  We propose the new technique of physical-layer cryptography based on using a
massive MIMO channel as a key between the sender and desired receiver, which
need not be secret. The goal is for low-complexity encoding and decoding by the
desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard
in terms of prohibitive complexity. The decoding complexity is analyzed by
mapping the massive MIMO system to a lattice. We show that the eavesdropper's
decoder for the MIMO system with M-PAM modulation is equivalent to solving
standard lattice problems that are conjectured to be of exponential complexity
for both classical and quantum computers. Hence, under the widely-held
conjecture that standard lattice problems are hard to solve in the worst-case,
the proposed encryption scheme has a more robust notion of security than that
of the most common encryption methods used today such as RSA and
Diffie-Hellman. Additionally, we show that this scheme could be used to
securely communicate without a pre-shared secret and little computational
overhead. Thus, by exploiting the physical layer properties of the radio
channel, the massive MIMO system provides for low-complexity encryption
commensurate with the most sophisticated forms of application-layer encryption
that are currently known.
