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This study introduces hidden identity-based signatures (Hidden-IBS), a type of digital signatures that provide mediated signer-anonymity on top of Shamir's identity-based signatures. The motivation of the new signature primitive is to resolve an important issue with the kind of anonymity offered by 'group signatures' where it is required that either the group membership list be public for opening signatures or that the opening authority be dependent on the group manager for its operation. Contrary to this, Hidden-IBS does not require the maintenance of a group membership list for opening signatures and they enable an opening authority that is totally independent of the group manager. As the authors argue this makes Hidden-IBS much more attractive than group signatures for a number of applications. In this study, the authors provide a formal model of Hidden-IBS as well as two efficient constructions that realise the new primitive. To demonstrate the power of the new primitive, the authors apply it to solve a problem of current onion-routing systems focusing on the Tor system in particular.