Abstract
A mix-net is a cryptographic protocol executed by a set of mix-servers that provides anonymity for a group of senders. The main application is electronic voting.
Numerous mix-net constructions and stand-alone definitions of security are proposed in the literature, but only partial proofs of security are given for most constructions and no construction has been proved secure with regards to any kind of composition.
We define an ideal mix-net in the universally composable security framework of Canetti [6]. Then we describe a mix-net based on Feldman [13] and using similar ideas as Desmedt and Kurosawa [10], and prove that it securely realizes the ideal mix-net with respect to static adversaries that corrupt a minority of the mix-servers and arbitrarily many senders.
The mix-net executes in a hybrid model with access to ideal distributed key generation, but apart from that our only assumption is the existence of a group in which the Decision Diffie-Hellman Problem is hard.
If there are relatively few mix-servers or a strong majority of honest mix-servers our construction is practical.
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References
Abe, M.: Universally Verifiable Mix-Net with Verification Work Independent of the Number of Mix-Servers. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 437–447. Springer, Heidelberg (1998)
Abe, M.: 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)
Beaver, D.: Foundations of secure interactive computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)
Canetti, R.: Towards realizing random oracles: Hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)
Canetti, R.: Security and composition of multi-party cryptographic protocols. Journal of Cryptology 13(1) (Winter 2000)
Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols, http://eprint.iacr.org/2000/067 and ECCC TR 01–24; Extended abstract appears in 42nd FOCS. IEEE Computer Society, Los Alamitos (2001)
Chaum, D.: Untraceable Electronic Mail, Return Addresses and Digital Pseudonyms. Communications of the ACM - CACM 1981 24(2), 8-4–88 (1981)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally Composable Two-Party and Multi-Party Secure Computation. In: 34th STOC, pp. 494–503 (2002)
Cramer, R., Shoup, V.: A Practical Public Key Cryptosystem Provably Secure against Adaptive Chosen Ciphertext Attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)
Desmedt, Y., Kurosawa, K.: How to break a practical MIX and design a new one. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 557–572. Springer, Heidelberg (2000)
Dolev, D., Dwork, C., Naor, M.: Non-Malleable Cryptography. In: 23rd STOC, pp. 542–552 (1991)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory 31(4), 469–472 (1985)
Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: Proceedings of the 28th FOCS, pp. 427–438 (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)
Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer, Heidelberg (2001)
Furukawa, J., Miyauchi, H., Mori, K., Obana, S., Sako, K.: An implementation of a universally verifiable electronic voting scheme based on shuffling. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357. Springer, Heidelberg (2003)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure Distrubuted Key Generation for Discrete-Log Based Cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)
Goldreich, O., Micali, S., Wigderson, A.: How to Play Any Mental Game. In: 19th STOC, pp. 218–229 (1987)
Goldwasser, S., Levin, L.: Fair computation of general functions in presence of immoral majority. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 77–93. Springer, Heidelberg (1991)
Goldwasser, S., Lindell, Y.: Secure Multi-Party Computation Without Agreement. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 17–32. Springer, Heidelberg (2002)
Goldwasser, S., Micali, S.: Probabilistic Encryption. Journal of Computer and System Sciences (JCSS) 28(2), 270–299 (1984)
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)
Groth, N.: A Verifiable Secret Shuffle of Homomorphic Encryptions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2002)
Jakobsson, M.: A Practical Mix. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 448–461. Springer, Heidelberg (1998)
Jakobsson, M.: Flash Mixing. In: Proceedings of the 18th ACM Symposium on Principles of Distributed Computing - PODC 1998, pp. 83–89 (1998)
Jakobsson, M., Juels, A.: Millimix: Mixing in small batches, DIMACS Techical report 99-33 (June 1999)
Jakobsson, M., Juels, A.: An optimally robust hybrid mix network. In: Proceedings of the 20th ACM Symposium on Principles of Distributed Computing - PODC 2001, pp. 284–292 (2001)
Lindell, Y., Lysyanskaya, A., Rabin, T.: On the Composition of Authenticated Byzantine Agreement. In: 34th STOC, pp. 514–523 (2002)
Micali, S., Rackoff, C., Sloan, B.: The notion of security for probabilistic cryptosystems. SIAM Journal of Computing 17(2), 412–426 (1988)
Micali, S., Rogaway, P.: Secure Computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)
Michels, M., Horster, P.: Some remarks on a reciept-free and universally verifiable Mix-type voting scheme. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 125–132. Springer, Heidelberg (1996)
Mitomo, M., Kurosawa, K.: Attack for Flash MIX. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 192–204. Springer, Heidelberg (2000)
Neff, A.: A verifiable secret shuffle and its application to E-Voting. In: Proceedings of the 8th ACM Conference on Computer and Communications Security - CCS 2001, pp. 116–125 (2001)
Neff, A.: Personal communication (2003)
Niemi, V., Renvall, A.: How to prevent buying of votes in computer elections. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 164–170. Springer, Heidelberg (1995)
Ogata, W., Kurosawa, K., Sako, K., Takatani, K.: Fault Tolerant Anonymous Channel. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol. 1334, pp. 440–444. Springer, Heidelberg (1997)
Park, C., Itoh, K., Kurosawa, K.: Efficient Anonymous Channel and All/Nothing Election Scheme. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 248–259. Springer, Heidelberg (1994)
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)
Pfitzmann, B.: Breaking an Efficient Anonymous Channel. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 332–340. Springer, Heidelberg (1995)
Pfitzmann, B., Pfitzmann, A.: How to break the direct RSA-implementation of mixes. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 373–381. Springer, Heidelberg (1990)
Pfitzmann, B., Waidner, M.: Composition and Integrity Preservation of Secure Reactive Systems. In: 7th Conference on Computer and Communications Security of the ACM, pp. 245–254 (2000)
Rackoff, C., Simon, D.: Noninteractive zero-knowledge proofs of knowledge and chosen ciphertext attacks. In: 22nd STOC, pp. 433–444 (1991)
Sako, K., Kilian, J.: Receipt-Free Mix-Type Voting Scheme. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 393–403. Springer, Heidelberg (1995)
Schnorr, C., Jakobsson, M.: Security of Signed El Gamal Encryption. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 73–89. Springer, Heidelberg (2000)
Tsiounis, Y., Yung, M.: On the Security of El Gamal based Encryption. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 117–134. Springer, Heidelberg (1998)
Wikström, D.: Five Practical Attacks for “Optimistic Mixing for Exit-Polls”. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006. Springer, Heidelberg (2004)
Wikström, D.: A Universally Composable Mix-Net, manuscript will be available at: http://eprint.iacr.org/
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Wikström, D. (2004). A Universally Composable Mix-Net. In: Naor, M. (eds) Theory of Cryptography. TCC 2004. Lecture Notes in Computer Science, vol 2951. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24638-1_18
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