Packing Steiner trees: a cutting plane algorithm and computational results
Mathematical Programming: Series A and B
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Graph Theory
New bounds in secret-key agreement: the gap between formation and secrecy extraction
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Perfect omniscience, perfect secrecy, and Steiner tree packing
IEEE Transactions on Information Theory
Secrecy capacities for multiple terminals
IEEE Transactions on Information Theory
Secrecy Capacities for Multiterminal Channel Models
IEEE Transactions on Information Theory
Perfect omniscience, perfect secrecy, and Steiner tree packing
IEEE Transactions on Information Theory
Multi-user wireless channel probing for shared key generation with a fuzzy controller
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We consider secret key generation for a "pairwise independent network" model in which every pair of terminals observes correlated sources that are independent of sources observed by all other pairs of terminals. The terminals are then allowed to communicate publicly with all such communication being observed by all the terminals. The objective is to generate a secret key shared by a given subset of terminals at the largest rate possible, with the cooperation of any remaining terminals. Secrecy is required from an eavesdropper that has access to the public interterminal communication. A (single-letter) formula for secret key capacity brings out a natural connection between the problem of secret key generation and a combinatorial problem of maximal packing of Steiner trees in an associated multigraph. An explicit algorithm is proposed for secret key generation based on a maximal packing of Steiner trees in a multigraph; the corresponding maximum rate of Steiner tree packing is thus a lower bound for the secret key capacity. When only two of the terminals or when all the terminals seek to share a secret key, the mentioned algorithm achieves secret key capacity in which case the bound is tight.