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 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.
M. Clear—The author’s work is funded by the Irish Research Council EMBARK Initiative.
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Notes
- 1.
for the specific case of parameters N and \(\lambda \).
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Clear, M., McGoldrick, C. (2016). Attribute-Based Fully Homomorphic Encryption with a Bounded Number of Inputs. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2016. AFRICACRYPT 2016. Lecture Notes in Computer Science(), vol 9646. Springer, Cham. https://doi.org/10.1007/978-3-319-31517-1_16
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DOI: https://doi.org/10.1007/978-3-319-31517-1_16
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