Building Resilience in Wireless Communication Systems With a Secret-Key Budget

TL;DR

This work addresses resilience in wireless systems that generate and use secret-key bits by modeling the available key material as a secret-key budget $B(t)$ with initial amount $b_0$. It introduces physical-layer resilience metrics—especially alert outage $\varepsilon(t)$ and resilience outage $\alpha(t)$—and a budget-based resilience framework that guides power-control decisions under stochastic key-generation dynamics. The authors propose and compare three schemes: Constant Power, Adaptive Power Control, and Reinforcement Learning (SAC-based), analyzing trade-offs between transmit power and resilience, and providing bounds and long-term behavior using ruin-theory concepts. Numerical results in Rayleigh fading illustrate how adaptive and RL-based schemes can achieve substantial power savings while maintaining resilience close to targeted thresholds, offering practical guidance for designers of secure, energy-efficient wireless systems with secret-key budgets.

Abstract

Resilience and power consumption are two important performance metrics for many modern communication systems, and it is therefore important to define, analyze, and optimize them. In this work, we consider a wireless communication system with secret-key generation, in which the secret-key bits are added to and used from a pool of available key bits. We propose novel physical layer resilience metrics for the survivability of such systems. In addition, we propose multiple power allocation schemes and analyze their trade-off between resilience and power consumption. In particular, we investigate and compare constant power allocation, an adaptive analytical algorithm, and a reinforcement learning-based solution. It is shown how the transmit power can be minimized such that a specified resilience is guaranteed. These results can be used directly by designers of such systems to optimize the system parameters for the desired performance in terms of reliability, security, and resilience.

Figures (13)

• Figure 1: Overview of the system model. Alice and Bob generate key bits and add them to the budget. Before each transmission, key bits from the budget are used as one-time pad to encrypt the message, such that Eve is not able to decrypt it. For the sake of clarity, we omit the fact that the communication channels are also used for secret-key generation (SKG). Therefore, it is also affected by $\bm{H}_{\textnormal{B}}^2$, $\bm{H}_{\textnormal{E}}^2$, and $P_{\textnormal{T}}$, cf. \ref{['eq:skg-rate']}.
• Figure 2: Illustration of the scheduling model in the normal state. In each time slot $t$, there is a probability $p$ that a message of length $L$ is transmitted. If no message is transmitted, is performed instead, which adds key bits to the budget.
• Figure 3: Illustration of the budget idea. If is performed, new key bits are generated and added to the budget at Alice and Bob. If a message of length $L$ arrives, the oldest $L$ key bits are used as a one-time pad to encrypt it and removed from the budget. (\ref{['ex:sk-budget']})
• Figure 4: General resilience model with four different phases. For the system considered in this work, the performance corresponds to the budget. In the normal state, messages are transmitted with probability $p$ while is performed the rest of the time. During the alert state, a message is transmitted in each time slot, i.e., $p=1$. The duration of the alert state $\bm{T}$ is random but follows a known distribution.
• Figure 5: Illustration of the relation between budget, alert outage probability $\varepsilon$, and resilience outage events. The target maximum alert outage probability is set to $\tilde{\varepsilon}=10^{-1}$. The highlighted areas indicate the time slots $t$ at which the alert outage probability exceeds the threshold, i.e., $\varepsilon(t)>\tilde{\varepsilon}$. (\ref{['ex:resilience-metric']})

Theorems & Definitions (11)

• Example 1: Budget
• Remark 1: Connection Between Ruin Theory and Our Model
• Example 2: Resilience Metrics
• Theorem 1: Bounds on the Resilience Outage Probability
• proof
• Lemma 1: Besser2024SKGbudget
• Theorem 2: Long-Term Resilience Outage Probability
• proof
• Example 3: Constant Power -- Rayleigh Fading
• Proposition 1: Adaptive Power Control