Perfect Omniscience, Perfect Secrecy and Steiner Tree Packing

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Executive Summary

The authors consider perfect secret key generation for a "Pair-wise independent network" model in which every pair of terminals share a random binary string, with the strings shared by distinct terminal pairs being mutually independent. The terminals are then allowed to communicate interactively over a public noiseless channel of unlimited capacity. All the terminals as well as an eavesdropper observe this communication. The objective is to generate a perfect secret key shared by a given set of terminals at the largest rate possible, and concealed from the eavesdropper.

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