Abstract
There are a number of scenarios where users wishing to communicate, share a weak secret. Often, they are also part of a common social network. Connections (edges) from the social network are represented as shared link keys between participants (vertices). We propose mechanisms that utilise the graph topology of such a network, to increase the entropy of weak pre-shared secrets. Our proposal is based on using random walks to identify a chain of common acquaintances between Alice and Bob, each of which contribute entropy to the final key. Our mechanisms exploit one-wayness and convergence properties of Markovian random walks to, firstly, maximize the set of potential entropy contributors, and second, to resist any contribution from dubious sources such as Sybill sub-networks.
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References
Maurer, U., Wolf, S.: Secret key agreement over a non-authenticated channel – part i: Definitions and bounds. IEEE Transactions on Information Theory 49(4), 822–831 (2003)
Maurer, U., Wolf, S.: Secret key agreement over a non-authenticated channel – part ii: The simulatability condition. IEEE Transactions on Information Theory 49(4), 832–838 (2003)
Maurer, U., Wolf, S.: Secret key agreement over a non-authenticated channel – part iii: Privacy amplification. IEEE Transactions on Information Theory 49(4), 839–851 (2003)
Wyner, A.D.: The wire-tap channel. Bell Systems Technical Journal 41(54), 1355–1387 (1995)
Maurer, U.: Secret key agreement by public discussion. IEEE Transaction on Information Theory 39(3), 733–742 (1993)
Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994)
Bennett, C.H., Brassard, G., Robert, J.M.: Privacy amplification by public discussion. SIAM J. Comput. 17(2), 210–229 (1988)
Bennett, C.H., Brassard, G., Crépeau, C., Maurer, U.: Generalized privacy amplification. IEEE Transaction on Information Theory 41(6), 1915–1923 (1995)
Bleichenbacher, D., Maurer, U.: Optimal tree-based one-time digital signature schemes. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 363–374. Springer, Heidelberg (1996)
Juels, A., Peinado, M.: Hiding cliques for cryptographic security. Designs, Codes and Cryptography 20(3), 269–280 (2000)
Yu, H., Kaminsky, M., Gibbons, P.B., Flaxman, A.: Sybilguard: defending against sybil attacks via social networks. In: SIGCOMM 2006: Proceedings of the 2006 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 267–278. ACM Press, New York (2006)
Marti, S., Ganesan, P., Garcia-Molina, H.: DHT routing using social links. In: Voelker, G.M., Shenker, S. (eds.) IPTPS 2004. LNCS, vol. 3279, pp. 100–111. Springer, Heidelberg (2005)
Danezis, G., Lesniewski-Laas, C., Kaashoek, M.F., Anderson, R.: Sybil-resistant DHT routing. In: Proceedings of the 10th European Symposium On Research In Computer Security, Milan, Italy (2005)
Levien, R.: Attack-resistant trust metrics (2001)
Milgram, S.: The small world problem. Psychology Today 2, 60–67 (1967)
ESDS – economic and social data service, http://www.esds.ac.uk
Morris, R., Thompson, K.: Password security: A case history. CACM 22(11), 594–597 (1979)
Erdos, P., Rnyi, A.: On random graphs. Publicationes Mathemticae (Debrecen) 6, 290–297 (1959)
Bollobas, B.: Random Graphs. Cambridge University Press, Cambridge (2001)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393(6684), 440–442 (1998)
Barabasi, A.L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physica A 272, 173–187 (1999)
Kleinberg, J.: The Small-World Phenomenon: An Algorithmic Perspective. In: Proceedings of the 32nd ACM Symposium on Theory of Computing (2000)
Sinclair, A.: Algorithms for random generation and counting: a Markov chain approach. Birkhauser Verlag, Basel (1993)
Mihail, M., Papadimitriou, C., Saberi, A.: On certain connectivity properties of the internet topology. In: FOCS 2003: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, Washington, DC, USA, vol. 28, IEEE Computer Society, Los Alamitos (2003)
Aiello, W., Chung, F., Lu, L.: A random graph model for massive graphs. In: STOC 2000: Proceedings of the Thirty-Second Annual ACM symposium on Theory of Computing, pp. 171–180. ACM Press, New York (2000)
Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. In: SIGCOMM 1999: Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 251–262. ACM Press, New York (1999)
Mahadevan, P., Krioukov, D., Fomenkov, M., Huffaker, B., Dimitropoulos, X., Claffy, K.C., Vahdat, A.: Lessons from three views of the internet topology. Technical report, Cooperative Association for Internet Data Analysis, (CAIDA) (2005)
Klingberg, T., Manfredi, R.: Gnutella 0.6 (2002)
Clarke, I., Sandberg, O., Wiley, B., Hong, T.: Freenet: A distributed anonymous information storage and retrieval system. In: Proceedings of Designing Privacy Enhancing Technologies: Workshop on Design Issues in Anonymity and Unobservability, pp. 46–66 (2000)
Ripeanu, M., Foster, I., Iamnitchi, A.: Mapping the gnutella network: Properties of large-scale peer-to-peer systems and implications for system design. IEEE Internet Computing Journal 6(1) (2002)
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Nagaraja, S. (2010). Privacy Amplification with Social Networks. In: Christianson, B., Crispo, B., Malcolm, J.A., Roe, M. (eds) Security Protocols. Security Protocols 2007. Lecture Notes in Computer Science, vol 5964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17773-6_7
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DOI: https://doi.org/10.1007/978-3-642-17773-6_7
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