Limitations of Generating a Secret Key Using Wireless Fading Under Active Adversary

Recently, many research studies have explored the use of wireless fading to generate an information-theoretic shared secret key over an open wireless channel. While this line of research is now mature enough to be built into demonstrative working systems for scenarios involving a (limited) passive/eavesdropping adversary model, the case of an active (jamming) adversary has not been sufficiently studied. Under an active adversary, information-bits that need to be exchanged during the process of key setup will not only be subject to eavesdropping, but also message disruptions that could lead to a high communication cost per bit of secret key generated. Measuring efficiency of key exchange as the ratio of communication cost to the size of secret key generated, in this paper, we address the following question: Is generating a secret key by exploiting wireless fading an efficient process? We obtain analytical results that quantify the minimum number of information-bits that must be exchanged to obtain one bit of shared secret key and show that this number rapidly increases with an active adversary's signal power. Thus, through our analysis, we conclude that the effectiveness of generating a secret key from wireless fading is limited when considering active adversaries.