Group homomorphic encryption and beyond

Homomorphic encryption is a method of maintaining confidentiality of data while still allowing it to be processed. By providing an encryption function defined over a suitable algebraic structure, such as a group, ciphertexts can be combined using the alge braic operation. The resulting combined ciphertext has predictable structure in terms of a combination of the plaintexts of the input ciphertexts. This allows outsourcing computation on the data to third parties without the need to reveal its content. Thi s property has resulted in homomorphic encryption lying at the heart of several important applications, such as electronic voting, private information retrieval, outsourcing computations, or multiparty computation. The overall aim of this project is to e xplore the fundamental structure of homomorphic encryption in the context of: the range of homomorphic properties; the efficiency of the algorithms; and the practical applications of homomorphic encryption. Building on previous work by the project team, t he focus will be on extending the results on group homomorphic encryption to (i) symmetric key homomorphic encryption schemes and (ii) homomorphic encryption schemes that only indirectly use the algebraic structure of the plaintext and ciphertext spaces, e.g., current fully homomorphic encryption schemes. The aims of this research are to: 1. explore the fundamental properties of homomorphic encryption related to algebraic structure; 2. consider how existing homomorphic encryption schemes can be capture s within a generic framework; 3. design better solutions for practical homomorphic encryption; and 4. analyse applications of homomorphic encryption in higher level cryptographic protocols.