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 Σ -protocols and a corresponding threshold relation Rk,ℓ, provides an efficient Σ -protocol for Rk,ℓ with improved communication complexity w.r.t. prior results. Our transformation preserves statistical/perfect honest-verifier zero knowledge