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Title:
Efficient Proofs of Knowledge for Threshold Relations
Authors: Gennaro Avitabile, Vincenzo Botta, Daniele Friolo, and Ivan Visconti
Abstract: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 \ell 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 \mathcal{R}_\mathsf{k,\ell}, provides an efficient \Sigma-protocol for \mathcal{R}_\mathsf{k,\ell} with improved communication complexity w.r.t. prior results. Moreover, our transformation preserves statistical/perfect honest-verifier zero knowledge.
ePrint: https://eprint.iacr.org/2022/746
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