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Anonymity Preserving Byzantine Vector Consensus

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12308)

Abstract

Collecting anonymous opinions has applications from whistleblowing to complex voting where participants rank candidates by order of preferences. Unfortunately, as far as we know there is no efficient distributed solution to this problem. Previous solutions either require trusted third parties, are inefficient or sacrifice anonymity.

In this paper, we propose a distributed solution called the Anonymised Vector Consensus Protocol (AVCP) that reduces the problem of agreeing on a set of anonymous votes to the binary Byzantine consensus problem. The key idea to preserve the anonymity of voters—despite some of them acting maliciously—is to detect double votes through traceable ring signatures. AVCP is resilient-optimal as it tolerates up to a third of Byzantine participants. We show that our algorithm is correct and that it preserves anonymity with at most a linear communication overhead and constant message overhead when compared to a recent consensus baseline. Finally, we demonstrate empirically that the protocol is practical by deploying it on 100 machines geo-distributed in three continents: America, Asia and Europe. Anonymous decisions are reached within 10 s with a conservative choice of traceable ring signatures.

Keywords

  • Anonymity
  • Byzantine agreement
  • Consensus
  • Vector consensus
  • Distributed computing

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Fig. 1.

Notes

  1. 1.

    https://docs.python.org/2/library/ctypes.html.

  2. 2.

    https://metrics.torproject.org/.

References

  1. Adida, B.: Helios: web-based open-audit voting. In: USENIX Security, pp. 335–348 (2008)

    Google Scholar 

  2. Back, A., Möller, U., Stiglic, A.: Traffic analysis attacks and trade-offs in anonymity providing systems. In: International Workshop on Information Hiding, pp. 245–257 (2001)

    Google Scholar 

  3. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: CCS, pp. 62–73 (1993)

    Google Scholar 

  4. Ben-Or, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience. In: PODC, pp. 183–192 (1994)

    Google Scholar 

  5. Bracha, G.: Asynchronous Byzantine agreement protocols. Inf. Comput. 75(2), 130–143 (1987)

    MathSciNet  CrossRef  Google Scholar 

  6. Bracha, G., Toueg, S.: Resilient consensus protocols. In: PODC, pp. 12–26 (1983)

    Google Scholar 

  7. Bracha, G., Toueg, S.: Asynchronous consensus and broadcast protocols. JACM 32(4), 824–840 (1985)

    MathSciNet  CrossRef  Google Scholar 

  8. Cachin, C., Collins, D., Crain, T., Gramoli, V.: Anonymity preserving Byzantine vector consensus. CoRR abs/1902.10010 (2020). http://arxiv.org/abs/1902.10010

  9. Cachin, C., Kursawe, K., Petzold, F., Shoup, V.: Secure and efficient asynchronous broadcast protocols. In: CRYPTO, pp. 524–541 (2001)

    Google Scholar 

  10. Cachin, C., Kursawe, K., Shoup, V.: Random oracles in constantinople: practical asynchronous Byzantine agreement using cryptography. J. Cryptol. 18(3), 219–246 (2005)

    MathSciNet  CrossRef  Google Scholar 

  11. Camp, J., Harkavy, M., Tygar, J.D., Yee, B.: Anonymous atomic transactions. In: In Proceedings of the 2nd USENIX Workshop on Electronic Commerce (1996)

    Google Scholar 

  12. Castro, M., Liskov, B.: Practical Byzantine fault tolerance. In: OSDI, vol. 99, pp. 173–186 (1999)

    Google Scholar 

  13. Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) Advances in Cryptology, pp. 199–203. Springer, Boston, MA (1983). https://doi.org/10.1007/978-1-4757-0602-4_18

    CrossRef  Google Scholar 

  14. Chaum, D.: The dining cryptographers problem: unconditional sender and recipient untraceability. J. Cryptol. 1(1), 65–75 (1988)

    MathSciNet  CrossRef  Google Scholar 

  15. Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. CACM 24(2), 84–90 (1981)

    CrossRef  Google Scholar 

  16. Correia, M., Neves, N.F., Veríssimo, P.: From consensus to atomic broadcast: time-free Byzantine-resistant protocols without signatures. Comput. J. 49(1), 82–96 (2006)

    CrossRef  Google Scholar 

  17. Crain, T., Gramoli, V., Larrea, M., Raynal, M.: DBFT: efficient leaderless Byzantine consensus and its application to blockchains. In: NCA, pp. 1–8 (2018)

    Google Scholar 

  18. Cramer, R., Franklin, M., Schoenmakers, B., Yung, M.: Multi-authority secret-ballot elections with linear work. In: Eurocrypt, pp. 72–83 (1996)

    Google Scholar 

  19. Danezis, G., Diaz, C.: A survey of anonymous communication channels. Technical report, MSR-TR-2008-35, Microsoft Research (2008)

    Google Scholar 

  20. Desmedt, Y.: Threshold cryptosystems. In: Seberry, J., Zheng, Y. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 1–14. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57220-1_47

    CrossRef  Google Scholar 

  21. Diamantopoulos, P., Maneas, S., Patsonakis, C., Chondros, N., Roussopoulos, M.: Interactive consistency in practical, mostly-asynchronous systems. In: ICPADS, pp. 752–759 (2015)

    Google Scholar 

  22. Dingledine, R., Mathewson, N., Syverson, P.: Tor: the second-generation onion router. In: USENIX Security, pp. 21–21 (2004)

    Google Scholar 

  23. Doudou, A., Schiper, A.: Muteness failure detectors for consensus with Byzantine processes. In: PODC, p. 315 (1997)

    Google Scholar 

  24. Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. JACM 35(2), 288–323 (1988)

    MathSciNet  CrossRef  Google Scholar 

  25. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)

    MathSciNet  CrossRef  Google Scholar 

  26. Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. JACM 32(2), 374–382 (1985)

    MathSciNet  CrossRef  Google Scholar 

  27. Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_1

    CrossRef  Google Scholar 

  28. Fujisaki, E.: Sub-linear size traceable ring signatures without random oracles. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E95.A, 393–415 (2011)

    Google Scholar 

  29. Fujisaki, E., Suzuki, K.: Traceable ring signature. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 181–200. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_13

    CrossRef  Google Scholar 

  30. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)

    Google Scholar 

  31. Gilad, Y., Herzberg, A.: Spying in the dark: TCP and Tor traffic analysis. In: Fischer-Hübner, S., Wright, M. (eds.) PETS 2012. LNCS, vol. 7384, pp. 100–119. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31680-7_6

    CrossRef  Google Scholar 

  32. Golle, P., Jakobsson, M., Juels, A., Syverson, P.: Universal re-encryption for mixnets. In: Okamoto, T. (ed.) CT-RSA 2004. LNCS, vol. 2964, pp. 163–178. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24660-2_14

    CrossRef  Google Scholar 

  33. Golle, P., Juels, A.: Dining cryptographers revisited. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 456–473. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_27

    CrossRef  Google Scholar 

  34. Groth, J.: Efficient maximal privacy in boardroom voting and anonymous broadcast. In: Juels, A. (ed.) FC 2004. LNCS, vol. 3110, pp. 90–104. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27809-2_10

    CrossRef  Google Scholar 

  35. Gu, K., Dong, X., Wang, L.: Efficient traceable ring signature scheme without pairings. Adv. Math. Commun. 14(2), 207–232 (2019)

    MathSciNet  CrossRef  Google Scholar 

  36. Halpern, J.Y., O’Neill, K.R.: Anonymity and information hiding in multiagent systems. J. Comput. Secur. 13(3), 483–514 (2005)

    CrossRef  Google Scholar 

  37. Jakobsson, M.: A practical mix. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 448–461. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054145

    CrossRef  Google Scholar 

  38. Juels, A., Catalano, D., Jakobsson, M.: Coercion-resistant electronic elections. In: Chaum, D., Jakobsson, M., Rivest, R.L., Ryan, P.Y.A., Benaloh, J., Kutylowski, M., Adida, B. (eds.) Towards Trustworthy Elections. LNCS, vol. 6000, pp. 37–63. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12980-3_2

    CrossRef  MATH  Google Scholar 

  39. Kulyk, O., Neumann, S., Volkamer, M., Feier, C., Koster, T.: Electronic voting with fully distributed trust and maximized flexibility regarding ballot design. In: EVOTE, pp. 1–10 (2014)

    Google Scholar 

  40. Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. TOPLAS 4(3), 382–401 (1982)

    CrossRef  Google Scholar 

  41. Liu, J.K., Wei, V.K., Wong, D.S.: Linkable spontaneous anonymous group signature for ad hoc groups. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 325–335. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27800-9_28

    CrossRef  Google Scholar 

  42. Mathewson, N., Dingledine, R.: Practical traffic analysis: extending and resisting statistical disclosure. In: Martin, D., Serjantov, A. (eds.) PET 2004. LNCS, vol. 3424, pp. 17–34. Springer, Heidelberg (2005). https://doi.org/10.1007/11423409_2

    CrossRef  Google Scholar 

  43. Mostéfaoui, A., Moumen, H., Raynal, M.: Signature-free asynchronous binary Byzantine consensus with \(t< n/3\), \({O}(n^2)\) messages, and \({O}(1)\) expected time. JACM 62(4), 31 (2015)

    MathSciNet  CrossRef  Google Scholar 

  44. Murdoch, S.J., Danezis, G.: Low-cost traffic analysis of Tor. In: S&P, pp. 183–195 (2005)

    Google Scholar 

  45. Neff, C.A.: A verifiable secret shuffle and its application to e-voting. In: CCS, pp. 116–125 (2001)

    Google Scholar 

  46. Neves, N.F., Correia, M., Verissimo, P.: Solving vector consensus with a wormhole. TPDS 16(12), 1120–1131 (2005)

    Google Scholar 

  47. 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). https://doi.org/10.1007/3-540-48910-X_16

    CrossRef  Google Scholar 

  48. Raymond, J.-F.: Traffic analysis: protocols, attacks, design issues, and open problems. In: Federrath, H. (ed.) Designing Privacy Enhancing Technologies. LNCS, vol. 2009, pp. 10–29. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44702-4_2

    CrossRef  Google Scholar 

  49. Raynal, M.: Reliable broadcast in the presence of Byzantine processes. In: Fault-Tolerant Message-Passing Distributed Systems, pp. 61–73. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94141-7_4

  50. Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_32

    CrossRef  Google Scholar 

  51. Serjantov, A., Danezis, G.: Towards an information theoretic metric for anonymity. In: Dingledine, R., Syverson, P. (eds.) PET 2002. LNCS, vol. 2482, pp. 41–53. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36467-6_4

    CrossRef  Google Scholar 

  52. Shoup, V., Gennaro, R.: Securing threshold cryptosystems against chosen ciphertext attack. J. Cryptol. 15(2), 75–96 (2002)

    MathSciNet  CrossRef  Google Scholar 

  53. Tsang, P.P., Wei, V.K.: Short linkable ring signatures for E-voting, E-cash and attestation. In: Deng, R.H., Bao, F., Pang, H.H., Zhou, J. (eds.) ISPEC 2005. LNCS, vol. 3439, pp. 48–60. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31979-5_5

    CrossRef  Google Scholar 

  54. Tsang, P.P., Wei, V.K., Chan, T.K., Au, M.H., Liu, J.K., Wong, D.S.: Separable linkable threshold ring signatures. In: Canteaut, A., Viswanathan, K. (eds.) INDOCRYPT 2004. LNCS, vol. 3348, pp. 384–398. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30556-9_30

    CrossRef  Google Scholar 

  55. Yao, A.C.C.: How to generate and exchange secrets. In: FOCS, pp. 162–167 (1986)

    Google Scholar 

  56. Zantout, B., Haraty, R.: I2P data communication system. In: ICN, pp. 401–409 (2011)

    Google Scholar 

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Acknowledgment

This research is supported under Australian Research Council Discovery Projects funding scheme (project number 180104030) entitled “Taipan: A Blockchain with Democratic Consensus and Validated Contracts” and Australian Research Council Future Fellowship funding scheme (project number 180100496) entitled “The Red Belly Blockchain: A Scalable Blockchain for Internet of Things”.

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Cachin, C., Collins, D., Crain, T., Gramoli, V. (2020). Anonymity Preserving Byzantine Vector Consensus. In: Chen, L., Li, N., Liang, K., Schneider, S. (eds) Computer Security – ESORICS 2020. ESORICS 2020. Lecture Notes in Computer Science(), vol 12308. Springer, Cham. https://doi.org/10.1007/978-3-030-58951-6_7

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