  We propose a novel physical layer security scheme that exploits an
optimization method as a one-way function. The proposed scheme builds on
nonsquare differential multiple-input multiple-output (MIMO), which is capable
of noncoherent detection even in massive MIMO scenarios and thus resilient
against risky pilot insertion and pilot contamination attacks. In contrast to
conventional nonsquare differential MIMO schemes, which require space-time
projection matrices designed via highly complex, discrete, and combinatorial
optimization, the proposed scheme utilizes projection matrices constructed via
low-complexity continuous optimization designed to maximize the coding gain of
the system. Furthermore, using a secret key generated from the true randomness
nature of the wireless channel as an initial value, the proposed continuous
optimization-based projection matrix construction method becomes a one-way
function, making the proposed scheme a physical layer secure differential MIMO
system. An attack algorithm to challenge the proposed scheme is also devised,
which demonstrates that the security level achieved improves as the number of
transmit antennas increases, even in an environment where the eavesdropper can
perfectly estimate channel coefficients and experience asymptotically large
signal-to-noise ratios.
