Packing Steiner trees: a cutting plane algorithm and computational results
Mathematical Programming: Series A and B
A unification of network coding and tree-packing (routing) theorems
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Common randomness and secret key generation with a helper
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
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We investigate perfect 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 interactively in multiple rounds over a public noiseless channel of unlimited capacity. This communication is observed by all the terminals as well as by an eavesdropper. The objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible. All the terminals cooperate in generating the secret key, with perfect secrecy being required from the eavesdropper. For this model, we introduce the concept of communication for perfect omniscience using which we first obtain a single-letter characterization of the perfect secret key capacity. Moreover, this perfect secret key capacity is shown to be achieved by linear noninteractive communication, and coincides with the (standard) secret key capacity. Our second contribution, exploiting the notion of communication for perfect omniscience, is a new nonasymptotic and computable upper bound for the combinatorial problem of maximal Steiner tree packing in a multigraph. Thus, our work establishes certain connections among perfect secrecy generation and communication for perfect omniscience for the pairwise independent network model, and Steiner tree packing.