Attribute-based fully homomorphic encryption with a bounded number of inputs (Q1626137)

Summary: 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.