Abstract
Quadratic voting is an intriguing new method for public choice suggested by Lalley and Weyl, which they showed to be utilitarian efficient. Voters are given a budget of credits and can assign each of the candidates a (perhaps negative) value, where the price paid for their voting choice is the sum of the squared values. From a security viewpoint, we generally request elections to be private and have integrity, and even further (end-to-end) verifiability which entails public bulletin boards. Such public data might be troublesome when considering future adversaries capable of breaking current cryptographic primitives, either due to computational power advances, broken primitives or scientific breakthroughs. This calls for election schemes with everlasting privacy and perfectly private audit trails. In the case of quadratic voting this is even more crucial since budget balances have to be linked between elections in a verifiable way, and revealing old budget values partially break privacy in later elections. In this paper, we suggest an efficient construction of electronic quadratic voting with end-to-end verifiability and a perfectly private audit trail inspired by the methods of Cuvelier, Pereira and Peters, but adapted to include the quadratic relations and keeping budget balances everlasting private.
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References
Adida, B., De Marneffe, O., Pereira, O., Quisquater, J.-J.: Electing a university president using open-audit voting: analysis of real-world use of Helios. In: Proceedings of the 2009 Conference on Electronic Voting Technology/Workshop on Trustworthy Elections, EVT/WOTE 2009, Berkeley, CA, USA, p. 10. USENIX Association (2009)
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). https://doi.org/10.1007/11693383_22
Bellare, M., Goldwasser, S.: Verifiable partial key escrow. In: Proceedings of the 4th ACM Conference on Computer and Communications Security, pp. 78–91. ACM (1997)
Benaloh, J.: Ballot casting assurance via voter-initiated poll station auditing. In: USENIX/ACCURATE Electronic Voting Technology Workshop, EVT 2007. USENIX Association (2007)
Bernhard, D., Pereira, O., Warinschi, B.: How not to prove yourself: pitfalls of the fiat-shamir heuristic and applications to Helios. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 626–643. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_38
Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_18
Camenisch, J.: Group signature schemes and payment systems based on the discrete logarithm problem. PhD thesis, ETH Zurich (1998)
Chandar, B., Weyl, E.G.: Quadratic voting in finite populations (2017)
Chuengsatiansup, C., Naehrig, M., Ribarski, P., Schwabe, P.: PandA: pairings and arithmetic. In: Cao, Z., Zhang, F. (eds.) Pairing 2013. LNCS, vol. 8365, pp. 229–250. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04873-4_14
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_19
Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_9
Cuvelier, É., Pereira, O., Peters, T.: Election verifiability or ballot privacy: do we need to choose? In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 481–498. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_27
Damgård, I.: On sigma protocols (2010). http://www.daimi.au.dk/~ivan/Sigma.pdf
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. Cryptol. 20(1), 51–83 (2007)
Lalley, S.P., Weyl, E.G.: Nash equilibria for a quadratic voting game. CoRR, abs/1409.0264 (2014)
Park, S., Rivest, R.L.: Towards secure quadratic voting. Public Choice 172(1–2), 151–175 (2017). https://eprint.iacr.org/2016/400
Pedersen, T.P.: A threshold cryptosystem without a trusted party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_47
Quarfoot, D., von Kohorn, D., Slavin, K., Sutherland, R., Goldstein, D., Konar, E.: Quadratic voting in the wild: real people, real votes. Public Choice 172(1), 283–303 (2017). https://doi.org/10.1007/s11127-017-0416-1
Sasson, E.B., et al.: Decentralized anonymous payments from Bitcoin. In: Proceedings of the 2014 IEEE Symposium on Security and Privacy, SP 2014, Washington, DC, USA, pp. 459–474. IEEE Computer Society (2014)
Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_22
Wikström, D.: Simplified submission of inputs to protocols. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 293–308. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85855-3_20
Acknowledgements
The authors acknowledge support from the Luxembourg National Research Fund (FNR) and Belgium Fonds de la Recherche Scientifique for the joint FNR/F.R.S.-FNRS project SeVoTe. PBR also acknowledges the FNR INTER project VoteVerif. This work has also been funded in part by the European Union (EU) and the Walloon Region through the FEDER project USERMedia (convention number 501907-379156).
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Pereira, O., Rønne, P.B. (2020). End-to-End Verifiable Quadratic Voting with Everlasting Privacy. In: Bracciali, A., Clark, J., Pintore, F., Rønne, P., Sala, M. (eds) Financial Cryptography and Data Security. FC 2019. Lecture Notes in Computer Science(), vol 11599. Springer, Cham. https://doi.org/10.1007/978-3-030-43725-1_22
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