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Learn about secret-sharing of NP statements (NPSS) and their applications in zero-knowledge proofs through this conference talk that presents the first information-theoretic construction of NPSS for arbitrary threshold values. Explore how a t-out-of-n secret sharing scheme maps circuit-SAT instances into multiple instances while maintaining privacy guarantees, where any collection of t-1 partial assignments reveals no information about the witness, yet t assignments can efficiently reconstruct a satisfying assignment. Discover the novel secure multiparty computation protocols underlying these constructions and examine their applications in zero-knowledge proofs and secure computation. Delve into leakage-resilient NPSS constructions that enable NIZK amplifiers, addressing open questions in the field, with insights from collaborative research with Eliran Kachlon presented at the Simons Institute's Secure Computation program.
