Paper 2016/018

Private Functional Encryption: Indistinguishability-Based Definitions and Constructions from Obfuscation

Afonso Arriaga, Manuel Barbosa, and Pooya Farshim

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. Our feasibility results go beyond previous constructions in a number of ways. In particular, a keyword search scheme that we base on point obfuscators tolerates arbitrary and possibly low-entropy correlations between encrypted data and queried keywords, even under (mildly restricted) adaptive token-extraction queries. Our more elaborate keyword search scheme achieves the strongest notion of privacy that we put forth (with no restrictions), but relies on stronger forms of obfuscation. We also develop a composable and distributionally secure inner-product obfuscator and use it to build an inner-product encryption scheme that achieves an unprecedented level of privacy. This, in particular, positively answers a question left open by Boneh, Raghunathan and Segev (ASIACRYPT 2013) concerning the extension and realization of enhanced security for hyperplane membership.