Abstract
Private functional encryption guarantees that not only the information in ciphertexts is hidden but also the circuits in decryption tokens are protected. A notable use case of this notion is query privacy in searchable encryption. Prior privacy models in the literature were fine-tuned for specific functionalities (namely, identity-based encryption and inner-product encryption), did not model correlations between ciphertexts and decryption tokens, or fell under strong uninstantiability results. We develop a new indistinguishability-based privacy notion that overcomes these limitations and give constructions supporting different circuit classes and meeting varying degrees of security. Obfuscation is a common building block that these constructions share, albeit the obfuscators necessary for each construction are based on different assumptions. In particular, we develop a composable and distributionally secure hyperplane membership obfuscator and use it to build an inner-product encryption scheme that achieves an unprecedented level of privacy, positively answering a question left open by Boneh, Raghunathan and Segev (ASIACRYPT 2013) concerning the extension and realization of enhanced security for schemes supporting this functionality.
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Notes
- 1.
We do not impose that \(\mathbf {C}_0(\mathsf {m}) = \mathbf {C}_1(\mathsf {m})\) within the \(\textsc {Func}\) oracle as this is exactly the event that \(\mathcal {P}\) is aiming to invoke to win the game. The restriction we do impose allows for a sampler to be unpredictable while possibility outputting low-entropy messages that might even differ on left and right.
- 2.
We limit samplers to ppt because in proving the security of our constructions, samplers are used to construct computational adversaries against other schemes. In general, one could consider unbounded samplers.
- 3.
When the restriction here is imposed on the \(\mathrm {IND}\text {-}\mathrm {CPA}\) model for point function, the resulting model remains as strong as the full \(\mathrm {IND}\text {-}\mathrm {CPA}\) model.
- 4.
Consider a sampler which does not output any circuits and simply returns (possibly low-entropy) messages included in the state \({st}\) passed to it. This sampler is trivially unpredictable. Furthermore, the legitimacy conditions in the two games exactly match.
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Acknowledgements
Afonso Arriaga was supported by the National Research Fund, Luxembourg (AFR Grant No. 5107187). Manuel Barbosa was funded by project “NanoSTIMA: Macro-to-Nano Human Sensing: Towards Integrated Multimodal Health Monitoring and Analytics/NORTE-01-0145-FEDER-000016”, which is financed by the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, and through the European Regional Development Fund (ERDF). Pooya Farshim was supported in part by grant ANR-14-CE28-0003 (Project EnBid).
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Arriaga, A., Barbosa, M., Farshim, P. (2016). Private Functional Encryption: Indistinguishability-Based Definitions and Constructions from Obfuscation. In: Dunkelman, O., Sanadhya, S. (eds) Progress in Cryptology – INDOCRYPT 2016. INDOCRYPT 2016. Lecture Notes in Computer Science(), vol 10095. Springer, Cham. https://doi.org/10.1007/978-3-319-49890-4_13
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