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, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption by exploiting the physical layer properties of the radio channel.
By Thomas Dean, Andrea Goldsmith
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