Alternative Variants of Zero-Knowledge Proofs by Rafael Pass PDF

By Rafael Pass

ISBN-10: 9172839333

ISBN-13: 9789172839335

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3-round special-sound public-coin honest-verifier perfect zero-knowledge proofs). – On the theoretical side, we construct a 2-round argument for N P that is straight-line concurrent black-box strict-npoly(logn) -simulatable2 , under the assumption that one-to-one one-way functions secure against subexponential circuits exists, and the existence of zaps [66] . 1 no longer hold in our relaxed setting. 3 More specifically, under cryptographic assumptions, we show that 2 rounds are necessary and sufficient for quasi-polynomial time simulatable arguments, while 3 rounds are necessary and sufficient for quasi-polynomial time simulatable proofs.

In fact, the proof of the sequential composition lemma for ZK of Goldreich and Oren [37] can be used unchanged. 44 CHAPTER 3. SIMULATABLE PROOFS Lemma 4 (Sequential Composition Lemma for Strong T (n)-Simulatability) Let T (n) be a class of functions that is closed under composition with any polynomial, and let (P, V ) be a strongly T (n)-simulatable interactive proof for the language L ∈ N P. Let Q(n) be a polynomial, and let (PQ , VQ ) be an interactive proof that on common input x ∈ {0, 1}n proceeds in Q(n) phases, each on them consisting of executing the interactive proof (P, V ) on common input x (each time with independent random coins).

Since most natural problems that we believe are hard (on the average) for polynomial time are also believed hard for quasi-polynomial time, this assumption seems rather mild. Definition extends to general protocol security Whereas the definition of witness indistinguishability only relates to interactive proofs (where there is a witness), the notion of T (·)-simulatability applies also to other definitions that rely on the simulation paradigm, such as for example the definition of secure computation.

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Alternative Variants of Zero-Knowledge Proofs by Rafael Pass

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