We introduce the notion of Cross-Unlinkability for group signature schemes. Considering groups organized in a tree structure, where belonging to the parent group is required to join a new group, Cross-Unlinkability enables a cascade revocation process that takes into account the underlying tree structure, while ensuring anonymity for non-revoked users, in particular, towards the managers of the other groups. We show how to achieve Cross-Unlinkability using the Verifier-Local Revocation group signature scheme of Bringer and Patey at Secrypt 2012, by exploiting its property of Backward Unlinkability.
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