Distributed protocols against mobile eavesdroppers
We propose and study the following pursuit-evation problem in distributed enviroments: Members of a team of guards (e.g. antivirus programs) traverse the links of a network represented by a graph G, in pursuit of a fugitive (e.g. worm) which moves along the links of the graph without any other knowledge about the locations of the guards than whatever it can collect as it moves (e.g. the worm is oblivious to dynamic network behaviour). The fugitive's purpose is just to read local information at each node and to stay in the net as long as possible. When a guard meets a fugitive, the fugitive is destroyed. We combinatorially characterize and compare such problems, and we present network protocols that allow an efficient (in terms of number of guards and messages) elimination of the fugitive. Note that the problem we study is fundamentally different from distributed graph searching, since the fugitive does not know the locations of the guards. Our protocols make use of accidental meetings in random walks. The analysis and the proof techniques are based on a novel extension of multiple, parameterized random walk properties which may be of independent theoretical interest.
KeywordsTheory of Distributed Computation Privacy and Security Algorithms and Data Structures
Unable to display preview. Download preview PDF.
- [Aleliunas et al, 79]R. Aleliunas, R. Karp, R. Lipton, L. Lovasz, C. Rackoff, “Random walks, universal traversal sequences and the complexity of maze problems”, 20th ACM FOCS, pp. 218–223.Google Scholar
- [Brightwell,Winkler,90]G. Brightwell and P. Winkler, “Maximum hitting time for random walks on graphs”, J. Random Structures and Algorithms, No. 3 (1990), pp. 263–276.Google Scholar
- [Franklin et al. 93]M. Franklin, Z. Galil and M. Yung, “Eavesdropping Games: A Graph-Theoretic Approach to Privacy in Distributed Systems”, ACM FOCS 1993, 670–679.Google Scholar
- [Gillman, 93]D. Gillman, A Chernoff bound for random walks on expander graphs”, ACM FOCS 93, pp. 680–691.Google Scholar
- [Kortsarz,Peleg,93]G. Kortsarz, D. Peleg, “ On Choosing a Dense Subgraph” ACM FOCS 93, pp. 692–701.Google Scholar
- [Megiddo et al. 88]
- [Ostrovsky, Yung 91]R. Ostrovsky and M. Yung, “Robust Computation in the presence of mobile viruses”, ACM PODC 1991, 51–59.Google Scholar
- [Reif 79]J.H. Reif, “Universal Games of Incomplete Information”, ACM STOC 11 (1979) pp. 288–308.Google Scholar
- [Securenet 92]CEC RACE II Programme SECURENET (R 2057) “Network Security and Protection”, Final Report, 1992.Google Scholar
- [Spirakis,Tampakas,94]P.Spirakis and B. Tampakas, “Distributed Pursuit-Evation: Some aspects of Privacy and Security in Distributed Computing”, short paper, ACM PODC 94.Google Scholar
- [Tetali, Winkler,91]P. Tetali and P. Winkler, “ On a Random Walk problem arising in Self-stabilizing Token Management”, ACM PODC 91, pp. 273–280.Google Scholar