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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.
Syllabus
How to Share an NP Statement or Combiners for Zero-Knowledge Proofs
Taught by
Simons Institute