Homomorphic Encryption with Access Policies: Characterization and New Constructions

TL;DR

This paper characterizes predicate encryption with homomorphic properties, introduces a new XOR-homomorphic IBE scheme based on quadratic residuosity, and discusses its security, anonymity, and potential applications.

Contribution

It provides a formal characterization of homomorphic predicate encryption and presents a novel XOR-homomorphic IBE scheme with security and anonymity considerations.

Findings

The XOR-homomorphic IBE scheme is strongly homomorphic.

Anonymity is achieved for a weaker, non-universal homomorphic encryption.

The paper discusses potential applications and open problems in homomorphic encryption.

Abstract

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.