New bounds for randomized busing

We consider anonymous secure communication, where parties not only wish to conceal their communications from outside observers, but also wish to conceal the very fact that they are communicating. We consider the bus framework introduced by Beimel and Dolev (J. Cryptology 16 (2003) 25), where messages are delivered by a bus traveling on a random walk. We generalize this idea to consider more than one bus. We show that if w buses are allowed, then the expected delivery time for a message can be decreased from Θ(n) to Θ(n/√w) in the case of a complete graph. Additionally, we introduce a class of graphs called r-partite directed collars and obtain analogous bounds on the expected delivery time for these graphs. We also propose several new features that resolve possible shortcomings in the systems proposed by Beimel and Dolev.

[1]  David J. Aldous,et al.  Lower bounds for covering times for reversible Markov chains and random walks on graphs , 1989 .

[2]  László Lovász,et al.  Random Walks on Graphs: A Survey , 1993 .

[3]  O. Bunke.  Feller, F.: An Introduction to Probability Theory and its Applications, Vol. II, John Wiley & Sons, Inc., New York‐London‐Sydney, 1966. XVIII + 626 S., 3 Abb., 2 Tab., Preis $ 12,00 , 1969 .

[4]  Uriel Feige,et al.  Random Walks on Regular and Irregular Graphs , 1996, SIAM J. Discret. Math..

[5]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[6]  Daniel R. Simon,et al.  Cryptographic defense against traffic analysis , 1993, STOC.

[7]  Rafail Ostrovsky,et al.  Xor-trees for efficient anonymous multicast and reception , 2000, TSEC.

[8]  Frank Thomson Leighton,et al.  Processor-Ring Communication: A Tight Asymptotic Bound on Packet Waiting Times , 1998, SIAM J. Comput..

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

[10]  Shlomi Dolev,et al.  Buses for Anonymous Message Delivery , 2003, Journal of Cryptology.

[11]  David Chaum,et al.  Multiparty unconditionally secure protocols , 1988, STOC '88.

[12]  David Chaum,et al.  The dining cryptographers problem: Unconditional sender and recipient untraceability , 1988, Journal of Cryptology.

[13]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[14]  ChaumD..  The dining cryptographers problem , 1988 .

[15]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[16]  Andreas Pfitzmann.  How to implement ISDNs without user observability---Someremarks , 1987, SGSC.

[17]  Paul F. Syverson,et al.  Anonymous connections and onion routing , 1997, Proceedings. 1997 IEEE Symposium on Security and Privacy (Cat. No.97CB36097).

[18]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[19]  Moni Naor,et al.  Adaptively secure multi-party computation , 1996, STOC '96.