error 2−n ). However, knowing the value of σ in advance allows the simulation of the protocol: whenever the simulator may cause the verifier 0 1 to reveal both σi,j and σi,j for some i, j (as in the RK protocol, this is done by rk,j r1,j , . . , σk,j have been the means of rewinding the verifier after the values σ1,j revealed), it can simulate the rest of the protocol (and specifically Stage 2) by adjusting the first message of the Hamiltonicity protocol according to the 0 1 value of σ = σi,j ⊕σi,j (which, as we said, is obtained before entering Stage 2).

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