Fully Homomorphic Encryption (FHE) involves the ability to perform any computation on encrypted data without knowing the secret key. Attribute Based Encryption (ABE) provides fine-grained access control over data by allowing an entity to encrypt data with attributes which must be satisfied by a decryptor's access policy in order for decryption to succeed. A special case of ABE is identity-based encryption (IBE) where the access policies are simple equality relations.

A natural question is whether we can have both the functionality of ABE and the functionality of FHE in the same cryptographic primitive. In this talk we take a look at Attribute-Based Fully Homomorphic Encryption (ABFHE). We show that ABFHE is possible for all polynomial-time access policies by using indistinguishability obfuscation. We also obtain results for special cases such as Identity-Based FHE by relying on weaker assumptions such as Learning with Errors.

We also take a look at multi-key FHE, which is used in some constructions of ABFHE. We consider a construction of multi-key FHE from the Learning with Errors problem.