Group Signatures: Unconditional Security for Members

Abstract

First a detailed definition of group signatures, originally suggested by Chaum and van {Heijst}, is given. Such signatures allow members of a group to sign messages anonymously on behalf of the group subject to the constraint that, in case of disputes later on, a designated authority can identify the signer. It is shown that if such schemes are to provide information theoretic anonymity, then the length of the secret information of the members and the authority increases with the number of members and the number of signatures each member is allowed to make. A dynamic scheme meeting these lower bounds is described. Unlike previous suggestions it protects each member unconditionally against framing, i.e.\ being held responsible for a signature made by someone else.