Multi-Input Functional Encryption for Inner Products: Function-Hiding Realizations and Constructions Without Pairings
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We present new constructions of multi-input functional encryption (MIFE) schemes for the inner-product functionality that improve the state of the art solution of Abdalla et al. (Eurocrypt 2017) in two main directions.
First, we put forward a novel methodology to convert single-input functional encryption for inner products into multi-input schemes for the same functionality. Our transformation is surprisingly simple, general and efficient. In particular, it does not require pairings and it can be instantiated with all known single-input schemes. This leads to two main advances. First, we enlarge the set of assumptions this primitive can be based on, notably, obtaining new MIFEs for inner products from plain DDH, LWE, and Decisional Composite Residuosity. Second, we obtain the first MIFE schemes from standard assumptions where decryption works efficiently even for messages of super-polynomial size.
Our second main contribution is the first function-hiding MIFE scheme for inner products based on standard assumptions. To this end, we show how to extend the original, pairing-based, MIFE by Abdalla et al. in order to make it function hiding, thus obtaining a function-hiding MIFE from the MDDH assumption.
Michel Abdalla was supported in part by SAFEcrypto (H2020 ICT-644729) and by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement 780108 (FENTEC). Dario Fiore was partially supported by the Spanish Ministry of Economy under project references TIN2015-70713-R (DEDETIS), RTC-2016-4930-7 (DataMantium), and by the Madrid Regional Government under project N-Greens (ref. S2013/ICE-2731). Romain Gay was partially supported by a Google PhD Fellowship in Privacy and Security and by the ERC Project aSCEND (H2020 639554). Bogdan Ursu was partially supported by ANR-14-CE28-0003 (Project EnBiD) and by the ERC Project PREP-CRYPTO (H2020 724307).
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