Theory of linear and integer programming
Theory of linear and integer programming
Packing Steiner trees: a cutting plane algorithm and computational results
Mathematical Programming: Series A and B
Edge-disjoint trees containing some given vertices in a graph
Journal of Combinatorial Theory Series B
A unification of network coding and tree-packing (routing) theorems
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
On achieving maximum multicast throughput in undirected networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Secret key generation for a pairwise independent network model
IEEE Transactions on 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
Secret key generation for a pairwise independent network model
IEEE Transactions on Information Theory
Hi-index | 754.90 |
We consider perfect secret key generation for a "pairwise 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. First, we show how the notion of perfect omniscience plays a central role in characterizing perfect secret key capacity. Second, a multigraph representation of the underlying secrecy model leads us to an efficient algorithm for perfect secret key generation based on maximal Steiner tree packing. This algorithm attains capacity when all the terminals seek to share a key, and, in general, attains at least half the capacity. Third, when a single "helper" terminal assists the remaining "user" terminals in generating a perfect secret key, we give necessary and sufficient conditions for the optimality of the algorithm; also, a "weak" helper is shown to be sufficient for optimality.