Access Control Encryption for Equality, Comparison, and More.

Access Control Encryption ACE is a novel paradigm for encryption which allows to control not only what users in the system are allowed to read but also what they are allowed to write. The original work of Damgård et al.﾿[DHO16] introducing this notion left several open questions, in particular whether it is possible to construct ACE schemes with polylogarithmic complexity in the number of possible identities in the system from standard cryptographic assumptions. In this work we answer the question in the affirmative by giving efficient constructions of ACE for an interesting class of predicates which includes equality, comparison, interval membership, and more. We instantiate our constructions based both on standard pairing assumptions SXDH or more efficiently in the generic group model.