Abstract
We consider a mix-network as a cryptographic primitive that provides anonymity. A mix-network takes as input a number of ciphertexts and outputs a random shuffle of the corresponding plaintexts. Common applications of mix-nets are electronic voting and anonymous network traffic. In this paper, we present a novel construction of a mix-network, which is based on shuffling ElGamal encryptions. Our scheme is the first mix-net to meet the strongest security requirements: it is robust and secure against chosen ciphertext attacks as well as against active attacks in the Universally Composable model. Our construction allows one to securely execute several mix-net instances concurrently, as well as to run multiple mix-sessions without changing a set of keys. Nevertheless, the scheme is efficient: it requires a linear work (in the number of input messages) per mix-server.
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References
Abe, M.: Mix-Networks on Permutation Networks. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 258–273. Springer, Heidelberg (1999)
Abe, M., Hoshino, F.: Remarks on Mix-Network Based on Permutation Networks. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992. Springer, Heidelberg (2001)
Abe, M., Imai, H.: Flaws in Some Robust Optimistic Mix-Nets. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727. Springer, Heidelberg (2003)
Backes, M., Pfitzmann, B., Waidner, M.: A general composition theorem for secure reactive systems. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 336–354. Springer, Heidelberg (2004)
Blum, M., Feldman, P., Micali, S.: Non-Interactive Zero-Knowledge and Its Applications. In: Proc. of the 20th ACM STOC. ACM, New York (1988)
Camenisch, J.L., Shoup, V.: Practical Verifiable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)
Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: Proc. of the 42nd IEEE FOCS. IEEE, Los Alamitos (2001)
Canetti, R., Kushilevitz, E., Lindell, Y.: On the Limitations of Universally Composable Two-Party Computation Without Set-Up Assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656. Springer, Heidelberg (2003)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: Proc. of the 34th ACM STOC. ACM, New York (2002)
Chaum, D.: Untraceable electronic mail, return addresses, and digital pseudonyms. Communications of the ACM 24(2), 84–90 (1981)
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)
Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: Proc. of the 28th IEEE FOCS. IEEE, Los Alamitos (1987)
Groth, J.: 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., Juels, A.: An optimally robust hybrid mix network. In: PODC 2001 (2001)
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)
Lindell, Y., Lysyanskaya, A., Rabin, T.: On the Composition of Authenticated Byzantine Agreement. In: Proc. of the 34th ACM STOC. ACM, New York (2002)
Naor, M., Yung, M.: Public-key Cryptosystems Provably Secure against Chosen Ciphertext Attacks. In: Proc. of the 22nd ACM STOC. ACM, New York (1990)
Park, C.-s., 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)
Pass, R.: On Deniability in the Common Reference String and Random Oracle Model. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 316–337. Springer, Heidelberg (2003)
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., Waidner, M.: A model for asynchronous reactive systems and its application to secure message transmission. In: Proceedings of the IEEE Symposium on Research in Security and Privacy, pp. 184–200. IEEE Computer Society Press, Los Alamitos (2001)
Shamir, A.: How to Share a Secret. Communications of ACM 22(11), 612–613 (1979)
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. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 317–335. Springer, Heidelberg (2004)
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Camenisch, J., Mityagin, A. (2006). Mix-Network with Stronger Security. In: Danezis, G., Martin, D. (eds) Privacy Enhancing Technologies. PET 2005. Lecture Notes in Computer Science, vol 3856. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11767831_9
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DOI: https://doi.org/10.1007/11767831_9
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