Abstract
We construct the first mix-net that is secure against adaptive adversaries corrupting any minority of the mix-servers and any set of senders. The mix-net is based on the Paillier cryptosystem and analyzed in the universal composability model without erasures under the decisional composite residuosity assumption, the strong RSA-assumption, and the discrete logarithm assumption. We assume the existence of ideal functionalities for a bulletin board, key generation, and coin-flipping.
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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)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136–145. IEEE Computer Society Press, Los Alamitos (2001)
Chaum, D.: Untraceable electronic mail, return addresses and digital pseudo-nyms. Communications of the ACM 24(2), 84–88 (1981)
Damgård, I., Fujisaki, E.: A statistically-hiding integer commitment scheme based on groups with hidden order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125–142. Springer, Heidelberg (2002)
Damgård, 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)
Damgård, I., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–267. Springer, Heidelberg (2003)
Furukawa, J.: Efficient and verifiable shuffling and shuffle-decryption. IEICE Transactions 88-A(1), 172–188 (2005)
Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer Verlag, Heidelberg (2001)
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)
Lysyanskaya, A., Peikert, C.: Adaptive security in the threshold setting: From cryptosystems to signature schemes. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 331–350. Springer, Heidelberg (2001)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attack. In: 22th ACM Symposium on the Theory of Computing (STOC), pp. 427–437 (1990)
Neff, A.: A verifiable secret shuffle and its application to e-voting. In: 8th ACM Conference on Computer and Communications Security (CCS), pp. 116–125. ACM Press, New York (2001)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer Verlag, Heidelberg (1999)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Wikström, D.: A universally composable mix-net. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 315–335. Springer Verlag, Heidelberg (2004)
Wikström, D.: A sender verifiable mix-net and a new proof of a shuffle. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 273–292. Springer Verlag, Heidelberg (2005)
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Wikström, D., Groth, J. (2006). An Adaptively Secure Mix-Net Without Erasures. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_24
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DOI: https://doi.org/10.1007/11787006_24
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