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

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