## Cryptology ePrint Archive: Report 2016/099

Attribute-Based Fully Homomorphic Encryption with a Bounded Number of Inputs

Michael Clear and Ciaran McGoldrick

Abstract: The only known way to achieve Attribute-based Fully Homomorphic Encryption (ABFHE) is through indistinguishability obfsucation. The best we can do at the moment without obfuscation is Attribute-Based Leveled FHE which allows circuits of an a priori bounded depth to be evaluated. This has been achieved from the Learning with Errors (LWE) assumption. However we know of no other way without obfuscation of constructing a scheme that can evaluate circuits of unbounded depth. In this paper, we present an ABFHE scheme that can evaluate circuits of unbounded depth but with one limitation: there is a bound N on the number of inputs that can be used in a circuit evaluation. The bound N could be thought of as a bound on the number of independent senders. Our scheme allows N to be exponentially large so we can set the parameters so that there is no limitation on the number of inputs in practice. Our construction relies on multi-key FHE and leveled ABFHE, both of which have been realized from LWE, and therefore we obtain a concrete scheme that is secure under LWE.

Category / Keywords: public-key cryptography / attribute based encryption, fully homomorphic encryption, LWE

Original Publication (in the same form): Africacrypt 2016