Exploiting the non-commutativity of nonlinear operators for information-theoretic security in disadvantaged wireless environments

Information-theoretic security guarantees that a message is kept secret from potential eavesdroppers regardless of their current or future computational abilities. But current information-theoretic security approaches generally rely on an advantage of the channel of the desired recipient over the adversary, and such an advantage can be difficult to guarantee in a wireless network where an eavesdropper might be very near the transmitter. This paper initiates an approach to everlasting security for wireless communication links by exploiting a fundamental concept from systems theory: that nonlinear systems are not (necessarily) commutative. This property is exploited by employing a short-term cryptographic key to force the eavesdropper´s signal to be subjected to nonlinear operations in the reverse order of that of the signal at the desired recipient. After introducing the idea and providing analysis for the general case, we next consider a simple (and practical) instantiation where the transmitter uses the ephemeral cryptographic key to rapidly power modulate the transmitted signal. Secrecy rates with this rapid power modulation under various assumptions establish the promise of the approach, even in the case of an eavesdropper with uniformly better conditions (channel and receiver quality) than the intended recipient.