Efficient Set Membership Proofs using MPC-in-the-Head

Abstract Set membership proofs are an invaluable part of privacy preserving systems. These allow a prover to demonstrate knowledge witness w corresponding secret element x public set, such that they jointly satisfy given NP relation, i.e. ?( w, ) = 1 and is member set { , . ???? }. This allows the identity remain hidden, eg. ring signatures confidential transactions in cryptocurrencies. In this work, we develop new technique for efficiently adding logarithmic-sized any MPC-in-the-head based zero-knowledge protocol (Ishai et al. [STOC’07]). We integrate our into open source implementation state-of-the-art, post quantum secure Katz [CCS’18].We find using techniques construct results (based only on symmetric key primitives) between 5 10 times smaller than state-of-the-art same assumptions. also show can be used post-quantum RingCT from primitives.