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Sensors

Delay-Doppler Domain Time-Hopping Key Generation and Security Analysis for Orthogonal Time Frequency Space Satellite Communication Systems

Wei Li, Zhendie Bai, Jikang Wang, Xiaofan Xu, Xianggeng Zhu

Published May 20, 2026• 0 citations
Publisher

Abstract

Physical-layer key generation (PLKG) is a technique that produces symmetric encryption keys by exploiting the inherent characteristics of wireless channels. It offers advantages including high physical-layer security, elimination of pre-shared keys, dynamic upgradability, and resistance to quantum attacks, making PLKG a promising security solution for next-generation (6G) networks. However, satellite communication channels exhibit high dynamics and long propagation delays. Characteristics such as large Doppler shifts, short coherence times, and orbital predictability pose severe challenges to PLKG, including reciprocity degradation, low key generation rate (KGR), and susceptibility to channel-prediction attacks. This work proposes a delay-Doppler domain time-hopping key generation scheme (KE-DD-TH) based on Orthogonal Time Frequency Space (OTFS) modulation for high-speed links between Low-Earth-Orbit (LEO)/Medium-Earth-Orbit (MEO) satellites and ground terminals in Ka/Ku bands. The scheme performs non-uniform sampling on the DD domain grid of OTFS symbols using an ephemeris-driven pseudo-random time-hopping sequence generated by cascaded linear feedback shift registers (LFSRs) and a nonlinear matrix transformation. Both legitimate parties estimate the channel only at time-hopping instants and multiply two adjacent estimates to construct an "equivalent channel" matrix, yielding a random source with high entropy, high reciprocity, and low predictability. The eavesdropper's key disagreement rate (KDR) remains close to 0.5 under all signal-to-noise ratio (SNR) conditions, corresponding to the ideal random-guessing baseline. This indicates that Eve obtains negligible mutual information, i.e., I(KA;KE)≈0. By contrast, the conventional KE-DD scheme allows Eve's KDR to degrade to 0.014 at 30 dB SNR, indicating near-complete key recovery. The generated keys pass all 12 randomness tests of the NIST SP 800-22 statistical test suite.

DOI
10.3390/s26103230

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Physical-layer key generation (PLKG) is a technique that produces symmetric encryption keys by exploiting the inherent characteristics of wireless channels. It offers advantages including high physical-layer security, elimination of pre-shared keys, dynamic upgradability, and resistance to quantum attacks, making PLKG a promising security solution for next-generation (6G) networks. However, satellite communication channels exhibit high dynamics and long propagation delays. Characteristics such as large Doppler shifts, short coherence times, and orbital predictability pose severe challenges to PLKG, including reciprocity degradation, low key generation rate (KGR), and susceptibility to channel-prediction attacks. This work proposes a delay-Doppler domain time-hopping key generation scheme (KE-DD-TH) based on Orthogonal Time Frequency Space (OTFS) modulation for high-speed links between Low-Earth-Orbit (LEO)/Medium-Earth-Orbit (MEO) satellites and ground terminals in Ka/Ku bands. The scheme performs non-uniform sampling on the DD domain grid of OTFS symbols using an ephemeris-driven pseudo-random time-hopping sequence generated by cascaded linear feedback shift registers (LFSRs) and a nonlinear matrix transformation. Both legitimate parties estimate the channel only at time-hopping instants and multiply two adjacent estimates to construct an "equivalent channel" matrix, yielding a random source with high entropy, high reciprocity, and low predictability. The eavesdropper's key disagreement rate (KDR) remains close to 0.5 under all signal-to-noise ratio (SNR) conditions, corresponding to the ideal random-guessing baseline. This indicates that Eve obtains negligible mutual information, i.e., I(KA;KE)≈0. By contrast, the conventional KE-DD scheme allows Eve's KDR to degrade to 0.014 at 30 dB SNR, indicating near-complete key recovery. The generated keys pass all 12 randomness tests of the NIST SP 800-22 statistical test suite.
Low earth orbit (LEO) satellite signals cover extensive areas with high intensity, rendering them vulnerable to interception. However, the rapid movement of LEO satellites leads to severe Doppler frequency shift, making it extremely challenging to generate a consistent key using traditional physical key generation techniques. In response to these issues, we have fully utilized Orthogonal Time Frequency Space (OTFS) in dynamic environments and propose a physical layer key generation (PLKG) scheme based on delay- Doppler (DD) domain signal processing. In the preprocessing stage, we propose a Linearly Weighted Moving Average Coding (LW-MAC) algorithm that dynamically adjusts weights with varying channel response intensities, significantly reducing the inconsistency in channel estimation. Subsequently, to address the reduction in key security caused by insufficient key length, we propose a Maximum of Real and Imaginary parts of channel response Assisted Amplitude Quantization (MRIAAQ) algorithm, which increases the key length and enhances the key entropy value. Simulation results demonstrate that our proposed PLKG scheme has substantial advantages over bidirectional difference quantization (BDQ) and equal probability quantization schemes in terms of key disagreement rate (KDR). Moreover, our PLKG scheme significantly reduces the bit error rate (BER) by approximately 71.37%\%%on average compared to artificial noise-aided physical layer security scheme, thereby greatly enhancing the security of dynamic satellite-to-ground communication.
Key generation for secure communication is challenging in high-mobility scenarios due to the low coherence time. This is further exacerbated in frequency-division duplex systems due to the non-reciprocal wireless channel in uplink and downlink. The current work leverages the symplectic Fourier transform to convert fast-varying time-frequency domain signals to slow-varying delay-Doppler (DD) domain and utilizes the wireless channel representation in the DD domain to generate shared keys. The proposed approach is evaluated in terms of key generation and mismatch rates considering correlated eavesdropper, as well as the various randomness criteria provided by the National Institute of Standards and Technology.
Physical layer key generation (PLKG) has emerged as a promising strategy for securing wireless communication using shared channel knowledge between two legitimate users. Traditional PLKG systems rely on time-frequency domain channels using metrics such as Received Signal Strength Indicator (RSSI) or Channel State Information (CSI) to generate secure keys. As a result of the rapid variation in the time-frequency domain channels, these systems are prone to error and suffer from a high reconciliation overhead requirement. Conversely, the same channels have a sparse and static representation in the delay-Doppler domain, which is utilized by the recently introduced Orthogonal Time Frequency Space (OTFS) modulation scheme. Furthermore, the channel representation in the delay-Doppler domain is uniquely determined by the scattering environment between the transmitter-receiver pair. In this paper, we leverage the sparsity of the delay-Doppler domain channel as well as the uniqueness of the channel representation to introduce two OTFS based PLKG schemes. We show through extensive simulations that the introduced OTFS schemes can get < 10% bit disagreement ratio (BDR) in scenarios where time-frequency domain based RSSI methods break down.
With the rapid advancement of Low Earth Orbit (LEO) satellite constellations, ensuring the security of satellite-to-ground communication has become a critical concern. Traditional cryptographic techniques, while effective against classical attacks, face increasing threats from quantum computing. This paper proposes a quantum key secure transmission method tailored for LEO satellite-ground communication scenarios. The method integrates quantum key distribution (QKD) with dynamic channel estimation and orbital mobility prediction to support secure and low-latency key handshakes between satellites and ground stations. A hybrid encryption strategy is introduced, where QKD-generated keys are used to refresh symmetric session keys in real time, significantly enhancing resistance to eavesdropping and man-in-the-middle attacks. Simulation results demonstrate that the proposed method ensures stable key distribution under Doppler-shifted and intermittent link conditions, achieving improved secrecy capacity and resilience against quantum-level adversaries. This work provides a viable and scalable quantum-safe communication solution for future secure satellite networks.
Physical layer key generation techniques aim to extract secret keys from the information contained in wireless channels. However, existing key generation schemes often rely on time-frequency domain waveforms for channel estimation, which not only makes secret extraction less reliable but may also compromise the confidentiality of the extracted secret information. This paper presents physical layer key generation methods relying on the Orthogonal Time Frequency and Space (OTFS) waveform. We present analysis showing that the delay-Doppler domain channel estimates obtained using OTFS are conducive to more secure and reliable secret extraction than time-frequency domain channel estimates obtained using the prevalent Orthogonal Frequency Division Multiplexing (OFDM). This analysis provides theoretical guarantees under certain simple assumptions. We then relax those assumptions in extensive time-division duplex (TDD) simulations and show that under realistic settings, OTFS offers the expected benefits to reliability and security. Our simulations show that the introduced OTFS schemes can reliably extract secret keys from channel estimates in scenarios where time-frequency domain methods deteriorate.
Wireless secret key generation has emerged as a promising technique for Internet-of-Things (IoT) systems to establish shared encryption keys between the server and legitimate mobile user. This article focuses on the use of multidomain joint information to achieve a high key generation rate (KGR) and the implementation of a reliable, low-complexity secret key generation mechanism for distributed antenna systems (DAS) with orthogonal-frequency division multiplexing (OFDM). We present a space-time-frequency channel state information (CSI)-based key generation scheme based on a two-step approach of adaptive link selection and stepwise decorrelation algorithms. The performance is evaluated in terms of KGR, key disagreement rate (KDR), randomness, and computational complexity by using both a standardized channel model and real-world measurements. Numerical results show that our proposed low-complexity algorithms effectively utilize the space-time-frequency CSI to multiply the KGR in both indoor and outdoor environments. Through adaptive link selection in DAS, the KDR is maintained within a correctable range, thereby ensuring the validity of generated keys in dynamic environments. Further applying stepwise decorrelation reduces the computational complexity by more than half while satisfying all eight key generation randomness tests in the NIST test suite.