Efficient Proofs of Knowledge for Threshold Relations

Recently, there has been great interest towards constructing efficient zero-knowledge proofs for practical languages. In this work, we focus on proofs for threshold relations, in which the prover is required to prove knowledge of witnesses for k out of l statements. The main contribution of our work is an efficient and modular transformation that starting from a large class of Sigma-protocols and a corresponding threshold relation R-k,R-l, provides an efficient Sigma-protocol for R-k,R-l with improved communication complexity w.r.t. prior results. Our transformation preserves statistical/perfect honest-verifier zero knowledge.