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 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.
CITATION STYLE
Clear, M., & McGoldrick, C. (2016). Attribute-based fully homomorphic encryption with a bounded number of inputs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9646, pp. 307–324). Springer Verlag. https://doi.org/10.1007/978-3-319-31517-1_16
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