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IEEE Internet of Things Journal

Covert Secret Key Agreement Scheme Based on the Underwater Acoustic Dynamic Hypergraph

Ming Xu, Ming Hao

Published Jan 17, 2025• 4 citations
Publisher

Abstract

In order to cope with the problem of how to agree on a covert secret key with high reliability and strong secrecy among an arbitrary number of legitimate nodes in underwater acoustic channel (UAC), a Covert Secret key agreement scheme based on underwater acoustics dynamic hypergraph called CSDH is proposed. The CSDH scheme is novel in three aspects. First, we utilize attention mechanism for extracting the feature of node in UAC and construct a dynamic hypergraph model by its characteristics, which has less storage space and lower computational complexity. Second, we design a spatio-temporal hypergraph convolution method based on the spatial and temporal variation characteristics of UAC in which the number of the nodes is arbitrary, the hyperedge is dynamic, and each hyperedge can encompass an arbitrary number of nodes. Third, we utilize covert communication and polar coding to construct high-entropy bit indices set and very high-entropy bit indices set to generate a common covert key among arbitrary number of legitimate nodes to ensure that not only the key is secret but the entire key agreement process remains covert to eavesdroppers. The reliability, uniformity, secrecy, covertness and secrecy capacity of the CSDH scheme are proved by the information theory and hypergraph theory. The simulation results demonstrate the performance of the CSDH scheme is better than that of existing schemes.

DOI
10.1109/jiot.2025.3529425

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In order to cope with the problem of how to agree on a covert secret key with high reliability and strong secrecy among an arbitrary number of legitimate nodes in underwater acoustic channel (UAC), a Covert Secret key agreement scheme based on underwater acoustics dynamic hypergraph called CSDH is proposed. The CSDH scheme is novel in three aspects. First, we utilize attention mechanism for extracting the feature of node in UAC and construct a dynamic hypergraph model by its characteristics, which has less storage space and lower computational complexity. Second, we design a spatio-temporal hypergraph convolution method based on the spatial and temporal variation characteristics of UAC in which the number of the nodes is arbitrary, the hyperedge is dynamic, and each hyperedge can encompass an arbitrary number of nodes. Third, we utilize covert communication and polar coding to construct high-entropy bit indices set and very high-entropy bit indices set to generate a common covert key among arbitrary number of legitimate nodes to ensure that not only the key is secret but the entire key agreement process remains covert to eavesdroppers. The reliability, uniformity, secrecy, covertness and secrecy capacity of the CSDH scheme are proved by the information theory and hypergraph theory. The simulation results demonstrate the performance of the CSDH scheme is better than that of existing schemes.
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.
Preestablished secret keys are often used to encrypt and decrypt data in communication systems, which are not secure once the keys are compromised. One desirable method is to generate secret keys dynamically using correlated channel measurements. We explore this concept in underwater acoustic (UWA) channels, and present a protocol that can generate secret keys dynamically based on the channel frequency response (CFR) in orthogonal frequency-division multiplexing systems. The multi-bit quantization is carried out on the amplitude of each tone, and the Bose-Chaudhuri-Hocquenghem codes are used for information reconciliation. Part of the protocol was implemented in lake tests, and multiple data sets were collected. The lake test results verify that the amplitude of CFR can be used as a randomness source for key generation in UWA channels, and we also find the low correlation between the mutual channels of the legitimate users. Based on the lake test results, we incorporate two modules into the protocol for performance improvement. The first module employs the adaptively weighted probing signaling to increase the channel correlation, and the second module of block-sliced key verification is used to deal with channel dynamics and increase the key agreement probability. The simulation results demonstrate the improved performance of the enhanced protocol.
Symmetric cryptography is the de-facto approach to information security for ad-hoc underwater acoustic networks. The requirement is that all network nodes possess the same cryptographic keys and key distribution that happens offline. Thus, it is hardly possible to include a new keyless node during network operation. In addition, online key replenishment is an open problem. In this article, we tackle key distribution/replenishment by formulating a new protocol that generates a key between two trusted underwater acoustic nodes (Alice and Bob) without the need to exchange the key itself. The proposed protocol initially extracts common acoustic channel features between Alice and Bob after some signal exchanges. Then, each party uses these features to generate his/her own secret bits via a random sequence generator. To correct any differences in their secret bits, we propose two reconciliation methods that employ Reed–Solomon codes. At the last step of the protocol, a 256-bit cryptographic key is generated by feeding the reconciled secret bit string to the Secure Hash Algorithm 3. We evaluate the key generation rate of the proposed protocol with real acoustic data recorded from a littoral environment, in which Alice and Bob exchanged 915 channel probes over different link geometries. To assess security performance, we invent a passive eavesdropper, Eve, who is able to simulate the acoustic link between Alice and Bob. She uses her simulated channels and the same protocol to generate her keys. Our analysis demonstrates a tradeoff between the key generation rate of Alice and Bob and Eve's ability to extract the same key. Our best result shows that Alice and Bob can independently generate 567 keys out of 915 attempts while Eve does not have access to any of the keys.
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.
Underwater acoustic communications (UWACs) are being adopted in several applications, and their security mechanisms require periodically renewed symmetric keys among legitimate devices. To this end, a secret key agreement (SKA) exploiting the UWAC context can be implemented. In this paper, we focus on one step of the source-based SKA protocol, i.e., the advantage distillation, when the legitimate users pre-process the channel measurement to increase the agreement while decreasing the attacker's knowledge about the key. We propose to learn the advantage distillation process by using a dataset of observed channels from the legitimate parties and the attacker, respectively. In turn, also the attacker uses such data to extract the key from its own underwater channel observations. The key extraction functions are derived through a computationally efficient data-driven adversarial strategy based on a metric related to the secret key rate that can be computed with a lower computational cost. The proposed strategy is tested considering experimental UWAC data, derived from a sea experiment. Results prove the quick convergence of the algorithm and the advantage of using the proposed techniques.