Everlasting secrecy in disadvantaged wireless environments against sophisticated eavesdroppers

Secure communication over a wireless channel in the presence of a passive eavesdropper is considered. Our main interest is in the disadvantaged wireless environment, where the channel from the transmitter Alice to the eavesdropper Eve is (possibly much) better than that from Alice to Bob, hence making information-theoretic secrecy challenging. We present a method to exploit inherent vulnerabilities of the eavesdropper´s receiver through the use of “cheap” cryptographically-secure key-bits, which only need be kept secret from Eve for the (short) transmission period of the message, to obtain information-theoretic (i.e. everlasting) secret bits at Bob. In particular, based on an ephemeral cryptographic key pre-shared between Alice and Bob, a random jamming signal with large variations is added to each symbol. The legitimate receiver Bob uses the key to subtract the jamming signal immediately, while Eve is forced to perform the inherently nonlinear operation of recording the signal; when Eve then obtains the key, which we assume pessimistically (for Alice) happens right after message transmission, Eve can then immediately subtract the jamming signal from the recorded signal. But, because of the intervening non-linear operation in Eve´s receiver and the non-commutativity of nonlinear operations, Bob´s channel and Eve´s channel have different achievable rates and information-theoretic secrecy can be obtained, hence achieving the goal of converting the vulnerable cryptographic secret key into information-theoretic secure bits. The achievable secrecy rates for different settings are evaluated. Among other results, it is shown that, even when the eavesdropper has perfect access to the output of the transmitter (albeit through an imperfect analog-to-digital converter), the method can still achieve a positive secrecy rate.