Recently, Gentry and others have established the feasibility of constructing fully homomorphic encryption schemes. Briefly, a fully homomorphic encryption (FHE) scheme is one that allows a third-party who has ciphertexts of several messages to construct---without knowing the decryption key---a new ciphertext that corresponds to an arbitrary efficiently computable function applied to the original messages. Fully homomorphic encryption has the potential to allow disparate organizations to compute basic functions on their pooled data-sets without revealing such data to each other. It is thus an ultimate solution for implementing ``need-to-know'' privacy.
Until Gentry's discovery, few researchers believed that FHE could be constructed. As a result, the concept has not been well-studied despite its clear potential to solve important tasks in a privacy-preserving manner. In particular, the basic relationship between FHE and traditional public-key cryptography remains unclear. The goals of this research project are to formalize this relationship, to build notions of FHE that satisfy stronger security guarantees such as security even when the adversary has access to a restricted decryption oracle, and to potentially use these stronger security guarantees to apply FHE in secure and privacy preserving computation.
To ensure the broader impact of the research, this project includes mentoring of students at all levels from undergraduate to post-doctoral and outreach activities to traditionally under-represented students and K-12 students. Research from this project will be disseminated through presentations and publications in conferences, journals and on the Internet.
