Group Secret Key Generation Algorithms

We consider a pair-wise independent network in which every pair of terminals observes a common pair-wise source that is independent of all the sources accessible to the other pairs. We propose a method for secret key agreement in such a network that is based on well-established point-to- point techniques and repeated application of the one-time pad over a graphical representation of the network. Three specific problems are investigated. (1) Each terminal´s observations are correlated only with the observations of a central terminal. All these terminals wish to generate a common secret key. (2) Two designated terminals wish to generate a secret key with the help of other terminals. (3) All terminals wish to generate a common secret key. In each of these cases, we show that our two-step approach can yield an optimal protocol, in terms of the resulting secret key rates. Furthermore, such a protocol is provided for the first two problems, while an efficient protocol is given for the third problem.