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arXiv:2309.14529

Secret-Message Transmission by Echoing Encrypted Probes -- STEEP

Yingbo Hua

Published Sep 25, 2023• 5 citations
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Abstract

This paper examines the properties of the lower and upper bounds established by Maurer, Ahlswede and Csiszar (MAC) for secret-key capacity in the case of channel probing over single-input and single-output (SISO) channels. Inspired by the insights into MAC's bounds, a scheme called secret-message transmission by echoing encrypted probes (STEEP) is proposed. STEEP consists of two phases: in phase 1, Alice sends random probes over a probing channel to Bob; in phase 2, Bob echoes back an estimated version of the probes, but encrypted by a secret, over a high-quality return channel. Provided that Eve is unable to obtain the exact probes transmitted by Alice in phase 1, STEEP guarantees a positive secrecy rate from Bob to Alice over the return channel even if Eve's channel strength during channel probing is stronger than Bob's. STEEP is applicable to both physical layer and upper layers in connected networks.

DOI
10.48550/arxiv.2309.14529

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This paper examines the properties of the lower and upper bounds established by Maurer, Ahlswede and Csiszar (MAC) for secret-key capacity in the case of channel probing over single-input and single-output (SISO) channels. Inspired by the insights into MAC's bounds, a scheme called secret-message transmission by echoing encrypted probes (STEEP) is proposed. STEEP consists of two phases: in phase 1, Alice sends random probes over a probing channel to Bob; in phase 2, Bob echoes back an estimated version of the probes, but encrypted by a secret, over a high-quality return channel. Provided that Eve is unable to obtain the exact probes transmitted by Alice in phase 1, STEEP guarantees a positive secrecy rate from Bob to Alice over the return channel even if Eve's channel strength during channel probing is stronger than Bob's. STEEP is applicable to both physical layer and upper layers in connected networks.
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.
This paper presents further insights into a recently developed round-trip communication scheme called “Secret-message Transmission by Echoing Encrypted Probes (STEEP)”. A legitimate wireless channel between a multi-antenna user (Alice) and a single-antenna user (Bob) in the presence of a multi-antenna eavesdropper (Eve) is focused on. STEEP does not require full-duplex, channel reciprocity or Eve's channel state information, but is able to yield a positive secrecy rate in bits per channel use between Alice and Bob in every channel coherence period as long as Eve's receive channel is not noiseless. This secrecy rate does not diminish as coherence time increases. Various statistical behaviors of STEEP's secrecy capacity due to random channel fading are also illustrated.
Secure communications over SIMO and MISO channels between wireless nodes are commonly encountered in applications and widely considered in the literature. This paper investigates such a problem by considering a newly proposed scheme called secrecy-message transmission by echoing encrypted probes (STEEP). We focus on a type of heavily eavesdropped channels where an aggressive eavesdropper (Eve) has multiple antennas and is capable of jamming and eavesdropping in the full-duplex mode. Assuming optimal jamming and eavesdropping by Eve, we present the secrecy rates achievable by STEEP in two forms: using SIMO channel in phase 1 and using MISO channel in phase 2, and vice versa. With any given channel condition between every pair of nodes and any finite jamming power by Eve, the secrecy rate of STEEP in either form is shown to be positive subject to a positive power in phase 1 and a sufficiently large power in phase 2. The connections between STEEP in either form and the conventional SIMO and MISO schemes are provided, and their secrecy rates are compared comprehensively subject to random fading channels and finite transmit powers.
Secret-message transmission by echoing encrypted probes (STEEP) using phase-shift-keying (PSK) constellation of asymmetric sizes is investigated, and compared with a prior scheme which is limited to binary signaling. While both schemes can yield positive secrecy rates over a wiretap channel with eavesdropping channel being stronger than user’s, PSK-STEEP is more general and results in higher secrecy rates than the prior scheme. The secrecy rate of PSK-STEEP is shown to be increasing with the size of PSK constellation in phase 1 but is maximized by a binary PSK constellation in phase 2.
Unmanned Aerial Vehicle (UAV) assisted wireless communication has emerged as a highly promising element in the landscape of future wireless networks. This paper investigates the application of “Secret-message Transmission by Echoing Encrypted Probes (STEEP)” to secure UAV communications between a ground station (Alice) and a UAV (Bob). Even with the presence of strong jamming from a full-duplex eavesdropper (Eve), STEEP shows resilience and maintains a strong positive secrecy rate in bits per channel use in every channel coherence period as long as Eve's observations during the probing phase of STEEP are not noiseless. STEEP is a novel round-trip transmission scheme for secure communications, overcoming limitations where prior schemes fail to achieve a positive secrecy rate when Eve's receive channel is stronger than users'.
A transmission scheme for secure communications, called secret-message transmission by echoing encrypted probes (STEEP), can deliver a positive secrecy rate, even when eavesdropping channels are much stronger than that between users, subject to sufficient asymmetric power allocations from users. This paper considers an optimization problem for STEEP applied to MIMO (or MIMOME) channels between multi-antenna users and multi-antenna Eve. We reveal for the first time a significant increase of the achievable secrecy rate of MIMO STEEP using optimized precoders.