Towards a Practical Cryptographic Voting Scheme Based on Malleable Proofs

  • David Bernhard
  • Stephan Neumann
  • Melanie Volkamer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7985)

Abstract

Mixnets are one of the main approaches to deploy secret and verifiable electronic elections. General-purpose verifiable mixnets however suffer from the drawback that the amount of data to be verified by observers increases linearly with the number of involved mix nodes, the number of decryptors, and the number of voters. Chase et al. proposed a verifiable mixnet at Eurocrypt 2012 based on so-called malleable proofs - proofs that do not increase with the number of mix nodes. In work published at PKC 2013, the same authors adapted malleable proofs to verifiable distributed decryption, resulting in a cryptographic voting scheme. As a result, the amount of data to be verified only increases linearly with the number of voters. However, their scheme leaves several questions open which we address in this paper: As a first contribution, we adapt a multi-party computation protocol to build a distributed key generation protocol for the encryption scheme underlying their voting scheme. As a second contribution, we decompress their abstract scheme description, identify elementary operations, and count the number of such operations required for mixing and verification. Based on timings for elementary operations, we extrapolate the running times of the mixing and verification processes, allowing us to assess the feasibility of their scheme. For the German case, we conclude that the replacement of postal voting by cryptographic voting based on malleable proofs is feasible on an electoral district level.

Keywords

Malleable Proofs Distributed Key Generation Performance 

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References

  1. 1.
    Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. Communications of the ACM 24(2), 84–90 (1981)CrossRefGoogle Scholar
  2. 2.
    Wikström, D.: A commitment-consistent proof of a shuffle. In: Boyd, C., González Nieto, J. (eds.) ACISP 2009. LNCS, vol. 5594, pp. 407–421. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Terelius, B., Wikström, D.: Proofs of restricted shuffles. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 100–113. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Wikström, D.: A commitment-consistent proof of a shuffle. Cryptology ePrint Archive, Report 2011/168 (2011), http://eprint.iacr.org/
  5. 5.
    Lipmaa, H., Zhang, B.: A More Efficient Computationally Sound Non-Interactive Zero-Knowledge Shuffle Argument. IACR Cryptology ePrint Archive, 394 (2011)Google Scholar
  6. 6.
    Bayer, S., Groth, J.: Efficient Zero-Knowledge Argument for Correctness of a Shuffle. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 263–280. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Malleable Proof Systems and Applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 281–300. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Groth, J., Sahai, A.: Efficient Non-interactive Proof Systems for Bilinear Groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Verifiable Elections That Scale for Free. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 479–496. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Geisler, M., Smart, N.P.: Distributing the Key Distribution Centre in Sakai–Kasahara Based Systems. In: Parker, M.G. (ed.) Cryptography and Coding 2009. LNCS, vol. 5921, pp. 252–262. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    CertiVox: MIRACL Crypto SDK, https://certivox.com/solutions/miracl-crypto-sdk/ (accessed March 22, 2013)
  13. 13.
    Fouque, P.A., Poupard, G., Stern, J.: Sharing Decryption in the Context of Voting or Lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Shamir, A.: How to share a secret. Communications of the ACM 22, 612–613 (1979)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Cramer, R., Damgård, I., Ishai, Y.: Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Pedersen, T.: A Threshold Cryptosystem without a Trusted Party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  17. 17.
    Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty Computation, an Introduction, http://www.cs.au.dk/~jbn/smc.pdf (accessed March 22, 2013)
  19. 19.
    Bar-Ilan, J., Beaver, D.: Non-cryptographic fault-tolerant computing in constant number of rounds of interaction. In: Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing, Edmonton, Alberta, Canada, August 14-16, pp. 201–209. ACM (1989)Google Scholar
  20. 20.
    Kate, A., Goldberg, I.: Asynchronous distributed private-key generators for identity-based cryptography. IACR Cryptology ePrint Archive, 355 (2009)Google Scholar
  21. 21.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and Reed-Solomon codes. Communications of the ACM 24, 583–584 (1981)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Cohen, H., Frey, G. (eds.): Handbook of elliptic and hyperelliptic curve cryptography. CRC Press (2005)Google Scholar
  23. 23.
    Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  24. 24.
    European Network of Excellence in Cryptology II: Ecrypt II Yearly Report on Algorithms and Key Sizes, http://www.keylength.com/en/3 (accessed March 22, 2013)
  25. 25.
    Ghadafi, E., Smart, N.P., Warinschi, B.: Groth–Sahai Proofs Revisited. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 177–192. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  26. 26.
    Smart, N.P.: Personal communicationGoogle Scholar
  27. 27.
    CertiVox: CertiVox Wiki, Benchmarks and Subs, https://wiki.certivox.com/display/EXT/Benchmarks+and+Subs (accessed March 22, 2013)
  28. 28.
    Beuchat, J.L., Diaz, J.E.G., Mitsunari, S., Okamoto, E., Rodriguez-Henriquez, F., Teruya, T.: High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves. Cryptology ePrint Archive, Report 2010/354 (2010)Google Scholar
  29. 29.
    Mitsunari, S.: High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves, http://homepage1.nifty.com/herumi/crypt/ate-pairing.html (accessed March 22, 2013)
  30. 30.
    Der Bundeswahlleiter: Pressemitteilung (February 16, 2009)Google Scholar
  31. 31.
    Citizens Registration Office, D.E.M.N.: Personal communicationGoogle Scholar
  32. 32.
    Smart, N.P.: Personal communicationGoogle Scholar
  33. 33.
    Damgard, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical Covertly Secure MPC for Dishonest Majority — or: Breaking the SPDZ Limits. Cryptology ePrint Archive, Report 2012/642 (2012)Google Scholar
  34. 34.
    Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D.: Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 218–235. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  35. 35.
    Knuth, D.: The Art of Computer Programming, vol. 4A. Addison-Wesley Professional (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David Bernhard
    • 1
  • Stephan Neumann
    • 2
  • Melanie Volkamer
    • 2
  1. 1.University of BristolUnited Kingdom
  2. 2.CASEDTU DarmstadtGermany

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