Common Randomness, Multiuser Secrecy and Tree Packing

Inherent connections are known to exist between common randomness generated by multiterminal source coding and channel coding on the one hand, and information theoretic secrecy generation by means of public communication on the other hand. Based on these connections, points of contact have been found recently also between secrecy generation for a special model for the latter and the combinatorial problem of tree packing in a multigraph. This paper provides a brief (and partial) survey of these links, especially those between secrecy generation and combinatorial tree packing. Our objective is to highlight specific connections between common randomness, secrecy and tree packing.