Wireless Secret Sharing Game for Internet of Things

In the era of Internet of Things (IoT), billions of small but smart wireless devices work together to make our cities more intelligent and sustainable. One challenge is that many IoT devices do not have human interfaces and are very difficult for humans to manage. This creates sustainability and security issues. Enabling automatic secret sharing across heterogeneous devices for cryptography purposes will provide the needed security and sustainability for the underlying IoT infrastructure. Therefore, wireless secret sharing is crucial to the success of smart cities. One secret sharing method is to utilize the effect of the randomness of the wireless channel in the data link layer to generate the common secret between legitimate users. This paper models this secret sharing mechanism from the perspective of game theory. In particular, we formulate a non-cooperative zero-sum game between the legitimate users (Alice and Bob) and an eavesdropper (Eve). Alice and Bob's strategy is deciding how to exchange packets to protect the secret, and Eve's strategy is choosing where to stay to better intercept the secret. In a symmetrical game where Eve has the same probability of successfully receiving a packet from Alice and Bob when the transmission distance is the same, we show that both pure and mixed strategy Nash equilibria exist. In an asymmetric game where Eve has different probabilities of successfully receiving a packet from Alice and Bob, a pure strategy may not exist; in this case, we show how a mixed strategy Nash equilibrium can be found. We run simulations to show that our results are better than other approaches.