Homomorphic Encryption with Access Policies: Characterization and New Constructions
This work addresses the challenge of combining homomorphic encryption with access control for secure data processing, but it is incremental as it builds on existing predicate encryption and IBE constructions.
The paper tackles the problem of constructing homomorphic encryption schemes with access policies, specifically presenting an XOR-homomorphic identity-based encryption scheme based on the quadratic residuosity problem, which is shown to be strongly homomorphic, though an anonymous variant was not achieved for this property.
A characterization of predicate encryption (PE) with support for homomorphic operations is presented and we describe the homomorphic properties of some existing PE constructions. Even for the special case of IBE, there are few known group-homomorphic cryptosystems. Our main construction is an XOR-homomorphic IBE scheme based on the quadratic residuosity problem (variant of the Cocks' scheme), which we show to be strongly homomorphic. We were unable to construct an anonymous variant that preserves this homomorphic property, but we achieved anonymity for a weaker notion of homomorphic encryption, which we call \emph{non-universal}. A related security notion for this weaker primitive is formalized. Finally, some potential applications and open problems are considered.