An authentication key agreement method suitable for underwater acoustic communication

Abstract

This invention belongs to the field of underwater acoustic communication information security, and relates to an authentication key negotiation method suitable for underwater acoustic communication. This method uses Kyber512 as its cryptographic foundation, combines OTFS for channel modeling in the delay-Doppler domain, and utilizes the bit sequence obtained from channel estimation to enhance the randomness of the private key and error term, thereby constructing a quantum-resistant key encapsulation mechanism. During the negotiation process, node ID, location information, and timestamps are introduced to achieve joint verification of the legitimacy and message freshness of both communicating parties. Addressing the high latency and narrow bandwidth characteristics of underwater acoustic communication, a low-overhead continuous session key update mechanism is designed, reducing the number of one-way transmissions per round after the initial session to achieve subsequent key updates. The method of this invention reduces the possibility of key prediction or reproduction, saves bandwidth, reduces the number of interactions, improves communication efficiency, and achieves a low-overhead continuous session key update mechanism.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic communication information security, and more particularly to an authentication key negotiation method suitable for underwater acoustic communication, or more precisely, a method for two communicating parties to complete identity authentication and negotiate a session key in an underwater acoustic environment. Background Technology

[0002] Compared to general wireless communication environments, underwater acoustic communication faces more stringent bandwidth constraints. Underwater sound waves propagate at low speeds, increasing end-to-end propagation delays. Simultaneously, the available bandwidth of underwater acoustic channels is typically narrow, and environmental interference further reduces the effective communication rate compared to conventional wireless networks. In continuous session scenarios, the repeated transmission of public keys, ciphertext, and other information further consumes limited bandwidth, increasing error rates, retransmissions, and energy consumption. Therefore, reducing the amount of interaction and data transmitted during the key negotiation phase is a key issue in the design of secure underwater acoustic communication solutions.

[0003] Underwater acoustic communication networks are inherently open and vulnerable to attacks such as eavesdropping, spoofing, tampering, and replay attacks. Furthermore, the areas served by underwater acoustic communication often involve sensitive information; if communication security is compromised, it could lead to data leaks, critical node failures, and even threaten the stable operation of the entire underwater network. With the development of quantum computing, classical encryption algorithms will be unable to withstand attacks from quantum computers. Addressing long-term security needs, post-quantum cryptography is gradually becoming an important research direction for secure key establishment. Kyber512 is essentially a key encapsulation mechanism; its security is based on the module learning error problem, which is computationally difficult to solve even for quantum computers. However, its application in underwater acoustic communication still requires further reduction of communication overhead and improvement of adaptability to confined channel environments. Therefore, a suitable authentication key negotiation method for underwater acoustic communication is urgently needed. Summary of the Invention

[0004] To address the problems of limited bandwidth, large propagation delay, unstable links, and limited node computing and energy resources in underwater acoustic channels, the present invention aims to overcome the shortcomings of existing technologies and proposes an authentication key negotiation method suitable for underwater acoustic communication.

[0005] In view of this, the present invention proposes an authentication key negotiation method suitable for underwater acoustic communication, comprising: Initialization phase: Underwater nodes Alice and Bob pre-construct a polynomial ring. And determine the common parameters; Key generation phase: The underwater node Alice extracts the physical layer random features of the underwater acoustic channel using the local channel estimation results and quantizes them into a raw random bit sequence. This sequence is then hashed to obtain a random seed. The private key and error term are generated from the random seed, and the public key is calculated accordingly. And send it to the underwater node Bob; Encapsulation Phase: Underwater node Bob encapsulates the message containing authentication information along with the public key. Generate a pre-key, sample based on the randomness of the physical channel to generate the next round's private key and error term, encapsulate them into ciphertext through compression operations to generate the current round's session key. The encrypted message is sent to the underwater node Alice, and the public and private keys for the next round are saved for subsequent decryption. Decapsulation Phase: The underwater node Alice decompresses the ciphertext and performs joint verification of the ciphertext's legitimacy using authentication information. If legitimate, it generates the session key for this round. Otherwise, the decapsulation operation will be terminated.

[0006] As an improvement to the above method, both underwater nodes Alice and Bob employ OTFS modulation and possess local channel estimation capabilities. The two underwater nodes exhibit time-delay-Doppler domain inter-channel stability. Each delay grid and A Doppler grid.

[0007] As an improvement to the above method, the common parameters determined in the initialization phase include: Polynomial ring polynomial degree in Dimension of the module Modulus of polynomial coefficients Random seed and a random uniform matrix used for public key and ciphertext generation. .

[0008] As an improvement to the above method, in the key generation stage, the generated original random bit sequence is: ,in,

[0009] To perform channel estimation on the pilot signal, the estimation matrix is ​​obtained. This is a quantification threshold.

[0010] As an improvement to the above method, in the key generation stage, the original random bit sequence is... A random seed is generated after hash processing. Generate a private key according to the following formula. With error term :

[0011] in It is a central binomial distribution with parameters The range of values ​​for the distribution is defined. Indicates an expandable output function; according to , Calculate the public key ;in, Represents a random uniform matrix; Save private key and the public key Send the underwater node Bob.

[0012] As an improvement to the above method, the encapsulation stage specifically includes: The underwater node Bob concatenates its ID, location, and timestamp into a message containing authentication information. ,according to With the received public key Generate prekey ; The original random bit sequence is obtained through underwater acoustic channel estimation. Use hashing to generate random seeds And generate the private key for the next round. and error terms , ,Right now , ; Based on the private key and error terms , Original random bit sequence Using compression functions The message Encapsulated as ciphertext ; According to the prekey and ciphertext Generate the session key for this round. Send to the underwater node Alice; Retain the public key from this round and private key .

[0013] As an improvement to the above method, the decapsulation stage specifically includes: The underwater node Alice uses a decompression function For ciphertext Unzip and combine with the private key Restore message ; according to The authentication information in the file obtains the sender's ID number. ,Location and timestamp The following joint verification was performed: Check if it matches the local node list; if not, terminate authentication immediately. Timestamp Difference from the current time Comparison: If Then it is determined that the message has expired or been tampered with. For the current time, To delay the transmission time, This represents the maximum permissible delay. According to the current time Propagation delay Estimate the actual location of underwater node Bob ,like and If the deviation exceeds the set threshold, a position anomaly marker will be triggered; If all the above verifications pass, the ciphertext is determined to be encrypted. The sender is legitimate, according to and Regenerate the prekey This generates the session key for this round. .

[0014] As an improvement to the above method, the method further includes: the next round of the session phase: the two communicating parties use the public and private keys and session state retained in this round of the session to complete identity authentication and key update, and execute the process in a loop to achieve a low-overhead continuous session key update mechanism.

[0015] As an improvement to the above method, the method further includes: when a round of ciphertext loss or demodulation failure causes the states of both parties to become out of sync, both parties re-execute each stage of the above method.

[0016] Compared with the prior art, the advantages of the present invention are: 1. Extract the physical layer random features of the underwater acoustic channel using the local channel estimation results, and use them as random seeds in the generation process of public and private keys, thereby enhancing the randomness of the key generation process and reducing the possibility of the key being predicted or reproduced.

[0017] 2. The sender's ID, location, and timestamp are combined to construct authentication information and embedded in ciphertext, thus associating the ciphertext with the sender's legitimate information. Through joint verification of identity matching, message freshness, and location consistency, the legitimacy of the received ciphertext is comprehensively judged. Only when all three satisfy security constraints is the ciphertext determined to originate from a legitimate node; otherwise, it is marked as a malicious node. This achieves effective detection of replay and spoofing attacks in underwater acoustic communication.

[0018] 3. During the ciphertext encapsulation process, the public and private keys required for the next round of the session are generated and retained synchronously, avoiding subsequent additional public key transmission processes, thereby saving bandwidth, reducing the number of interactions, and improving communication efficiency. After the initial session is completed, both communicating parties use the public and private keys retained from the previous round of the session and the session state to complete identity authentication and key updates, realizing a low-overhead continuous session key update mechanism. Attached Figure Description

[0019] Figure 1 This is a flowchart of an authentication key negotiation method applicable to underwater acoustic communication according to the present invention; Figure 2 This is a diagram of the underwater acoustic channel response in the North Atlantic Ocean. Figure 3 This is a diagram of the underwater acoustic channel response in the waters near Hawaii. Detailed Implementation

[0020] This invention provides an authentication key negotiation method suitable for underwater acoustic communication. The method is based on Kyber512 cryptography, combines OTFS for channel modeling in the delay-Doppler domain, and utilizes the bit sequence obtained from channel estimation to enhance the randomness of the private key and error term, thereby constructing a quantum-resistant key encapsulation mechanism. During the negotiation process, node ID, location information, and timestamps are introduced to achieve joint verification of the legitimacy and message freshness of both communicating parties. Addressing the high latency and narrow bandwidth characteristics of underwater acoustic communication, a low-overhead continuous session key update mechanism is designed, reducing the number of one-way transmissions per round after the initial session to once to achieve subsequent key updates.

[0021] Specifically, the following steps are included: (1) System initialization phase: Alice and Bob, the two communicating parties, pre-output security parameters and construct a polynomial ring. Determine the common parameters of the system; (2) Key generation stage: Alice uses the local channel estimation results to extract the physical layer random features of the underwater acoustic channel and quantizes them into the original random bit sequence. The sequence hash is processed to obtain a random seed, which is then used to sample the private key. With error term Calculate the public key And send it to Bob; (3) Encapsulation stage: Bob encapsulates the message containing authentication information. With public key Generate prekey The next round of private keys is generated based on the randomness of physical channel sampling. and error terms , Encapsulate ciphertext through compression operations And generate the session key for this round. Finally, the encrypted text is sent to Alice, and the public and private keys for the next round are saved for subsequent decryption. (4) Decompression stage: Alice decompresses the ciphertext to obtain the message. It checks Bob's legitimacy based on the node ID, location, and timestamp; if legitimate, it generates the key for this round. Otherwise, terminate the decapsulation operation; (5) Next round of session phase: After the initial session is completed, the two communicating parties use the public and private keys and session state retained from the previous session to complete identity authentication and key update, realizing a low-overhead continuous session key update mechanism.

[0022] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0023] Example Embodiments of the present invention provide an authentication key negotiation method suitable for underwater acoustic communication.

[0024] 1. Specific implementation: Consider two legitimate underwater nodes, Alice and Bob, negotiating a key via an underwater acoustic channel. Both ends of the underwater nodes use OTFS modulation and have local channel estimation capabilities. Alice is responsible for key generation and publishing the public key. Bob uses the public key to encapsulate the key and sends the ciphertext back to Alice. Alice decapsulates the key, and both parties share the session key. In a continuous session scenario, roles are swapped in subsequent rounds to achieve two-way authentication. The scheme includes five steps: initialization, key generation, encapsulation, decapsulation, and the next session round. The specific process is as follows.

[0025] (1) Initialization During the initialization phase, Alice and Bob pre-entered security parameters. ,according to Select system common parameters , , And construct a polynomial ring In Kyber, a polynomial ring is defined over a finite field. Above, set , ,parameter , , Defined ring The properties of which The modulus of the polynomial coefficients. Indicates ring The degree of the polynomial in the middle Indicated as a module Dimension; random uniform matrix The generation is based on a random seed. It was decided that, in order to save the overhead of a 32-byte random seed when transmitting the public key, From public pilot With conversation rounds : According to the seed Sampling yields a random uniform matrix ,Right now ;in, For an expandable output function, if As input, the generator needs to follow a distribution. Output Then it is recorded as After initialization, both communicating parties obtain the common parameters required for subsequent key generation and encapsulation processes, including polynomial ring parameters. , , Random seed And random matrices used for public key and ciphertext generation .

[0026] (2) Key generation Underwater acoustic channels are affected by factors such as ocean currents, temperature, salinity, and environmental noise, and their channel characteristics change continuously over time, exhibiting strong randomness. In the key generation stage, this paper utilizes local channel estimation results to extract the physical layer random features of the underwater acoustic channel, using these features as random seeds in the public and private key generation process. This enhances the randomness of the key generation process and reduces the possibility of key prediction or reproduction.

[0027] Assuming the OTFS system contains in the delay-Doppler domain Each delay grid and A Doppler grid is used, and the receiver obtains the estimation matrix by performing channel estimation on the pilot signal. ,in Indicates that it is located in the delay With Doppler The complex gain at the given point is used to extract channel amplitude features and obtain the original random bit sequence through quantization. : in The quantization threshold is used. This sequence is generated by Alice and Bob's independent local physical layer processes, without being transmitted in plaintext through the channel, and its distribution is determined by the actual channel state, making it difficult for an adversary to reproduce.

[0028] Next, Alice will use the original random bit sequence A random seed is generated after hash processing. ,Right now random seed Used to generate a private key With error term : ,in The central binomial distribution is defined as: sampling Output ,parameter The range of values ​​for the distribution is defined.

[0029] Finally, Alice calculates the public key. , Store the private key and the public key The key generation is completed after it is sent to Bob.

[0030] (3) Packaging Traditional key encapsulation mechanisms only encrypt random messages to generate ciphertext. In the encapsulation stage, this paper constructs authentication information using the sender's ID, location, and timestamp, embedding it into the ciphertext to associate the ciphertext with the sender's legitimate information. Considering the large propagation delay, limited bandwidth, and high error rate of underwater acoustic channels, the public and private keys required for the next round of sessions are generated and retained simultaneously during the ciphertext encapsulation process. This avoids subsequent additional public key transmission processes, saving bandwidth, reducing the number of interactions, and improving communication efficiency.

[0031] First, Bob's... The message is obtained by concatenating the location and timestamp. Then generate a pre-key. : The original random bit sequence is obtained through underwater acoustic channel estimation. Use hashing to generate random seeds And generate the private key for the next round. and error terms , ,Right now .

[0032] Secondly, Bob used the compression function Encapsulated ciphertext The formula is .in, , These are the ciphertext compression parameters. The compression operation effectively reduces the ciphertext size while ensuring correct decapsulation, thus reducing the communication resources required for transmitting the ciphertext.

[0033] Finally, Bob generates the session key for this round. The formula is . ciphertext Send it to Alice and keep the public-private key pair for the next round. When the next session is established, Bob can directly use his private key to decrypt the ciphertext sent by Alice.

[0034] (4) Decapsulation The open nature of underwater acoustic channels makes the communication process vulnerable to various attacks. During the decapsulation stage, this paper uses a joint verification of identity matching, message freshness, and location consistency to comprehensively determine the legitimacy of the received ciphertext. Only when all three satisfy the security constraints is the ciphertext determined to originate from a legitimate node; otherwise, it is marked as a malicious node. This approach effectively detects attacks such as replay and spoofing in underwater acoustic communication.

[0035] Alice uses decompression functions For ciphertext Unzip: and with private key Restore message The formula is .

[0036] During the authentication phase, the first step is to check whether the sender Bob's identity is legitimate, i.e., to confirm the message. In Check if it matches the local node list; if not, terminate authentication immediately; calculate the timestamp received by Alice. Difference from the current time ,like ( To delay the transmission time, If the maximum allowable delay is used, the message is determined to be expired or tampered with. The position of the declaration in the middle It is in the timestamp Alice's location, based on the current time Propagation delay Estimate Bob's actual position If the location is declared and estimated position If the deviation exceeds a set threshold, a location anomaly marker is triggered. Considering that the propagation delay of the underwater acoustic channel is easily affected by environmental factors, location verification is mainly used as a supplementary basis to improve the ability to identify abnormal sessions. The final legitimacy needs to be comprehensively judged by combining the node ID and timestamp verification results. If it is determined to be an illegal node, the decapsulation operation is terminated.

[0037] Finally, Alice regenerates the prekey after verifying the sender's legitimacy. : And based on the formula Generate a session key.

[0038] (5) Next round of conversation After the initial session is completed, the two communicating parties use the public and private keys and session state retained from the previous session to complete identity authentication and key update, realizing a low-overhead continuous session key update mechanism.

[0039] After each round of conversation, the roles of the two parties are switched, with Alice becoming the encapsulating party in this round. Let Alice's role in this round be... The location and timestamp are respectively , , Received news Alice uses the public key embedded in the previous ciphertext. With messages Generate prekey And will embed the new ciphertext of the next round's public key. Send to Bob and receive the session key for this round. Bob based his analysis on the ciphertext. The private key retained from the previous round Decapsulation to obtain the message Then verify Alice's legitimacy and the correctness of the ciphertext, and generate the session key for this round. Subsequent rounds will execute this process cyclically. If the ciphertext is lost or demodulation fails in a round, causing the states of both parties to become out of sync, both parties will re-execute the initial session process, that is, the initiator will resend the public key and the receiver will return the ciphertext, and subsequent rounds will still be one-way transmissions.

[0040] 2. Performance Comparison Analysis (1) Communication overhead Table 1. Comparison of Communication Costs (B)

[0041] Table 1 compares the communication costs of the present invention and Kyber512, including the sender, receiver, amount of data to be transmitted at the cryptographic layer, and number of interactions in the session. In the present invention, the random number is generated by the session rounds during key generation, eliminating the need to transmit an additional seed, thus reducing the transmission volume by 32 bytes compared to the original Kyber512. The receiver uses a compression function to reduce the ciphertext size to 768 bytes. The next session round uses the information in the ciphertext as the public key. Therefore, only one one-way transmission is needed to generate the session key after the initial session.

[0042] (2) Key consistency rate To evaluate the robustness and adaptability of the proposed solution, two sets of measured channel data were used in the experiment. Data 1 was collected in June 2010 in the North Atlantic Ocean (40.2°N, 70.5°W), with a water depth of approximately 100 m. The transmitter and receiver were located at depths of approximately 30–60 m and 50 m, respectively, with a communication distance of 3–7 km. The signal center frequency was 13 kHz, the bandwidth was 5 kHz, the receiver was a 12-element vertical receiving array with an element spacing of 0.12 m, and the transceiver platform was in a mobile state. Data 2 was collected in June 2011 in the waters near Hawaii (22.1°N, 159.8°W), with a water depth of approximately 100 m. The transmitter and receiver were located approximately 50 m underwater, with a communication distance of 3 km. The signal center frequency was 13 kHz, the bandwidth was 6.25 kHz, the receiver was a 24-element vertical receiving array with an element spacing of 0.05 m, and the transceiver platform was stationary. Figure 2 , Figure 3 The figures show the underwater acoustic channel responses in two different sea areas. The OTFS parameters are set as follows: , The proposed method employs Quadrature Phase Shift Keying (QPSK) modulation. 1000 sessions were independently run in two different underwater acoustic channel environments, comparing the proposed method with Kyber512. Using key consistency rate As an evaluation metric, it is used to calculate the proportion of schemes that obtain the same session key after multiple key negotiations, and its definition is as follows: in, This indicates the number of experiments that the scheme generates completely consistent session keys. The total number of experiments is represented. Table 2 shows the comparison of key consistency rates for different schemes under two measured underwater acoustic channels.

[0043] Table 2 Comparison of key consistency rates of different schemes under different underwater acoustic channel conditions

[0044] As shown in Table 2, the key consistency rate of the proposed solution is higher than that of Kyber512 in both underwater acoustic channel environments. Specifically, under the North Atlantic near-shore channel conditions, the key consistency rate of the proposed solution is 92.1%, an improvement of 8.7% compared to Kyber512's 83.4%; under the Hawaiian near-shore channel conditions, the key consistency rate of the proposed solution is 84.8%, an improvement of 14.3% compared to Kyber512's 70.5%. The proposed solution, by introducing the random characteristics of the underwater acoustic channel physical layer and a low-interaction continuous session mechanism, can effectively reduce the impact of channel interference on the key negotiation results and increase the success probability of both communicating parties generating a consistent session key. Therefore, the proposed solution is more suitable for underwater acoustic communication scenarios with narrow bandwidth, high latency, and high bit error rate compared to Kyber512.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for authentication key negotiation suitable for underwater acoustic communication, comprising: Initialization phase: Underwater nodes Alice and Bob pre-construct a polynomial ring. And determine the common parameters; Key generation phase: The underwater node Alice extracts the physical layer random features of the underwater acoustic channel using the local channel estimation results and quantizes them into a raw random bit sequence. This sequence is then hashed to obtain a random seed. The private key and error term are generated from the random seed, and the public key is calculated accordingly. And send it to the underwater node Bob; Encapsulation Phase: Underwater node Bob encapsulates the message containing authentication information along with the public key. Generate a pre-key, sample based on the randomness of the physical channel to generate the next round's private key and error term, encapsulate them into ciphertext through compression operations to generate the current round's session key. The encrypted message is sent to the underwater node Alice, and the public and private keys for the next round are saved for subsequent decryption. Decapsulation Phase: The underwater node Alice decompresses the ciphertext and performs joint verification of the ciphertext's legitimacy using authentication information. If legitimate, it generates the session key for this round. Otherwise, the decapsulation operation will be terminated.

2. The authentication key negotiation method for underwater acoustic communication according to claim 1, characterized in that, Both underwater nodes Alice and Bob employ OTFS modulation and possess local channel estimation capabilities. The two underwater nodes exhibit time-delay-Doppler domain inter-channel characteristics. Each delay grid and A Doppler grid.

3. The authentication key negotiation method for underwater acoustic communication according to claim 1, characterized in that, The common parameters determined during the initialization phase include: Polynomial ring polynomial degree in Dimension of the module Modulus of polynomial coefficients Random seed and a random uniform matrix used for public key and ciphertext generation. .

4. The authentication key negotiation method for underwater acoustic communication according to claim 2, characterized in that, During the key generation stage, the generated original random bit sequence is: ,in, To perform channel estimation on the pilot signal, the estimation matrix is ​​obtained. This is a quantification threshold.

5. The authentication key negotiation method for underwater acoustic communication according to claim 2, characterized in that, In the key generation stage, the original random bit sequence A random seed is generated after hash processing. Generate a private key according to the following formula. With error term : in It is a central binomial distribution with parameters The range of values ​​for the distribution is defined. Indicates an expandable output function; according to , Calculate the public key ;in, Represents a random uniform matrix; Save private key and the public key Send the underwater node Bob.

6. The authentication key negotiation method for underwater acoustic communication according to claim 5, characterized in that, The packaging stage specifically includes: The underwater node Bob concatenates its ID, location, and timestamp into a message containing authentication information. ,according to With the received public key Generate prekey ; The original random bit sequence is obtained through underwater acoustic channel estimation. Use hashing to generate random seeds And generate the private key for the next round. and error terms , ,Right now , ; Based on the private key and error terms , Original random bit sequence Using compression functions Message Encapsulated as ciphertext ; According to the prekey and ciphertext Generate the session key for this round. Send to the underwater node Alice; Retain the public key from this round and private key .

7. The authentication key negotiation method for underwater acoustic communication according to claim 1, characterized in that, The decapsulation stage specifically includes: The underwater node Alice uses a decompression function For ciphertext Unzip and combine with the private key Restore message ; according to The authentication information in the file obtains the sender's ID number. ,Location and timestamp The following joint verification was performed: Check if it matches the local node list; if not, terminate authentication immediately. Timestamp Difference from the current time Comparison: If Then it is determined that the message has expired or been tampered with. For the current time, To delay the transmission time, This represents the maximum permissible delay. According to the current time Propagation delay Estimate the actual location of underwater node Bob ,like and If the deviation exceeds the set threshold, a position anomaly marker will be triggered; If all the above verifications pass, the ciphertext is determined to be encrypted. The sender is legitimate, according to and Regenerate the prekey This generates the session key for this round. .

8. The authentication key negotiation method for underwater acoustic communication according to claim 1, characterized in that, The method further includes: the next round of the session phase: the two communicating parties use the public and private keys and session state retained in this round of the session to complete identity authentication and key update, and execute it in a loop to realize a low-overhead continuous session key update mechanism.

9. The authentication key negotiation method for underwater acoustic communication according to claim 8, characterized in that, The method further includes: when a round of ciphertext loss or demodulation failure causes the states of both parties to become out of sync, both parties re-execute each stage of claim 1.

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