Advertisement

A Roadmap to Fully Homomorphic Elections: Stronger Security, Better Verifiability

  • Kristian Gjøsteen
  • Martin StrandEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10323)

Abstract

After the trials of remote internet voting for local elections in 2011 and parliamentary elections in 2013, a number of local referendums has renewed interest in internet voting in Norway.

The voting scheme used in Norway is not quantum-safe and it has limited voter verifiability. In this case study, we consider how we can use fully homomorphic encryption to construct a quantum-safe voting scheme with better voter verifiability.

While fully homomorphic cryptosystems are not efficient enough for the system we sketch to be implemented and run today, we expect future improvements in fully homomorphic encryption which may eventually make these techniques practical.

Keywords

Fully homomorphic encryption Remote internet voting Quantum-safe 

Notes

Acknowledgements

The authors wish to thank the anonymous reviewers for constructive and useful suggestions.

References

  1. 1.
    Armknecht, F., Boyd, C., Carr, C., Gjøsteen, K., Jäschke, A., Reuter, C.A., Strand, M.: A guide to fully homomorphic encryption. Cryptology ePrint Archive, Report 2015/1192 (2015). http://eprint.iacr.org/
  2. 2.
    Baum, C., Damgård, I., Toft, T., Zakarias, R.: Better preprocessing for secure multiparty computation. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 327–345. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-39555-5_18 Google Scholar
  3. 3.
    Baum, C., Damgård, I., Oechsner, S., Peikert, C.: Efficient commitments and zero-knowledge protocols from ring-sis with applications to lattice-based threshold cryptosystems. Cryptology ePrint Archive, Report 2016/997 (2016). http://eprint.iacr.org/2016/997
  4. 4.
    Benaloh, J., Moran, T., Naish, L., Ramchen, K., Teague, V.: Shuffle-sum: coercion-resistant verifiable tallying for STV voting. IEEE Trans. Inf. Forensics Secur. 4(4), 685–698 (2009)CrossRefGoogle Scholar
  5. 5.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 18, p. 111 (2011)Google Scholar
  6. 6.
    Cetin, G.S., Doroz, Y., Sunar, B., Martin, W.J.: Arithmetic using word-wise homomorphic encryption. Cryptology ePrint Archive, Report 2015/1195 (2015). http://eprint.iacr.org/2015/1195
  7. 7.
    Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-48071-4_7 CrossRefGoogle Scholar
  8. 8.
    Chillotti, I., Gama, N., Georgieva, M., Izabachène, M.: A homomorphic LWE based E-voting scheme. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 245–265. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-29360-8_16 CrossRefGoogle Scholar
  9. 9.
    Chung, H.W., Kim, M.: Encoding rational numbers for FHE-based applications. Cryptology ePrint Archive, Report 2016/344 (2016). http://eprint.iacr.org/
  10. 10.
    Dowlin, N., Gilad-Bachrach, R., Laine, K., Lauter, K., Naehrig, M., Wernsing, J.: Cryptonets: applying neural networks to encrypted data with high throughput and accuracy. Technical report, Microsoft Research (2016)Google Scholar
  11. 11.
    Emmadi, N., Gauravaram, P., Narumanchi, H., Syed, H.: Updates on sorting of fully homomorphic encrypted data. Cryptology ePrint Archive, Report 2015/995 (2015). http://eprint.iacr.org/
  12. 12.
    Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009). http://crypto.stanford.edu/craig
  13. 13.
    Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850–867. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_49 CrossRefGoogle Scholar
  14. 14.
    Gjøsteen, K.: The Norwegian internet voting protocol. Cryptology ePrint Archive, Report 2013/473 (2013). http://eprint.iacr.org/
  15. 15.
    Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 554–571. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_31 CrossRefGoogle Scholar
  16. 16.
    Halevi, S., Shoup, V.: Bootstrapping for HElib. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 641–670. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46800-5_25 Google Scholar
  17. 17.
    Kim, M., Lee, H.T., Ling, S., Wang, H.: On the efficiency of FHE-based private queries. IEEE Trans. Dependable Secur. Comput. PP(99) (2016)Google Scholar
  18. 18.
    Lauter, K.: Practical applications of homomorphic encryption (2015)Google Scholar
  19. 19.
    Naehrig, M., Lauter, K.E., Vaikuntanathan, V.: Can homomorphic encryption be practical? In: Cachin, C., Ristenpart, T. (eds.) Proceedings of the 3rd ACM Cloud Computing Security Workshop, CCSW, pp. 113–124. ACM (2011)Google Scholar
  20. 20.
    OSCE Office for Democratic Institutions and Human Rights. Norway, Parliamentary Elections 9 September 2013, Final Report. Technical report, December 2013Google Scholar
  21. 21.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pp. 84–93. ACM (2005)Google Scholar
  22. 22.
    Rivest, R., Adleman, L., Dertouzos, M.: On data banks and privacy homomorphisms. In: Foundations of Secure Computation, pp. 169–179. Academia Press, Cambridge (1978)Google Scholar
  23. 23.
    Salamonsen, K.: A security analysis of the helios voting protocol and application to the Norwegian county election (2014)Google Scholar
  24. 24.
    Smart, N.P., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13013-7_25 CrossRefGoogle Scholar
  25. 25.
    Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Cryptography 71(1), 57–81 (2014)CrossRefzbMATHGoogle Scholar
  26. 26.
    Lov om valg til stortinget, fylkesting og kommunestyrer (valgloven). http://lovdata.no, sep 2002. Translation at https://www.regjeringen.no/globalassets/upload/KRD/Kampanjer/valgportal/Regelverk/Representation_of_the_People_Act170609.pdf

Copyright information

© International Financial Cryptography Association 2017

Authors and Affiliations

  1. 1.Norwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations