Abstract
All the currently existing homomorphic e-voting schemes are based on additive homomorphism. In this paper a new e-voting scheme based on multiplicative homomorphism is proposed. In the tallying phase, a decryption is performed to recover the product of the votes, instead of the sum of them (as in the additive homomorphic e-voting schemes). Then, the product is factorized to recover the votes. The new e-voting scheme is more efficient than the additive homomorphic e-voting schemes and more efficient than other voting schemes when the number of candidates is small. Strong vote privacy and public verifiability are obtained in the new e-voting scheme.
The research in this paper was supported by Australian Research Grants DPO345458 and LX0346868.
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References
Abe, M., Imai, H.: Flaws in some robust optimistic mix-nets. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 39–50. Springer, Heidelberg (2003)
Aditya, R., Boyd, C., Dawson, E.P., Viswanathan, K.: Secure e-voting for preferential elections. In: Traunmüller, R. (ed.) EGOV 2003. LNCS, vol. 2739, pp. 246–249. Springer, Heidelberg (2003)
Adler, J.M., Dai, W., Green, R.L., Andrew Neff, C.: Computational details of the votehere homomorphic election system. Technical report, VoteHere Inc. (2000), Available from: http://www.votehere.net/technicaldocs/hom.pdf (last accessed June 22, 2002)
Baudron, O., Fouque, P.-A., Pointcheval, D., Stern, J., Poupard, G.: Practical multi-candidate election system. In: Twentieth Annual ACM Symposium on Principles of Distributed Computing, pp. 274–283 (2001)
Benaloh, J., Tuinstra, D.: Receipt-free secret-ballot elections. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on the Theory of Computing, pp. 544–553 (1994)
Benaloh, J.D.C.: Verifiable Secret-Ballot Elections. PhD thesis, Faculty of Graduate School, Yale University (1996)
Boneh, D., Golle, P.: Almost entirely correct mixing with applications to voting. In: 9th ACM Conference on Computer and Communications Security—CCS 2002, pp. 68–77 (2002)
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)
Chaum, D.: Secret-ballot receipts: True voter-verifiable elections. IEEE Security and Privacy 2(1), 38–47 (2004)
Cramer, R., Damgård, I.B., 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)
Cramer, R., Franklin, M., Schoenmakers, B., Yung, M.: Multi-authority secret-ballot elections with linear work. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 72–83. Springer, Heidelberg (1996)
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)
Damgaård, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: 28th Annual Symposium on Foundations of Computer Science, pp. 427–437 (1987)
Fujioka, A., Okamoto, T., Ohta, K.: A practical secret voting scheme for large scale elections. In: Zheng, Y., Seberry, J. (eds.) AUSCRYPT 1992. LNCS, vol. 718, pp. 244–251. Springer, Heidelberg (1993)
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. 123–139. Springer, Heidelberg (1999)
Golle, P., Zhong, S., Boneh, D., Jakobsson, M., Juels, A.: Optimistic mixing for exit-polls. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 451–465. Springer, Heidelberg (2002)
Hevia, A., Kiwi, M.: Electronic jury voting protocols (2000), http://eprint.iacr.org/2000/035/
Hirt, M., Sako, K.: Efficient receipt-free voting based on homomorphic encryption. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 539–556. Springer, Heidelberg (2000)
Jakobsson, M., Juels, A., Rivest, R.L.: Making mix nets robust for electronic voting by randomized partial checking. In: 11th USENIX Security Symposium, pp. 339–353 (2002)
Katz, J., Myers, S., Ostrovsky, R.: Cryptographic counters and applications to electronic voting. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 78–92. Springer, Heidelberg (2001)
Kiayias, A., Yung, M.: Self-tallying elections and perfect ballot secrecy. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 141–158. Springer, Heidelberg (2002)
Lee, B., Boyd, C., Dawson, E., Kim, K., Yang, J., Yoo, S.: Providing receipt-freeness in mixnet-based voting protocols. In: Information Security and Cryptology, ICISC 2003 (to appear, 2003)
Lee, B., Kim, K.: Receipt-free electronic voting through collaboration of voter and honest verifier. In: JW-ISC 2000, pp. 101–108 (2000)
Lee, B., Kim, K.: Receipt-free electronic voting scheme with a tamper-resistant randomizer. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 389–406. Springer, Heidelberg (2003)
Andrew Neff, C.: Conducting a universally verifiable electronic election using homomorphic encryption. White paper, VoteHere Inc. (2000)
Andrew Neff, C.: Verifiable, secret shuffles of elgamal encrypted data for secure multi-authority elections. In: 8th ACM Conference on Computer and Communications Security—CCS 2001, pp. 116–125 (2001)
Okamoto, T.: Receipt-free electronic voting schemes for large scale elections. In: Proc. Security Protocols, 5th International Workshop 1997, pp. 25–35 (1997)
Paillier, P.: Public key cryptosystem based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
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)
Riera, A., Borrell, J.: Practical approach to anonymity in large scale electronic voting schemes. In: Network and Distributed System Security Symposium—NDSS 1999, pp. 69–82 (1999)
Riera, A., Rifà, J., Borrell, J.: Efficient construction of vote-tags to allow open objection to the tally in electronic elections. Information Processing Letters 75(5), 211–215 (2000)
Sako, K., Kilian, J.: Secure voting using partially compatible homomorphisms. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 411–424. Springer, Heidelberg (1994)
Sako, K., Kilian, J.: Receipt-free mix-type voting scheme: A practical solution to the implementation of a voting booth. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 393–403. Springer, Heidelberg (1995)
Schoenmakers, B.: Fully auditable electronic secret-ballot elections. XOOTIC Magazine (July 2000)
Wikström, D.: How to break, fix and optimize “optimistic mix for exit-polls”. Technical report, Swedish Institute of Computer Science (2002), Available from: http://www.sics.se/libindex.html (last accessed October 08, 2003)
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Peng, K., Aditya, R., Boyd, C., Dawson, E., Lee, B. (2004). Multiplicative Homomorphic E-Voting. In: Canteaut, A., Viswanathan, K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30556-9_6
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