Title: Attribute-based fully homomorphic encryption with a bounded number of inputs

Authors: Michael Clear; Ciarán Mc Goldrick

Addresses: Computer Science Department, Georgetown University, USA; Computer Science Department, George Mason University, USA ' School of Computer Science and Statistics, Trinity College, Dublin, Ireland

Abstract: 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.

Keywords: attribute-based encryption; ABE; fully homomorphic encryption; FHE.

DOI: 10.1504/IJACT.2017.089356

International Journal of Applied Cryptography, 2017 Vol.3 No.4, pp.363 - 376

Received: 23 Feb 2017
Accepted: 29 Mar 2017

Published online: 21 Jan 2018 *

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