(A) study on Zero-knowledge sharing and and its application to group-identification and signature

Abstract

Until now, ZKPS is the proof system that has only one prover. But ZKPS must be extended to multi-prover ZKPS for application of ZKPS to social-oriencted cryptosystem in which a group of prover is the unit of interaction and t($<$ total member of prover-group) members of the group cannot successfully run the proof system. In this paper, we extended such one-porver ZKPS to case of multi-provers and we called this proof system "ZKPS of knowledge sharing". We introduced "completeness of knowledge sharing" among multi-prover and polynomial-time algorithm "shared-computer" so that multi-prover proof system becomes zeroknowledge, efficient and interactive proof system. Our "ZKPS of knowledge sharing" can serve as social-oriented cryptographic tools in zero-knowledge fashion. Specially, group identification scheme and group signature scheme can be directly constructed from "ZKPS of knowledge sharing". Also, It can be extended to threshold ZKPS of knowledge (or secret) sharing and this extension can serve as a method for constructing threshold scheme in zero-knowledge fashion.