Distributed Provers with Applications to Undeniable Signatures

This paper introduces distributed prover protocols. Such a protocol is a proof system in which a polynomially bounded prover is replaced by many provers each having partial information about the witness owned by the original prover. As an application of this concept, it is shown how the signer of undeniable signatures can distribute part of his secret key to n agents such that any k of these can verify a signature. This facility is useful in most applications of undeniable signatures, and as the proposed protocols are practical, the results in this paper makes undeniable signatures more useful. The first part of the paper describes a method for verifiable secret sharing, which allows non-interactive verification of the shares and is as secure as the Shamir secret sharing scheme in the proposed applications.