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IEEE Access

Group Secret Key Generation Using the Channel Phase: A Geometric Secrecy Approach

Mahyar Ghasedi, Paeiz Azmi, Mohammad Reza Yari, Ali Kuhestani

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Given the inherent constraint of low key generation rates in physical layer key generation schemes, mutual random phase injection is considered a viable solution for establishing common randomness quantities among legitimate nodes. This paper analyzes the confidentiality of a phase-based group key generation scheme for uncrewed aerial vehicle (UAV) communications, which is designed for a star topology and evaluated in a static environment. To this end, a geometric secrecy approach is utilized to determine both vulnerability and secrecy regions, incorporating a variety of eavesdropping strategies for a comprehensive analysis. In static environments characterized by a dominant line of sight (LoS), spatial correlation presents a security vulnerability in non-proximity regions. This issue is addressed using multiple carrier frequencies during the channel probing stage to enhance the secrecy regions. Accordingly, the extent of vulnerability regions is substantially affected by the selected carrier frequencies and the intervals between them. Furthermore, the analysis determined the significant dependence of the system’s optimal performance on the number of legitimate nodes and their spatial layouts. The performance of the proposed scheme is evaluated by analyzing both the required number of time slots for key generation and the bit mismatch rate (BMR), which is introduced to measure the quality of the generated keys. Moreover, the analysis confirms the randomness of the generated bit sequences via the NIST test suite and highlights the high scalability of our approach compared to existing work.

DOI
10.1109/access.2026.3708466

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Given the inherent constraint of low key generation rates in physical layer key generation schemes, mutual random phase injection is considered a viable solution for establishing common randomness quantities among legitimate nodes. This paper analyzes the confidentiality of a phase-based group key generation scheme for uncrewed aerial vehicle (UAV) communications, which is designed for a star topology and evaluated in a static environment. To this end, a geometric secrecy approach is utilized to determine both vulnerability and secrecy regions, incorporating a variety of eavesdropping strategies for a comprehensive analysis. In static environments characterized by a dominant line of sight (LoS), spatial correlation presents a security vulnerability in non-proximity regions. This issue is addressed using multiple carrier frequencies during the channel probing stage to enhance the secrecy regions. Accordingly, the extent of vulnerability regions is substantially affected by the selected carrier frequencies and the intervals between them. Furthermore, the analysis determined the significant dependence of the system’s optimal performance on the number of legitimate nodes and their spatial layouts. The performance of the proposed scheme is evaluated by analyzing both the required number of time slots for key generation and the bit mismatch rate (BMR), which is introduced to measure the quality of the generated keys. Moreover, the analysis confirms the randomness of the generated bit sequences via the NIST test suite and highlights the high scalability of our approach compared to existing work.
Mutual random phase injection can be considered an appropriate solution for tackling the low key generation rate issue in physical layer key generation schemes. In this paper, the confidentiality of a phase-based group secret key generation scheme has been analyzed by employing a geometric secrecy approach in a static environment. Accordingly, we exploit this approach to achieve some common randomness quantities in our group model. For this purpose, the process of key generation is defined for a star topology. Next, both vulnerability and secrecy regions are identified. To address the challenge of security vulnerability in non-proximity areas due to the spatial correlation in static environments with dominant line-of-sight (LoS), multiple carrier frequencies have been employed at the channel probing stage to enhance the secrecy regions. Finally, the key error probability is provided not only to establish an appropriate evaluation of the quality of the generated keys but also to show the efficiency of our proposed scheme in comparison with previous works.
In secret key generation (SKG), both communicating parties require access to a reciprocal entropy source. Free-space communication fails to provide this due to its strong line-of-sight (LoS) link and absence of multipath scattering. In general, in a free-space environment, SKG faces two primary challenges: a low key generation rate (KGR) and heightened security threats due to a lack of spatial decorrelation. In static free-space environments, the lack of temporal variation further exacerbates challenges. This paper aims to identify and enhance techniques from SKG literature to enable a location-based approach for secure key establishment. Important solutions include exploiting channel phase information as a common measurable parameter, adopting mutual random phase injection to involve the eavesdropper in the eavesdropping process while improving KGR, and introducing geometric secrecy as a security evaluation framework. A principal design objective in geometric secrecy is reducing the vulnerability region to restrict eavesdropping opportunities. To accomplish this, we propose a cooperative key generation (CKG) scheme to shrink this region. In our proposed CKG scheme, the sampling time is primarily governed by the switching time between transmit and receive modes. For information reconciliation, a selection algorithm for a shortened Bose–Chaudhuri–Hocquenghem (SBCH) code is proposed, and SBCH combined with a cyclic redundancy check (CRC) corrects bit mismatches. Worst-case channel sampling and information reconciliation leakage rates are analyzed. The leftover hash lemma is applied during privacy amplification to render leaked information useless. Simulation results indicate that the proposed CKG scheme achieves enhanced effectiveness with increased the number of quantization levels, while a wider angular guard zone plays a critical role in improving the KGR.
Unmanned aerial vehicle (UAV) will be an essential carrier for future wireless communications due to its flexible deployment and low cost. As such, the information security of UAV communications is of paramount concern. In this paper, a novel physical layer secret key generation scheme is proposed for air-to-ground (A2G) UAV multiple-input-multiple-output (MIMO) communications, which is applicable in frequency division duplex (FDD) systems. In UAV communications, line-of-sight (LoS) propagation is a distinctive feature, which significantly weakens the performance of channel state information (CSI) based keys. Therefore, a novel channel parameter, three-dimension (3D) spatial angle, is employed to combat against a novel active eavesdropping method, which is termed as Environment Reconstruction based Attack for SEcret keys (ERASE). Compared to the existing plane-angle-based method, our scheme can efficiently utilize spatial resources and provide a higher key generation rate (KGR). The advantages of the proposed scheme are shown through both theoretical analysis and simulations.
Recently, there has been great interest in physical layer security techniques that exploit the randomness of wireless channels for securely extracting cryptographic keys. Several interesting approaches have been developed and demonstrated for their feasibility. The state-of-the-art, however, still has much room for improving their practicality. This is because i) the key bit generation rate supported by most existing approaches is very low which significantly limits their practical usage given the intermittent connectivity in mobile environments; ii) existing approaches suffer from the scalability and flexibility issues, i.e., they cannot be directly extended to support efficient group key generation and do not suit for static environments. With these observations in mind, we present a new secret key generation approach that utilizes the uniformly distributed phase information of channel responses to extract shared cryptographic keys under narrowband multipath fading models. The proposed approach enjoys a high key bit generation rate due to its efficient introduction of multiple randomized phase information within a single coherence time interval as the keying sources. The proposed approach also provides scalability and flexibility because it relies only on the transmission of periodical extensions of unmodulated sinusoidal beacons, which allows effective accumulation of channel phases across multiple nodes. The proposed scheme is thoroughly evaluated through both analytical and simulation studies. Compared to existing work that focus on pairwise key generation, our approach is highly scalable and can improve the analytical key bit generation rate by a couple of orders of magnitude.
Unmanned aerial vehicles (UAVs) have attracted much attention for civil and military uses because of their high mobility and adaptable deployment capabilities in open spaces. They facilitate agile communications and ubiquitous connectivity. UAVs benefit from dominant line-of-sight communication links but are more susceptible to adversary eavesdropping attacks. Since upper-layer cryptography methods may be insufficient, physical-layer security (PLS) is an attractive alternative. PLS capitalizes on the inherent randomness of wireless channels to improve information confidentiality, particularly in UAV systems. This article provides a comprehensive overview of PLS in the context of UAV systems, examining various communication channels, including ground-to-air (G2A), ground-to-ground (G2G), air-to-ground (A2G), and air-to-air (A2A). First, we give a general review of UAV communications, emphasizing its functions as user equipment, base station (BS), and mobile relay. Following that, we provide an overview of PLS and its forms. The survey organizes the most advanced PLS techniques against passive wireless eavesdropping regarding the channels they are designed to protect. These schemes are further categorized into optimization and secrecy performance analysis. We examine technical aspects within each sub-category and classify core contributions based on approaches and objectives to improve secrecy performance. Moreover, we added summary tables of the identified schemes considering optimization and secrecy performance analysis domains for each category, providing an in-depth understanding of their technical aspects. In addition, we discuss open research issues and identify future research directions to address evolving threats and requirements in UAV communications to improve information confidentiality.
The rapid evolution of unmanned aerial vehicles (UAVs) has positioned air-ground networks as vital infrastructures for diverse applications. However, the open channels of air-ground networks remain inherently vulnerable to persistent eavesdropping threats. While physical-layer key generation (PLKG) offers a lightweight security mechanism by leveraging channel reciprocity to extract shared secrets, the inherent mobility of UAVs introduces a paradoxical tradeoff. Increased channel randomness from dynamic flight patterns enhances security through entropy amplification but simultaneously disrupts channel reciprocity, leading to key mismatch between legitimate parties. Existing PLKG schemes struggle to maintain reliability in key generation due to static channel characteristics and synchronization overhead, limiting their practical deployment in air-ground networks. To resolve this conflict, we propose a Doppler shift key generation (DSKG) scheme that systematically regulates Doppler shifts through UAV trajectory design to derive secure keys. By formulating the problem as a Markov decision process, we develop a proximal policy optimization (PPO)-clip-based reinforcement learning algorithm to dynamically control UAV speed and steering angle, ensuring robust Doppler shift reciprocity while maximizing both key entropy and generation rate. Experimental results quantify the improvements of our scheme over benchmarks in maintaining high key unpredictability and generation efficiency. Furthermore, the analysis provides valuable insights into parameter impacts, confirming the practical viability of the DSKG scheme for securing air-ground communications.