[Paper Review] Secret-Message Transmission by Echoing Encrypted Probes -- STEEP

Yingbo Hua|arXiv (Cornell University)|Sep 25, 2023

Wireless Communication Security Techniques4 citations

TL;DR

This paper proposes STEEP, a two-way secret-message transmission scheme that enables secure communication from Bob to Alice using encrypted probe echoes over a high-quality return channel. By leveraging Maurer-Ahlswede-Csiszár (MAC) bounds on secret-key capacity, STEEP guarantees a positive secrecy rate even when Eve's probing channel is stronger than Bob's, provided she cannot perfectly observe the transmitted probes.

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.

Motivation & Objective

• To bridge the gap between wire-tap channel (WTC) models and secret-key generation (SKG) theory in secret communication.
• To address the limitation of one-way WTC schemes, which yield zero secrecy rate when Eve's channel capacity exceeds Bob's.
• To develop a practical, two-way protocol that ensures positive secrecy rates regardless of eavesdropper channel strength.
• To unify existing WTC and SKG frameworks using a novel probing-and-echoing mechanism.

Proposed method

• In Phase 1, Alice transmits random probes over a probing channel to Bob, which are also received by Eve in a noisy form.
• In Phase 2, Bob estimates the probes and echoes them back to Alice after encrypting with a shared secret over a high-quality return channel.
• The return channel is modeled as a wire-tap channel from Bob to Alice and Eve, where Alice’s channel is guaranteed to be stronger than Eve’s due to the high return channel quality.
• The secrecy rate is derived using binary symmetric channel (BSC) models for the return links, with error probabilities $ P_{A|B} $ and $ P_{E|B} $ for Alice and Eve respectively.
• The scheme ensures $ P_{E|B} > P_{A|B} $, leading to a positive secrecy capacity $ \xi = f(P_{E|B}) - f(P_{A|B}) $, where $ f(p) = -p\log p - (1-p)\log(1-p) $.
• The method is applicable to both analog and digital channels, and does not require secret key exchange or iterative public communication.

Experimental results

Research questions

• RQ1 Can a two-way communication scheme achieve positive secrecy rates even when Eve’s channel is stronger than Bob’s during probing?
• RQ2 How can MAC’s lower and upper bounds on secret-key capacity be leveraged to design a practical secret-message transmission protocol?
• RQ3 Can a single round-trip communication scheme outperform existing one-way WTC and iterative SKG schemes in terms of secrecy and efficiency?
• RQ4 What is the optimal secrecy rate achievable via probe echoing, and how does it depend on error probabilities at the legitimate and eavesdropping receivers?

Key findings

• STEEP guarantees a positive secrecy rate $ \xi = f(P_{E|B}) - f(P_{A|B}) $ from Bob to Alice, even if Eve’s probing channel is stronger than Bob’s.
• The secrecy rate increases with the number of probing symbols, and remains positive as long as Eve cannot perfectly observe the probes.
• The scheme achieves optimal secrecy performance, as the lower and upper bounds on secret-key capacity match exactly: $ \xi_L = \xi_U = \xi $.
• The effective return channel from Bob to Alice is modeled as a binary symmetric channel with error probability $ P_{A|B} $, while Eve’s is worse with $ P_{E|B} > P_{A|B} $.
• The method is robust to public channel state information and works for both analog and digital probing channels.
• Unlike prior schemes, STEEP does not require secret key exchange or iterative public communication, enabling one-round, low-latency secure transmission.