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Efficient Function-Hiding Functional Encryption: From Inner-Products to Orthogonality

  • Manuel Barbosa
  • Dario Catalano
  • Azam SoleimanianEmail author
  • Bogdan Warinschi
Conference paper
First Online:
  • 554 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11405)

Abstract

We construct functional encryption (FE) schemes for the orthogonality (OFE) relation where each ciphertext encrypts some vector \(\varvec{\mathsf {x}}\) and each decryption key, associated to some vector \(\varvec{\mathsf {y}}\), allows to determine if \(\varvec{\mathsf {x}}\) is orthogonal to \(\varvec{\mathsf {y}}\) or not. Motivated by compelling applications, we aim at schemes which are function hidding, i.e. \(\varvec{\mathsf {y}}\) is not leaked.

Our main contribution are two such schemes, both rooted in existing constructions of FE for inner products (IPFE), i.e., where decryption keys reveal the inner product of \(\varvec{\mathsf {x}}\) and \(\varvec{\mathsf {y}}\). The first construction builds upon the very efficient IPFE by Kim et al. (SCN 2018) but just like the original scheme its security holds in the generic group model (GGM). The second scheme builds on recent developments in the construction of efficient IPFE schemes in the standard model and extends the work of Wee (TCC 2017) in leveraging these results for the construction of FE for Boolean functions. Conceptually, both our constructions can be seen as further evidence that shutting down leakage from inner product values to only a single bit for the orthogonality relation can be done with little overhead, not only in the GGM, but also in the standard model.

We discuss potential applications of our constructions to secure databases and provide efficiency benchmarks. Our implementation shows that the first scheme is extremely fast and ready to be deployed in practical applications.

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Notes

Acknowledgements

This work was supported in part by Royal Society grant for international collaboration and by the European Union Horizon 2020 Research and Innovation Programme under grant agreement 780108 (FENTEC). The first author is financed by Project NanoSTIMA (NORTE-01-0145-FEDER-000016) through the North Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement and the ERDF.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Manuel Barbosa
    • 1
  • Dario Catalano
    • 2
  • Azam Soleimanian
    • 3
    • 4
    Email author
  • Bogdan Warinschi
    • 5
  1. 1.INESC TEC and FCUPPortoPortugal
  2. 2.Università di CataniaCataniaItaly
  3. 3.Kharazmi UniversityTehranIran
  4. 4.École Normale SupérieureParisFrance
  5. 5.University of BristolBristolUK

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