Compressing Proofs of k-Out-Of-n Partial Knowledge

Abstract

In a proof of partial knowledge, introduced by Cramer, Damgard and Schoenmakers (CRYPTO 1994), a prover knowing witnesses for some k-subset of n given public statements can convince the verifier of this claim without revealing which k-subset. Their solution combines \(\varSigma \)-protocol theory and linear secret sharing, and achieves linear communication complexity for general k, n. Especially the “one-out-of-n” case \(k=1\) has seen myriad applications during the last decades, e.g., in electronic voting, ring signatures, and confidential transaction systems.