Witness-indistinguishable arguments with Σ-Protocols for bundled witness spaces and its application to global identities

Abstract

We propose a generic construction of a Σ-protocol of commit-and-prove type, which is an and-composition of Σ-protocols on the statements that include a common commitment. Our protocol enables a prover to convince a verifier that the prover knows a bundle of witnesses that have a common component which we call a base witness point. When the component Σ-protocols are of witness-indistinguishable argument systems, our Σ-protocol is also a witness-indistinguishable argument system as a whole. As an application, we propose a decentralized multi-authority anonymous authentication scheme. We first define a syntax and security notions of the scheme. Then we give a generic construction of a decentralized multi-authority anonymous authentication scheme. There a witness is a bundle of witnesses each of which decomposes into a common global identity string and a digital signature on it. We mention an instantiation of the generic scheme in the setting of bilinear groups.