Attribute-based fully homomorphic encryption with a bounded number of inputs
Michael Clear, Ciarán McGoldrick · International Journal of Applied Cryptography · 2017
The only known way to achieve attribute-based fully homomorphic encryption (ABFHE) is through indistinguishability obfuscation. The best we can do at the moment without obfuscation is attribute-based levelled 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 levelled ABFHE, both of which have been realised from LWE, and therefore we obtain a concrete scheme that is secure under LWE.