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Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption

  • Carmen Elisabetta Zaira Baltico
  • Dario Catalano
  • Dario Fiore
  • Romain Gay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10401)

Abstract

We present two practically efficient functional encryption schemes for a large class of quadratic functionalities. Specifically, our constructions enable the computation of so-called bilinear maps on encrypted vectors. This represents a practically relevant class of functions that includes, for instance, multivariate quadratic polynomials (over the integers). Our realizations work over asymmetric bilinear groups and are surprisingly efficient and easy to implement. For instance, in our most efficient scheme the public key and each ciphertext consist of \(2n+1\) and \(4n+2\) group elements respectively, where n is the dimension of the encrypted vectors, while secret keys are only two group elements. Our two schemes build on similar ideas, but develop them in a different way in order to achieve distinct goals. Our first scheme is proved (selectively) secure under standard assumptions, while our second construction is concretely more efficient and is proved (adaptively) secure in the generic group model.

As a byproduct of our functional encryption schemes, we show new predicate encryption schemes for degree-two polynomial evaluation, where ciphertexts consist of only O(n) group elements. This significantly improves the \(O(n^2)\) bound one would get from inner product encryption-based constructions.

Notes

Acknowledgements

The research of Dario Fiore is partially supported by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement 688722 (NEXTLEAP), the Spanish Ministry of Economy under project references TIN2015-70713-R (DEDETIS), RTC-2016-4930-7 (DataMantium), and under a Juan de la Cierva fellowship to Dario Fiore, and by the Madrid Regional Government under project N-Greens (ref. S2013/ICE-2731).

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Copyright information

© International Association for Cryptologic Research 2017

Authors and Affiliations

  • Carmen Elisabetta Zaira Baltico
    • 1
  • Dario Catalano
    • 1
  • Dario Fiore
    • 2
  • Romain Gay
    • 3
  1. 1.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly
  2. 2.IMDEA Software InstituteMadridSpain
  3. 3.Département d’informatique de l’ENS, École normale supérieure, CNRS, Inria, PSL Research UniversityParisFrance

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