Labeled Homomorphic Encryption

Scalable and Privacy-Preserving Processing of Outsourced Data
  • Manuel Barbosa
  • Dario CatalanoEmail author
  • Dario Fiore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10492)


In privacy-preserving processing of outsourced data a Cloud server stores data provided by one or multiple data providers and then is asked to compute several functions over it. We propose an efficient methodology that solves this problem with the guarantee that a honest-but-curious Cloud learns no information about the data and the receiver learns nothing more than the results. Our main contribution is the proposal and efficient instantiation of a new cryptographic primitive called Labeled Homomorphic Encryption (labHE). The fundamental insight underlying this new primitive is that homomorphic computation can be significantly accelerated whenever the program that is being computed over the encrypted data is known to the decrypter and is not secret—previous approaches to homomorphic encryption do not allow for such a trade-off. Our realization and implementation of labHE targets computations that can be described by degree-two multivariate polynomials. As an application, we consider privacy preserving Genetic Association Studies (GAS), which require computing risk estimates from features in the human genome. Our approach allows performing GAS efficiently, non interactively and without compromising neither the privacy of patients nor potential intellectual property of test laboratories.



The work of Dario Fiore was 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). 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).


  1. 1.
    Barbosa, M., Catalano, D., Fiore, D.: Labeled homomorphic encryption: scalable and privacy-preserving processing of outsourced data. IACR Cryptol. ePrint Arch. 2017, 326 (2017)Google Scholar
  2. 2.
    Barman, L., Elgraini, M.T., Raisaro, J.L., Hubaux, J., Ayday, E.: Privacy threats and practical solutions for genetic risk tests. In: 2015 IEEE Symposium on Security and Privacy Workshops, SPW 2015, pp. 27–31. IEEE (2015)Google Scholar
  3. 3.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88313-5_13 CrossRefGoogle Scholar
  4. 4.
    Bresson, E., Catalano, D., Pointcheval, D.: A simple public-key cryptosystem with a double trapdoor decryption mechanism and its applications. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 37–54. Springer, Heidelberg (2003). doi: 10.1007/978-3-540-40061-5_3 CrossRefGoogle Scholar
  5. 5.
    Catalano, D., Fiore, D.: Practical homomorphic MACs for arithmetic circuits. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 336–352. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38348-9_21 CrossRefGoogle Scholar
  6. 6.
    Catalano, D., Fiore, D.: Using linearly-homomorphic encryption to evaluate degree-2 functions on encrypted data. In: ACM CCS 2015–22nd ACM Conference on Computer and Communication Security, pp. 1518–1529 (2015)Google Scholar
  7. 7.
    Catalano, D., Fiore, D., Warinschi, B.: Homomorphic signatures with efficient verification for polynomial functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 371–389. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44371-2_21 CrossRefGoogle Scholar
  8. 8.
    Costache, A., Smart, N.P., Vivek, S., Waller, A.: Fixed point arithmetic in SHE scheme. IACR Cryptol. ePrint Arch. 2016, 250 (2016)zbMATHGoogle Scholar
  9. 9.
    Covolo, L., Rubinelli, S., Ceretti, E., Gelatti, U.: Internet-based direct-to-consumer genetic testing: a systematic review. J. Med. Internet Res. 17(12), e279 (2015)CrossRefGoogle Scholar
  10. 10.
    Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – Or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40203-6_1 CrossRefGoogle Scholar
  11. 11.
    Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32009-5_38 CrossRefGoogle Scholar
  12. 12.
    Danezis, G., Cristofaro, E.D.: Fast and private genomic testing for disease susceptibility. In: Privacy in the Electronic Society, WPES 2014, pp. 31–34. ACM (2014)Google Scholar
  13. 13.
    Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive, Report 2012/144 (2012).
  14. 14.
    Fiore, D., Gennaro, R., Pastro, V.: Efficiently verifiable computation on encrypted data. In: ACM CCS 14, pp. 844–855. ACM Press (2014)Google Scholar
  15. 15.
    Gennaro, R., Wichs, D.: Fully homomorphic message authenticators. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 301–320. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-42045-0_16 CrossRefGoogle Scholar
  16. 16.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: 41st ACM STOC, pp. 169–178. ACM Press (2009)Google Scholar
  17. 17.
    S. Goldwasser and S. Micali. Probabilistic encryption & how to play mental poker keeping secret all partial information. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, STOC ’82, pp. 365–377, 1982. ACMGoogle Scholar
  18. 18.
    Halevi, S., Shoup, V.: Helib.
  19. 19.
    Johnson, A.D., Bhimavarapu, A., Benjamin, E.J., Fox, C., Levy, D., Jarvik, G.P., O’Donnell, C.J.: CLIA-tested genetic variants on commercial SNP arrays: potential for incidental findings in genome-wide association studies. Genet. Med.: Off. J. Am. Coll. Med. Genet. 12(6), 355–363 (2010)CrossRefGoogle Scholar
  20. 20.
    Joye, M., Libert, B.: Efficient cryptosystems from 2k-th power residue symbols. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 76–92. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38348-9_5 CrossRefGoogle Scholar
  21. 21.
    Karvelas, N.P., Peter, A., Katzenbeisser, S., Tews, E., Hamacher, K.: Privacy-preserving whole genome sequence processing through proxy-aided ORAM. In: Privacy in the Electronic Society, WPES 2014, pp. 1–10. ACM (2014)Google Scholar
  22. 22.
    Kessler, T., Vilne, B., Schunkert, H.: The impact of genome-wide association studies on the pathophysiology and therapy of cardiovascular disease. EMBO Mol. Med. 8(7), 688–701 (2016)CrossRefGoogle Scholar
  23. 23.
    Madsen, B.E., Browning, S.R.: A groupwise association test for rare mutations using a weighted sum statistic. PLoS Genet. 5(2), 1–11 (2009)CrossRefGoogle Scholar
  24. 24.
    Nathan Dowlin, J.W., Gilad-Bachrach, R.: Manual for using homomorphic encryption for bioinformatics. Technical report, November 2015Google Scholar
  25. 25.
    Paillier, P.: Public-Key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). doi: 10.1007/3-540-48910-X_16 CrossRefGoogle Scholar
  26. 26.
    Parno, B., Howell, J., Gentry, C., Raykova, M.: Pinocchio: nearly practical verifiable computation. In: 2013 IEEE Symposium on Security and Privacy, pp. 238–252. IEEE (2013)Google Scholar
  27. 27.
    Rivest, R.L., Adleman, L., Dertouzos, M.L.: On Data Banks and Privacy Homomorphisms. Foundations of Secure Computation. Academia Press, Ghent (1978)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.INESC TEC and FCUPPortoPortugal
  2. 2.University of CataniaCataniaItaly
  3. 3.IMDEA Software Institute MadridMadridSpain

Personalised recommendations