[Paper Review] Authentication over Noisy Channels

Lifeng Lai, Hesham El Gamal+1 more|ArXiv.org|Feb 19, 2008

Wireless Communication Security Techniques9 references4 citations

TL;DR

This paper proposes a novel authentication scheme that jointly designs channel coding and authentication over noisy channels, leveraging channel noise to reduce an adversary's success probability. It establishes that the fundamental limit of message authentication is PD = 2−H(K), achieving optimal security by fully utilizing the secret key for both impersonation and substitution attacks, which is strictly better than the classical noiseless model where PD ≥ 2−H(K)/2.

ABSTRACT

In this work, message authentication over noisy channels is studied. The model developed in this paper is the authentication theory counterpart of Wyner's wiretap channel model. Two types of opponent attacks, namely impersonation attacks and substitution attacks, are investigated for both single message and multiple message authentication scenarios. For each scenario, information theoretic lower and upper bounds on the opponent's success probability are derived. Remarkably, in both scenarios, lower and upper bounds are shown to match, and hence the fundamental limit of message authentication over noisy channels is fully characterized. The opponent's success probability is further shown to be smaller than that derived in the classic authentication model in which the channel is assumed to be noiseless. These results rely on a proposed novel authentication scheme in which key information is used to provide simultaneous protection again both types of attacks.

Motivation & Objective

• To address the limitation of classical authentication models that assume a noiseless channel, which fails to reflect real-world physical layer conditions.
• To characterize the fundamental limits of message authentication in the presence of channel noise, particularly for both single and multiple message scenarios.
• To demonstrate that channel noise can be exploited to reduce the opponent's success probability below that of the noiseless model.
• To develop a unified authentication scheme that simultaneously protects against both impersonation and substitution attacks using the full key space.

Proposed method

• Proposes a joint design of channel coding and authentication using the wiretap channel model, where the legitimate receiver and adversary experience different noise levels.
• Uses secret key K to generate a ciphertext W = f(K, M) that is transmitted over a noisy channel, with the key information embedded in a way that exploits channel differences.
• Derives information-theoretic bounds on the opponent’s success probability using mutual information and conditional entropy, specifically I(K;W) and H(K|W), under noisy conditions.
• Applies the wiretap channel secrecy capacity concept to minimize information leakage to the opponent, ensuring that mutual information I(K;W) can be made arbitrarily small.
• For multiple messages, the scheme reuses the same key K across J transmissions, with bounds derived using Bayesian updating and maximum a posteriori key estimation by the opponent.
• Employs hypothesis testing and extremal distributions to derive tight upper and lower bounds on impersonation and substitution attack success probabilities, showing they match exactly.

Experimental results

Research questions

• RQ1 Can channel noise be leveraged to improve message authentication security beyond the classical noiseless model?
• RQ2 What is the fundamental limit of authentication success probability when the channel is noisy, and how does it compare to the noiseless case?
• RQ3 Can a single authentication scheme simultaneously protect against both impersonation and substitution attacks using the full secret key?
• RQ4 How does the opponent’s success probability evolve over multiple message transmissions in a noisy channel compared to a noiseless one?

Key findings

• The fundamental limit of message authentication over noisy channels is PD = 2−H(K), which is strictly smaller than the lower bound of 2−H(K)/2 in the classical noiseless model.
• The proposed scheme achieves optimal security by fully utilizing the entire secret key H(K) to defend against both impersonation and substitution attacks simultaneously.
• For single-message authentication, the upper and lower bounds on the opponent’s success probability match exactly, proving that PD = 2−H(K) is the tightest possible bound.
• In the multiple-message scenario with reuse of the same key, the opponent’s success probability remains bounded at PD = 2−H(K) for each transmission, even after observing multiple packets.
• The information leakage to the opponent is minimized via the wiretap channel framework, allowing the mutual information I(K;W) to be made arbitrarily small, which enables the tight upper bound.
• The results demonstrate that channel noise is not a detriment but a resource for authentication, enabling stronger security than achievable in noiseless settings.