Mix-Network with Stronger Security

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.

[1]  Douglas Wikström,et al.  A Universally Composable Mix-Net , 2004, TCC.

[2]  Douglas Wikström,et al.  Five Practical Attacks for "Optimistic Mixing for Exit-Polls" , 2003, Selected Areas in Cryptography.

[3]  David Chaum,et al.  Wallet Databases with Observers , 1992, CRYPTO.

[4]  Ernest F. Brickell,et al.  Advances in Cryptology — CRYPTO’ 92 , 2001, Lecture Notes in Computer Science.

[5]  Birgit Pfitzmann,et al.  A General Composition Theorem for Secure Reactive Systems , 2004, TCC.

[6]  Alfredo De Santis,et al.  Advances in Cryptology — EUROCRYPT'94 , 1994, Lecture Notes in Computer Science.

[7]  Rafael Pass,et al.  On Deniability in the Common Reference String and Random Oracle Model , 2003, CRYPTO.

[8]  Markus Jakobsson,et al.  Optimistic Mixing for Exit-Polls , 2002, ASIACRYPT.

[9]  Yehuda Lindell,et al.  On the composition of authenticated byzantine agreement , 2002, STOC '02.

[10]  Kaisa Nyberg,et al.  Advances in Cryptology — EUROCRYPT'98 , 1998 .

[11]  Birgit Pfitzmann,et al.  Breaking Efficient Anonymous Channel , 1994, EUROCRYPT.

[12]  Aggelos Kiayias,et al.  Polynomial Reconstruction Based Cryptography , 2001, Selected Areas in Cryptography.

[13]  Manuel Blum,et al.  Non-interactive zero-knowledge and its applications , 1988, STOC '88.

[14]  Walter M. Lioen,et al.  Factorization of RSA-140 Using the Number Field Sieve , 1999, CRYPTO 1999.

[15]  Jan Camenisch,et al.  Practical Verifiable Encryption and Decryption of Discrete Logarithms , 2003, CRYPTO.

[16]  Kaoru Kurosawa,et al.  Efficient Anonymous Channel and All/Nothing Election Scheme , 1994, EUROCRYPT.

[17]  Markus Jakobsson,et al.  A Practical Mix , 1998, EUROCRYPT.

[18]  Markus Jakobsson,et al.  An optimally robust hybrid mix network , 2001, PODC '01.

[19]  Yvo Desmedt.  Public Key Cryptography — PKC 2003 , 2002, Lecture Notes in Computer Science.

[20]  David Chaum,et al.  Untraceable electronic mail, return addresses, and digital pseudonyms , 1981, CACM.

[21]  Paul Feldman,et al.  A practical scheme for non-interactive verifiable secret sharing , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[22]  Masayuki Abe,et al.  Mix-Networks on Permutation Networks , 1999, ASIACRYPT.

[23]  Yehuda Lindell,et al.  On the Limitations of Universally Composable Two-Party Computation without Set-up Assumptions , 2003, EUROCRYPT.

[24]  Masayuki Abe,et al.  Remarks on Mix-Network Based on Permutation Networks , 2001, Public Key Cryptography.

[25]  Yuliang Zheng,et al.  Advances in Cryptology — ASIACRYPT 2002 , 2002, Lecture Notes in Computer Science.

[26]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[27]  Arto Salomaa,et al.  Public-Key Cryptography , 1991, EATCS Monographs on Theoretical Computer Science.

[28]  Jens Groth.  A Verifiable Secret Shuffle of Homomorphic Encryptions , 2003, Public Key Cryptography.

[29]  Birgit Pfitzmann,et al.  A model for asynchronous reactive systems and its application to secure message transmission , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[30]  Yehuda Lindell,et al.  Universally composable two-party and multi-party secure computation , 2002, STOC '02.

[31]  Moni Naor,et al.  Public-key cryptosystems provably secure against chosen ciphertext attacks , 1990, STOC '90.

[32]  Tor Helleseth,et al.  Advances in Cryptology — EUROCRYPT ’93 , 2001, Lecture Notes in Computer Science.

[33]  Hideki Imai,et al.  Flaws in Some Robust Optimistic Mix-Nets , 2003, ACISP.

[34]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[35]  Information Security and Privacy , 1996, Lecture Notes in Computer Science.

[36]  Dan Boneh,et al.  Advances in Cryptology - CRYPTO 2003 , 2003, Lecture Notes in Computer Science.