In the setting of Secure Multiparty Computation (MPC), n players jointly compute a function that takes n inputs where the i-th input is held by the i-th party such that by the end of the execution, nothing is revealed of the local inputs beyond the function output. Some of the seminal works in MPC such as the GMW protocol (by Goldreich, Micali and Wigderson) make use of Zero Knowledge Proofs (ZKP), which allow a prover to convince a verifier of the truth of a statement in such a manner that the proof reveals nothing beyond the validity of the statement.
In their work, Ishai, Kushilevitz, Ostrovsky and Sahai described how to construct Zero Knowledge Proofs for languages in NP from MPC protocols. This work is of particular interest because it kickstarted the 'MPC in the head' paradigm, which was subsequently used to obtain a host of round-optimal black-box constructions. In this talk, we will see constructions of ZKPs from MPC, and if time permits, we will see certain applications obtained by instantiating the MPC protocols in the constructions.
Reference: https://web.cs.ucla.edu/~rafail/PUBLIC/77.pdf
