Paper 2018/742

Witness-Indistinguishable Arguments with $\Sigma$-Protocols for Bundled Witness Spaces and its Application to Global Identities

Hiroaki Anada and Seiko Arita


We propose a generic construction of a $\Sigma$-protocol of commit-and-prove type, which is an AND-composition of $\Sigma$-protocols on 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 $\Sigma$-protocols are of witness-indistinguishable argument systems, our $\Sigma$-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 give a syntax and security definitions of the scheme. Then we give a generic construction of the 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 in the setting of bilinear groups.

Note: Major modification has been added in the definition of security against concurrent and collusion attacks; corrupted authorities are considered there. The proof for the security has been re-written. The appendices have been detailed. Some notations have been corrected.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Major revision. The 2018 International Conference on Information and Communications Security (ICICS2018)
interactive proofsigma protocolwitness indistinguishabilitydecentralizedanonymitycollusion resistance
Contact author(s)
anada @ sun ac jp
2020-06-23: last of 6 revisions
2018-08-15: received
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      author = {Hiroaki Anada and Seiko Arita},
      title = {Witness-Indistinguishable Arguments with $\Sigma$-Protocols for Bundled Witness Spaces and its Application to Global Identities},
      howpublished = {Cryptology ePrint Archive, Paper 2018/742},
      year = {2018},
      note = {\url{}},
      url = {}
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