By Rafael Pass
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Additional info for Alternative Variants of Zero-Knowledge Proofs
On a high-level, the intuition behind, and the structure of, our 2-round protocol is similar to that of . However, since the security definitions are quite different, the techniques used to instantiate the intuition behind the protocol, are very different. Indeed, the results of Dwork and Stockmeyer are quite limited in the setting where the prover’s running time is bounded, while we are able to prove security under standard type assumptions. We note, however, that this is due to the fact that the definition used in  is more restrictive than ours.
Then (PQ , VQ ) is a T (n)-simulatable interactive proof. Proof: We start by noting that it follows directly from the construction that (PQ , VQ ) is both sound and complete. Let us therefore turn to the T (n)-simulatability property. On a high level the proof follows the structure of the sequential composition lemma for ZK proofs of Goldreich and Oren . We start by “partitioning” the malicious verifier VQ∗ into Q(n) phases, each of which is the execution of a verifier for a “stand-alone” interactive proof (P, V ), called V ∗ .
Furthermore, whereas the notion of WI is only defined for N P-languages, our simulation-based characterization of WI can also be applied to languages outside of N P. • We show the robustness of the notion of T (n)-simulatability by demonstrating a sequential composition lemma. • We identify a certain class of T (n)-simulatable protocols that can be used in advanced composition operations. The power of such protocols is demonstrated in a composition theorem. , concurrent T (n)-simulatability without the use of rewinding) is a sufficient requirement for a general type of asynchronous protocol composition.
Alternative Variants of Zero-Knowledge Proofs by Rafael Pass