Statistical Zero-knowledge Arguments: Theory and Practice

During a statistical zero-knowledge argument, the arguer convinces the verifier on the truth of an assertment, without revealing next to nothing—but the truth of the assertment—even to an omnipotent verifier. The crucial part here is “next to nothing”: compared to perfect zero-knowledge arguments where absolutely nothing (but the truth of the assertment) can be revealed, statistical zero-knowledge arguments are often much more practical. In this presentation, we will survey some recent developments in this area. We will both touch the theoretical and practical aspects of statistical zero-knowledge, ending the survey with my recent results that connect Hilbert’s 10th problem to finding practical statistical zero-knowledge arguments.