Public-Coin Parallel Zero-Knowledge for NP

Zero - Knowledge for NP

The type of indistinguishability in the zero-knowledge condition can either be statistical (i.e., s ≈) or computational (i.e., c ≈). We also say that the proof system is efficient if the prover’s strategy can be implemented by a randomized algorithm P (x,w) that runs in time polynomial in the length of its first argument, and any x ∈ L has a “hint” (or witness) w for which P functions as it sho...

On the Composition of Public-Coin Zero-Knowledge Protocols

We show that only languages in BPP have public-coin black-box zero-knowledge protocols that are secure under an unbounded (polynomial) number of parallel repetitions. This result holds both in the plain model (without any set-up) and in the Bare Public-Key Model (where the prover and the verifier have registered public keys). We complement this result by constructing a public-coin black-box zer...

Public-Coin Concurrent Zero-Knowledge in the Global Hash Model

Public-coin zero-knowledge and concurrent zero-knowledge (cZK) are two classes of zero knowledge protocols that guarantee some additional desirable properties. Still, to this date no protocol is known that is both public-coin and cZK for a language outside BPP. Furthermore, it is known that no such protocol can be black-box ZK [Pass et.al,

Concurrent Zero-Knowledge Proofs for NP

Perfect Non-interactive Zero Knowledge for NP

Non-interactive zero-knowledge (NIZK) systems are fundamental cryptographic primitives used in many constructions, including CCA2-secure cryptosystems, digital signatures, and various cryptographic protocols. What makes them especially attractive, is that they work equally well in a concurrent setting, which is notoriously hard for interactive zero-knowledge protocols. However, while for intera...