Abstract
We analyze networks of mixes used for providing untraceable communication. We consider a network consisting of k mixes working in parallel and exchanging the outputs – which is the most natural architecture for composing mixes of a certain size into networks able to mix a larger number of inputs at once. We prove that after \(\mathcal{O}\)(1) rounds the network considered provides a fair level of privacy protection for any number of messages n. Number of required rounds does not dependent on number of mixes provided that n ≫ k 2 . No mathematical proof of this kind has been published before. We show that if at least one of server is corrupted we need substantially more rounds to meet the same requirements of privacy protection.
Partially supported by KBN grant 3T11C 011 26.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aldous, D.: Random Walks of Finite Groups and Rapidly Mixing Markov Chains. In: Azéma, J., Yor, M. (eds.) Séminare de Probabilités XVII 1981/1982. Lecture Notes in Mathematics, vol. 986, pp. 243–297. Springer, Heidelberg (1981)
Auletta, V., Caragiannis, I., Kaklamanis, C., Persiano, P.: Randomized Path Coloring on Binary Trees. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 60–71. Springer, Heidelberg (2000)
Berman, R., Fiat, A., Ta-Shma, A.: Provable Unlinkability Against Traffic Analysis. In: Juels, A. (ed.) FC 2004. LNCS, vol. 3110, pp. 266–280. Springer, Heidelberg (2004)
Bubley, B., Dyer, M.: Path Coupling: A Technique for Proving Rapid Mixing in Markov Chains. ACM-SIAM FOCS 38, 223–231 (1997)
Czumaj, A., Kanarek, P., Kutyłowski, M., Loryś, K.: Switching Networks for Generating Random Permutations. In: Switching Networks: Recent Advances, pp. 25–61. Kluwer Academic Publishers, Dordrecht (2001); ISBN 0-7923-6953-X
Czumaj, A., Kutyłowski, M.: Delayed Path Coupling and Generating Random Permutations. Random Structures and Algorithms 17(3-4), 238–259 (2000)
Dingledine, R.: Anonymity Bibliography, http://freehaven.net/anonbib/
Chaum, D.: Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms. CACM 24(2), 84–88 (1981)
Golle, P., Jakobsson, M., Juels, A., Syverson, P.F.: Universal re-encryption for mixnets. In: Okamoto, T. (ed.) RSA-CT 2004. LNCS, vol. 2964, pp. 163–178. Springer, Heidelberg (2004)
Golle, P., Juels, A.: Parallel Mixing. In: ACM Conference on Computer and Communications Security (CCS), pp. 220–226 (2004)
Gomułkiewicz, M., Klonowski, M., Kutyłowski, M.: Rapid Mixing and Security of Chaum’s Visual Electronic Voting. In: Snekkenes, E., Gollmann, D. (eds.) ESORICS 2003. LNCS, vol. 2808, pp. 132–145. Springer, Heidelberg (2003)
Gomułkiewicz, M., Klonowski, M., Kutyłowski, M.: Provable Unlinkability Against Traffic Analysis Already After \(\mathcal{O}(\log(n))\) Steps! In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol. 3225, pp. 354–366. Springer, Heidelberg (2004)
Gülcü, C., Tsudik, G.: Mixing E-mail with BABEL. In: ISOC Symposium on Network and Distributed System Security, pp. 2–16. IEEE, Los Alamitos (1996)
Kesdogan, D., Egner, J., Büschkes, R.: Stop-and-Go-MIXes Providing Probabilistic Anonymity in an Open System. In: Aucsmith, D. (ed.) IH 1998. LNCS, vol. 1525, pp. 83–98. Springer, Heidelberg (1998)
Rackoff, C., Simon, D.R.: Cryptographic Defense Against Traffic Analysis. In: ACM Symposium on Theory of Computing, vol. 25, pp. 672–681 (1993)
Syverson, P.F., Reed, M.G., Goldschlag, D.M.: Anonymous Connections and Onion Routing. IEEE Journal on Selected Areas in Communication 16(4), 482–494 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Klonowski, M., Kutyłowski, M. (2005). Provable Anonymity for Networks of Mixes. In: Barni, M., Herrera-Joancomartí, J., Katzenbeisser, S., Pérez-González, F. (eds) Information Hiding. IH 2005. Lecture Notes in Computer Science, vol 3727. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558859_3
Download citation
DOI: https://doi.org/10.1007/11558859_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29039-1
Online ISBN: 978-3-540-31481-3
eBook Packages: Computer ScienceComputer Science (R0)