We consider the generation of a secret key (SK) by the inputs and the output of a secure multipleaccess channel (MAC) that additionally have access to a noiseless public communication channel. Under specific restrictions on the protocols, we derive various upper bounds on the rate of such SKs. Specifically, if the public communication consists of only the feedback from the output terminal, then the rate of SKs that can be generated is bounded above by the maximum symmetric rate $R_f^\ast$ in the capacity region of the MAC with feedback. On the other hand, if the public communication is allowed only before and after the transmission over the MAC, then the rate of SKs is bounded above by the maximum symmetric rate $R^\ast$ in the capacity region of the MAC without feedback. Furthermore, for a symmetric MAC, we present a scheme that generates an SK of rate $R_f^\ast$, improving the best previously known achievable rate $R^\ast$. An application of our results establishes the SK capacity for adder MAC, without any restriction on the protocols.

This paper was presented at Allerton 2013. We were hoping to extend the results further, but it is clear that this is not going to happen soon. Now is as good a time as any for sharing this on arXiv. The results will be of interest for anyone working on secret key agreement or common randomness generation