Information-theoretic key agreement of multiple terminal: part II: channel model

This is the second part of a two-part paper on information-theoretically secure secret key agreement. This paper focuses on the secret key rate problem under the channel model. In the channel model, a set of two or more terminals wish to create a shared secret key that is information-theoretically secure from an eavesdropper. The first terminal can choose a sequence of inputs to a discrete memoryless broadcast channel, which has outputs at the other terminals and at the eavesdropper. After each channel use, the terminals can engage in arbitrarily many rounds of interactive authenticated communication over a public channel; thus, each input by the first terminal can depend on the previous inputs and the public communication so far. At the end of the process each terminal should be able to generate the key. We introduce a technique for proving that a given expression bounds the secrecy rate from above. Using this technique, a new upper bound on the secrecy rate in the general multi-terminal case is proposed that strictly improves the currently best known upper bound. We also derive a new lower bound on the secrecy rate and prove that it strictly improves what is essentially the best known lower bound.