In this paper, we will scrutinize the definition of ``black-box computational'' zero-knowledge, in which there exists one simulator \emph{for all} verifiers, the simulator has black-box access to the verifier, and the quality of simulation is such that the real and simulated views cannot be distinguished by polynomial tests (\emph{computational} indistinguishability).
Working in a theoretical model (the Random-Oracle Model), we show that the indistinguishability requirement is stated in a \emph{conceptually} inappropriate way: Present definitions allow the knowledge of the \emph{verifier} and \emph{distinguisher} to be independent, while the two entities are essentially coupled. Therefore, our main take on the problem will be \emph{conceptual} and \emph{semantic}, rather than \emph{literal}. We formalize the concept by introducing a ``knowledge extractor'' into the model, which tries to extract the extra knowledge hard-coded into the distinguisher (if any), and then helps the simulator to construct the view of the verifier. The new paradigm is termed \emph{Simulation-Extraction Paradigm}, as opposed to the previous \emph{Simulation Paradigm}. We also provide an important application of the new formalization: Using the simulation-extraction paradigm, we construct one-round (i.e. two-move) zero-knowledge protocols of proving ``the computational ability to invert some trapdoor permutation'' in the Random-Oracle Model. It is shown that the protocol cannot be proven zero-knowledge in the classical Simulation Paradigm. The proof of the zero-knowledge property in the new paradigm is interesting in that it does not require knowing the internal structure of the trapdoor permutation, or a polynomial-time reduction from it to another (e.g. an $\mathcal{NP}$-complete) problem.
Category / Keywords: Zero-Knowledge Proof, Proof of Computational Ability, Proof of Knowledge, Trapdoor One-Way Permutation, Random Oracle, Simulation Paradigm, Simulation-Extraction Paradigm Publication Info: --- Date: received 20 Mar 2010, last revised 5 Jun 2011 Contact author: dousti at ce sharif edu Available formats: PDF | BibTeX Citation Version: 20110605:195801 (All versions of this report) Discussion forum: Show discussion | Start new discussion