Ring Signatures: Logarithmic Size, No Setup -- from Standard Assumptions

Ring signatures allow for creating signatures on behalf of an ad hoc group of signers, hiding the true identity of the signer among the group. A natural goal is to construct a ring signature scheme for which the signature size is short in the number of ring members. Moreover, such a construction should not rely on a trusted setup and be proven secure under falsifiable standard assumptions. Despite many years of research this question is still open. In this paper, we present the first construction of logarithmic-size ring signatures which do not rely on a trusted setup or the random oracle heuristic. Specifically, our scheme can be instantiated from standard assumptions and the size of signatures grows only logarithmically in the number of ring members. We also extend our techniques to the setting of linkable ring signatures, where signatures created using the same signing key can be linked