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IEEE Wireless Communications Letters

Multi-Party Blinded Key Encapsulation Mechanism for Underwater Acoustic Communication

Ming Xu, Enbo Zhang

Published May 6, 2025• 1 citation
Publisher

Abstract

Underwater acoustic communication (UAC) is getting more and more attention in ocean exploration. In order to solve the problem of key transmission and secure communication in UAC environment, we propose a quantum computation-resistant multi-party Blinded Key Encapsulation Mechanism (BKEM), coined as Sea-BKEM. In Sea-BKEM, an orthogonal time frequency space (OTFS) based key generation algorithm is proposed to reduce the complexity of key generation by extracting random narrow distributions from the ocean noise in the delay-Doppler (DD) domain using the number theoretic transform (NTT) and symplectic finite Fourier transform (SFFT), and generating the encapsulation and decapsulation keys. On the NTRU lattice, the ciphertext obtained from the signal block computation is compressed, and the ciphertext is blinded using ocean noise factor in OTFS to reduce the ciphertext expansion and communication cost. On this basis, the indistinguishable security and rigidity of the Sea-BKEM scheme are proven in the DD domain of OTFS. Experimental results show that Sea-BKEM outperforms the existing lattice-based schemes in terms of computational cost, communication cost and bit error rate (BER).

DOI
10.1109/lwc.2025.3567441

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Underwater acoustic communication (UAC) is getting more and more attention in ocean exploration. In order to solve the problem of key transmission and secure communication in UAC environment, we propose a quantum computation-resistant multi-party Blinded Key Encapsulation Mechanism (BKEM), coined as Sea-BKEM. In Sea-BKEM, an orthogonal time frequency space (OTFS) based key generation algorithm is proposed to reduce the complexity of key generation by extracting random narrow distributions from the ocean noise in the delay-Doppler (DD) domain using the number theoretic transform (NTT) and symplectic finite Fourier transform (SFFT), and generating the encapsulation and decapsulation keys. On the NTRU lattice, the ciphertext obtained from the signal block computation is compressed, and the ciphertext is blinded using ocean noise factor in OTFS to reduce the ciphertext expansion and communication cost. On this basis, the indistinguishable security and rigidity of the Sea-BKEM scheme are proven in the DD domain of OTFS. Experimental results show that Sea-BKEM outperforms the existing lattice-based schemes in terms of computational cost, communication cost and bit error rate (BER).
With the increasing emphasis on safeguarding maritime sovereignty and developing marine resources, the security of underwater acoustic communication has risen to a new level of importance. Given the complex environmental challenges faced by underwater acoustic channels, this paper proposes an NTRU-based key encapsulation scheme designed to ensure secure and reliable underwater data transmission, while maintaining privacy and integrity. In the public–private key pair generation phase, a ring sampling technique is employed to generate a compact NTRU trapdoor, which not only guarantees security but also effectively reduces the communication overhead. During the encapsulation phase, underwater acoustic channel characteristics during communication are introduced as temporary identity information to ensure the confidentiality and reliability of the key encapsulation mechanism. Furthermore, the traditional key encapsulation mechanism is extended by integrating a digital signature process, where the encapsulated ciphertext is signed. The use of digital signature technology verifies the authenticity and integrity of the transmitted data, ensuring that communication data remain secure and unaltered in complex underwater acoustic environments. Finally, we conduct a rigorous correctness analysis and security proofs, demonstrating that the proposed scheme achieves chosen ciphertext security, while meeting the demands of low bandwidth and limited computational capacity in underwater acoustic communication.
In order to cope with the problem of information leakage of existing secret-key agreement protocols under the environment of underwater acoustic channel (UAC), a covert secret-key agreement protocol called CSAP is proposed. In CSAP, the transmitter sends the uniformly distributed random messages to the receiver within a certain range of power constraints to ensure the reliability and the covertness of the protocol. The receiver calculates the estimated messages with Gibbs sampling according to the variance information of the underwater noise and uses the Log-Likelihood Ratio (LLR) test to extract the secret-key so as to reduce the uncertainty and the bit error rate (BER) of data transmission between two legitimate parties. The complexity of the CSAP protocol isO{O}O(n{n}n), wheren{n}ndenotes the message length. The secrecy, covertness, and reliability of the CSAP protocol are proved by the information theory. The simulation results show that the CSAP protocol reduces the bit error rate (BER) by 28.88%, improves the secret-key generation rate by 25.70%, and decreases the communication cost by 11.32% on average compared to the existing protocol.
Concerning the problem of how to extract a highly confidential key for an arbitrary number of legitimate nodes under the circumstances of multipath and Doppler effects in underwater acoustic channels, we propose a multi-party secret key generation scheme over underwater acoustic channels against active attacks. In the proposed scheme, the α order Rényi entropy with multipath and Doppler effects is accurately depicted, and the uncertainty of the source sequence from the legitimate nodes and the eavesdropping node is also obtained. On this basis, a multi-party secret key generation protocol against active attacks is designed using bilinear mapping, which does not depend on the length and randomness of the random seed. Our results demonstrate the security of the proposed scheme in the metrics of the key leakage rate and the probability of a successful active attack.
Secure underwater communication is vital for maritime operations; however, acoustic channels pose significant challenges, including limited bandwidth, high latency, and complex propagation effects. With quantum computing threatening classical methods, there is a need for cryptographic schemes that can withstand quantum attacks. This study presents a quantum-resistant underwater communication system that integrates CRYSTALS-Kyber for key encapsulation, SPHINCS+ for digital signature authentication, and AES for efficient payload encryption. The proposed system is evaluated under realistic underwater channel simulations that account for propagation delay, multipath fading, and Doppler effects. Experimental benchmarks reveal that while post-quantum operations, such as CRYSTALS-Kyber key encapsulation (2.41-4.91ms) and SPHINCS+ signing (96.10ms) exhibit higher latencies compared to classical ECC/ECDSA methods, these latencies remain within acceptable limits given the substantial security advantages they offer. This approach bridges the gap between rigorous quantum-resistant security and practical underwater deployment, establishing a robust foundation for future enhancements in error correction and adaptive network strategies.
Communication in an underwater environment presents many challenges, due to its unique characteristics of throughput, delay, and error rates. The acoustic channels commonly used for underwater communication have inherent broadcast characteristics and require non-trivial solutions to achieve secure and authenticated communications. The complexity of security challenges is further increased by the ongoing transition to quantum-resistant cryptography. Our paper discusses post-quantum cryptographic solutions for underwater broadcast communication scenarios. Specifically, we present and analyze solutions for sender authentication and key management based on private key cryptography and discuss perfect forward secrecy of communication keys, taking into consideration the constraints of the underwater environment.
Quantum cryptography (QC) is envisioned as a solution for global key distribution through fiber optic, free space and underwater optical communication due to its unconditional security. In view of this, this paper investigates underwater free space quantum key distribution (QKD) model for enhanced transmission distance, secret key rates and security. It is reported that secure underwater free space QKD is feasible in the clearest ocean water with the sifted key rates up to 207[Formula: see text]kbps. This paper extends this work by testing performance of optimized decoy state QKD protocol with underwater free space communication model. The attenuation of photons, quantum bit error rate and the sifted key generation rate of underwater quantum communication is obtained with vector radiative transfer theory and Monte Carlo method. It is observed from the simulations that optimized decoy state QKD evidently enhances the underwater secret key transmission distance as well as secret key rates.