On Secret-Message Transmission by Echoing Encrypted Probes

A scheme for secure communications, called ``Secret-message Transmission by Echoing Encrypted Probes (STEEP)'', is revisited. STEEP is a round-trip scheme with a probing phase from one user to another and an echoing phase in the reverse direction. STEEP is broadly applicable to yield a positive secrecy rate in bits per channel use even if the receive channels at eavesdropper (Eve) are stronger than those between legitimate users in both directions. Differing from prior cases of STEEP, this paper presents STEEP in each of the following settings: using Gaussian channel probing (GCP) and Gaussian linear encryption (GLE) over MIMO channels; using phase-shift-keying (PSK) channel probing and PSK nonlinear encryption over SISO channels; and using GCP and GLE over multiple access channels. In each setting, Eve is assumed to have any number of antennas, and STEEP is shown to yield a positive secrecy rate subject to a sufficiently large power in the echoing phase relative to the power in the probing phase, as long as Eve's receive channel in the probing phase is not noiseless. Also shown is that the GCP-GLE based STEEP for two users, subject to a form of large powers from the users, has its secrecy rate approaching the secret-key capacity based on GCP.