arXiv2025
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 shown to be 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 forward and reverse directions. This paper focuses on STEEP in the following settings: using Gaussian probing signal and Gaussian linear encryption over MIMO Gaussian channel (G-STEEP); using phase-shift-keying probing signal and a nonlinear encryption over SISO channel (P-STEEP); and a variation of G-STEEP for multiple access communication (M-STEEP). In each of the settings, Eve is assumed to have any given number of antennas, and STEEP is shown to yield a positive secrecy rate subject to a sufficiently large power in the echoing phase, as long as Eve's receive channel in the probing phase is not noiseless. It is also shown that G-STEEP, subject to asymmetric large powers in forward and reverse directions, has its secrecy rate approaching the secret-key capacity based on Gaussian probing signal over MIMO Gaussian channel. STEEP does not require secure feedback channel, collaborative third party, in-band full-duplex or reciprocal channels between users, but only needs a design for echoing encrypted probes, asymmetric power allocation and/or collaborative round-trip coding.