Efficient Threshold Zero-Knowledge with Applications to User-Centric Protocols
In this paper, the authors investigate on threshold proofs, a framework for distributing the prover's side of interactive proofs of knowledge over multiple parties. Interactive Proofs of Knowledge (PoK) are widely used primitives of cryptographic protocols, including important user-centric protocols, such as identification schemes, electronic cash (e-cash), and anonymous credentials. They present a security model for threshold proofs of knowledge and develop threshold versions of well-known primitives such as range proofs, zero-knowledge proofs for preimages of homomorphisms (which generalizes PoKs of discrete logarithms, representations, p-th roots, etc.), as well as OR statements. These building blocks are proven secure in their model.