A secure collaborative computing method for drones based on certificateless homomorphic network coding signatures

Abstract

This invention belongs to the field of cryptography and network security and provides a method for secure collaborative computing of unmanned aerial vehicles (UAVs) based on certificateless homomorphic network coding signatures. It aims to address the security issues of data transmission in collaborative computing among UAV swarms. The method primarily includes: KGC (Keeper Group Code) initializes the Internet of Things (IoT) data transmission system by generating private and public parameters. It uses the security parameters and the dimension of the augmented vector as input, and runs the Setup algorithm to generate a bilinear group, a master key, and a hash function. The UAV sends its ID to the KGC for registration and obtains a portion of its private key from the KGC. To defend against contamination attacks, the user divides the data packet into several vectors before sending it and generates signatures for the vectors. After receiving the data packet transmitted over the channel, each UAV node performs an integrity check on the received data packet, discarding any damaged packets and merging the undamaged packets. If the node is an intermediate node, it sends the vector and signature data packet to the downstream node.

Description

Technical Field

[0001] The present invention belongs to the field of cryptography and network security, and proposes a secure collaborative computing method for unmanned aerial vehicles based on certificateless homomorphic network coding signatures. Background Art

[0002] With the rapid development of drone technology, its applications have expanded from its initial military applications to include civilian applications in agriculture, logistics, environmental monitoring, news reporting, search and rescue, and filmmaking. Drone swarm technology has been developed to address even more complex application scenarios. However, drone computing power is very limited, making it difficult to train neural network models or make complex decisions. The computing power of a single drone alone is insufficient to adapt to complex environments. Therefore, collaborative computing in drone swarms is particularly important in these scenarios. Drone swarms need to address the insufficient computing power of a single drone through edge-cloud or edge-edge collaboration.

[0003] Collaborative computing involves extensive data transmission and sharing, presenting numerous security challenges that need to be addressed in practice. For example, a malicious drone user could inject corrupted data packets into the communication network to launch a contamination attack. Honest nodes would then linearly combine the corrupted packets with valid data packets, causing the contaminated data to spread throughout the network. Since the destination node cannot reply to the original data, malicious attackers can easily launch a distributed denial-of-service attack against the information transmission system for drone collaborative computing based on network coding.

[0004] To this end, the present invention proposes a UAV secure collaborative computing technology based on certificateless homomorphic network coding signatures. This method does not require certificate generation, verification and management operations, and realizes the authentication of data packet validity and defense against pollution attacks.

[0005] Previously, signature authentication algorithms between drones mostly employed certificate-based or identity-based signature algorithms. Certificate-based signature algorithms not only require cumbersome certificate generation, storage, and verification, but also require a reliable third-party KGC to ensure the confidentiality of keys and certificates. While identity-based signature algorithms eliminate the need for certificates, avoiding the tedious certificate-related operations and reducing communication overhead, they still require a reliable third-party KGC for key generation and storage, making them vulnerable to attacks from collusion between the KGC and an adversary.

[0006] Drones have limited computing power and storage space. Excessive communication overhead can significantly impact the communication efficiency and operational speed of the drone network. Furthermore, extensive operations such as certificate storage, management, and verification consume the drone's memory and limited computing power. Therefore, the signature authentication scheme used in drone systems needs to minimize communication, computing, and storage overhead to accommodate the limited computing power of the drone itself.

[0007] The introduction of a certificateless signature system solves this problem. Not only does it eliminate the need for certificates in the algorithm, but the KGC only holds a portion of the private key, preventing collusion with an adversary to attack the system. However, existing certificateless signature algorithms are vulnerable to contamination attacks. Malicious drone users can inject corrupted data packets into the communication network to carry out a contamination attack. Honest nodes will then linearly combine the corrupted data packets with valid data packets, causing the contaminated data to spread throughout the network.

[0008] Therefore, we propose a secure collaborative computing method for drones based on certificateless homomorphic network coding signatures. This method introduces network coding signatures on top of certificateless signature algorithms. By authenticating and verifying the integrity of messages in the communication network, we prevent the spread of corrupted or malicious data within the drone communication network, thereby defending against adversary contamination attacks. Summary of the Invention

[0009] The present invention provides a method for secure collaborative computing of unmanned aerial vehicles (UAVs) based on certificateless homomorphic network coding signatures. This method supports the verification of data validity and defense against contamination attacks in the data transmission link of collaborative computing. Considering that traditional signature keys based on certificates or identifiers require trusted third-party custody, this solution adopts a certificateless signature mechanism that does not require certificate generation, verification, and management, thus eliminating the need to worry about private key leakage by a third-party KGC. However, existing certificateless signature systems cannot resist contamination attacks, so the present invention introduces a network coding signature system to verify the correctness of messages to resist contamination attacks.

[0010] In order to achieve the above-mentioned purpose, the present invention adopts the following technical means:

[0011] The present invention provides a method for secure collaborative computing of unmanned aerial vehicles based on certificateless homomorphic network coding signatures, comprising the following steps:

[0012] A. System initialization: Input the security parameter λ and the dimension of the augmented vector N = N + m to the key generation center KGC, KGC initializes the authentication system, generates a bilinear group (G1, G2, G T ,P,e), from Select an s as the master key and calculate the master public key P pub =(g') s ;

[0013] Select four different cryptographic hash functions H1, H2, H3 and H4, which convert 0, 1 * Map to represents the multiplicative group of integers modulo p;

[0014] Among them, G1, G2, GT is a cyclic group of order p, where p is a prime number and p ≥ 2 λ , e is a bilinear mapping: G1×G2→G T , g' is the generator of G2\{1}, {1} represents the identity element in group G2, and G2\{1} represents the set of all elements in G2 excluding the identity element 1;

[0015] B User Registration: When the drone transmits data, it needs to register and obtain part of the private key from KGC The user sets the identity value ID and calculates the secret value X, and sends a registration application (ID, X) to KGC;

[0016] KGC selects a random number y and calculates Y, which is used to calculate part of the private key. And send it back to the drone, the drone verifies its validity, and if it is valid, calculates the complete private key and the complete public key, where X is (g') x , g' is the generator of G2\{1}, x is Random numbers in ;

[0017] C. Signature Generation: To defend against contamination attacks, the drone needs to divide the data into vectors and generate a signature before sending the data packet. Specifically:

[0018] The drone divides the generated data into m vectors And expand each vector to:

[0019]

[0020] The drone randomly selects an identifier id∈0,1 for V λ , and run the sign algorithm to generate the signature σ i , where V = span (v1, ..., v m ) is the subspace formed by m augmented vectors, and λ is the security parameter;

[0021] D. Data detection: Each drone node merges the data packets after receiving the data packets from the channel. The process is as follows: run the verification algorithm to perform integrity check on the received data packets, and perform integrity check on each vector v i and the corresponding signature σ i Verify the equation:

[0022]

[0023] Is it true? If so, all undamaged data with the same ID are combined and sent to the downstream drone node. and A data packet consisting of H1, H2, H3, and H4 are the hash functions selected in step A; Y represents a parameter used by KGC to calculate a partial private key in step B; j is an increment, representing the values ​​from g1 to g4. j , taking values ​​from h1 to h m ; X represents a secret value; e(·,·) represents a bilinear mapping; g j 、h j is a random number selected from G1\{1}; v i，j Represents the dimensions of the vector after splitting in step C; v i，n+j Take each dimension of vector V in turn; P pub Represents the master public key; in Represents H3(id, j) and v i，n+j The product of ; H3 represents the third hash function selected in step A; is the coding vector group divided in step C, For 's signature.

[0024] In the above technical solution, step A includes:

[0025] A1. Given the security parameter λ and the augmented vector dimension N = N + m as input, KGC runs the setup algorithm to perform the following operations:

[0026] A1.1. Generate a bilinear group tuple in and G T is a cyclic group of prime order p, p ≥ 2 λ , e: For a bilinear map, choose the generator and random selection where h m Indicates from Randomly select m h, g n Indicates from Randomly select n g;

[0027] A1.2. Randomly select an s as the master key and calculate the master public key P pub =(g′) s ;

[0028] A1.3. Choose four different {0, 1} λ Map to Cryptographic hash functions H1, H2, H3, H4;

[0029] A1.4. KGC publishes parameters params(λ, p, G1, G2, GT ,e,g′,P pub ,h1,…,h m ,g1,…,g m , H1, H2, H3, H4), and keep the master key msk=s confidential.

[0030] In the above technical solution, step B includes:

[0031] B1. The user sets his unique identity ID∈{0, 1}* and runs the set-secret-value algorithm to generate the drone’s secret value X:

[0032] Choose a random As a secret value calculation, calculate X = (g') x And send a registration application (ID, X) to KGC;

[0033] B2. After receiving the registration application, KGC runs the partial-private-key algorithm to generate a partial private key:

[0034] KGC chooses one Calculate Y = (g′) y And k = (y + H1 (ID, Y) · s) mod p and the partial private key d ID =(k, Y), then KGC calculates the hash mask Protecting Part of the Private Key and returns via the public drone communication network For drones, modp represents modular p operation;

[0035] B3. The drone receives After that, calculate And check the equation Is it true? If so, the drone ID considers k to be valid. After that, the drone sets the complete private key to SK ID ={k, x}, the complete public key is PK ID ={Y,X}.

[0036] In the above technical solution, step C includes:

[0037] C1. The drone divides the collected data into m vectors in Before transmission, the UAV sets the vector Expand to

[0038] V=span(v1,…,v m) is the subspace spanned by m augmented vectors;

[0039] C2. The drone randomly selects an identifier id∈0,1 for V λ , and run the Sign algorithm to generate a signature, that is, for each vector v i (i∈[1,m]) calculates the signature:

[0040]

[0041] In the above technical solution, step D includes:

[0042] D1. The drone node uses the verification algorithm to perform integrity verification on the received data packets, that is, for each vector v i and the corresponding signature σ i , check the equation:

[0043]

[0044] Is it established,

[0045] D2. The subset of indices of the packets to be combined, the coding coefficients Randomly selected, the intermediate node combines all undamaged packets with the same identifier id by running the Combine algorithm, and then the intermediate node transmits the packet generated by the combination vector to the downstream node. and signature The data packets that make up the

[0046]

[0047] The certificateless homomorphic network coding signature solution for secure collaborative computing of drones has the following advantages:

[0048] (1) Using a certificateless signature algorithm, no trusted third party is required.

[0049] (2) No need for tedious certificate authentication and management operations, saving communication overhead.

[0050] (3) Network coding can be used to efficiently authenticate the validity of messages.

[0051] (4) It can effectively resist pollution attacks from malicious users and ensure the reliability of data packets. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Flowchart of secure collaborative computing of drones with certificateless homomorphic network coding signatures. DETAILED DESCRIPTION

[0053] The following is a detailed description of the embodiments of the present invention. Although the present invention will be described and illustrated in conjunction with certain specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, modifications or equivalent substitutions of the present invention are intended to fall within the scope of the claims of the present invention.

[0054] In addition, in order to better illustrate the present invention, numerous specific details are given in the following detailed description. It will be understood by those skilled in the art that the present invention can also be implemented without these specific details.

[0055] The detailed algorithm flow is:

[0056] Step A, system initialization:

[0057] KGC initializes the certificateless homomorphic network coding signature UAV secure collaborative computing system by generating private and public parameters. The specific operations are as follows:

[0058] A1. Given the security parameter λ and the augmented vector dimension N = N + m as input, KGC runs the setup algorithm to perform the following operations:

[0059] A2. Generate a bilinear group tuple in and GT is a prime p-order cyclic group (p ≥ 2λ), e: For a bilinear map, Select the generator g′ and randomly select Select elements h1,…,h m ,g1,…,g n ;

[0060] A3. Randomly select an s as the master key and calculate the master public key P pub =(g′) s , g′ is the The generators selected in ;

[0061] A4. Select four different {0, 1} λ Map to Cryptographic hash functions H1, H2, H3, H4;

[0062] A5. KGC publishes parameters params = (λ, p, G1, G2, G T ,e,g′,P pub ,h1,…,h m ,g1,…,g m, H1, H2, H3, H4), and keep the master key msk=s confidential.

[0063] Step B, User Registration:

[0064] If a drone wants to transmit data securely through this system, it should register with the system and obtain a partial private key from KGC. The drone registration process consists of three steps:

[0065] B1. The drone sets its unique identity ID ∈ {0, 1}* and runs the set-secret-value algorithm to generate a secret value. The algorithm is as follows: Select a random As a secret value calculation, calculate X = (g') x And send a registration application (ID, X) to KGC.

[0066] B2. After receiving the registration application, KGC runs the partial-private-key algorithm to generate a partial private key: KGC selects a Calculate Y = (g′) y And k = (y + H1 (ID, Y) · s) mod p, and the partial private key d ID =(k, Y), then KGC calculates the hash mask Protecting Part of the Private Key and returned via the public drone communication network To the drone.

[0067] B3. The drone receives After that, calculate And check the equation Is it true? If so, the drone ID considers k to be valid. After that, the drone sets the complete private key to SK ID ={k, x}, the complete public key is PK ID ={Y,X}.

[0068] Step C, signature generation:

[0069] To defend against pollution attacks, the drone generates a valid signature for the data vector before sending the data packet. This process includes two steps:

[0070] C1. The drone divides the collected data into m vectors in Before transmission, the drone transforms the vector Expanded to:

[0071]

[0072] Let V = span (v1, ..., v m ) is the subspace spanned by m augmented vectors.

[0073] C2. The drone randomly selects an identifier id∈{0, 1} for V λ , and run the Sign algorithm to generate a signature, that is, for each vector v i (i∈[1,m]) calculates the signature:

[0074]

[0075] In drone communication networks, each data packet consists of a header and a payload. The header includes user information, a file identifier, and a signature of some augmentation vector. The payload carries the augmentation vector. Finally, the user sends the data packet to a downstream transmission node.

[0076] Step D, data detection:

[0077] After receiving the data packets from the channel, other drones will check the integrity of the data packets and merge the undamaged data packets. The processing steps are as follows:

[0078] D1. The drone node uses the verification algorithm to perform integrity verification on the received data packets. That is, for each vector v i and the corresponding signature σ i , check the equation: Is it established? If the above equation holds, the verification algorithm outputs 1, indicating that the packet is correct. Otherwise, the verification algorithm outputs 0 and the packet is discarded. If this drone node is the destination node, network coding decoding methods can be used to recover the original data. If this node is an intermediate node, the next step will be carried out.

[0079] D2. Note The subset of indices of the packets to be combined, the coding coefficients Randomly selected. The intermediate node combines all undamaged packets with the same identifier id by running the Combine algorithm. That is, it calculates: and the corresponding Afterwards, the intermediate node transmits the combined vector and signature The data packet consists of.

[0080] At this point, the secure certificateless message transmission process ends.

[0081] In summary, this secure drone collaborative computing solution, based on certificateless homomorphic network coding signature technology, aims to address the security issues of data transmission in drone swarm collaborative computing. Its technical effectiveness is analyzed as follows:

[0082] System Initialization: By generating bilinear groups and cryptographic hash functions, we address the issue of secure initialization of system parameters. This provides a fundamental security framework for subsequent user registration and data transmission. Compared to traditional certificate-based systems, this eliminates the need for a trusted third-party certificate authority, reducing security risks.

[0083] User registration: Part of the private key is obtained through user registration, which enables the verification of drone identity and the distribution of partial keys. This avoids security issues caused by collusion between a third party and an adversary to leak the private key.

[0084] Signature Generation: Data packets are divided into multiple vectors before transmission, and a signature is generated for each vector, authenticating the message within the network and effectively defending against contamination attacks. This ensures the integrity and reliability of data transmission while increasing the system's resistance to malicious attacks.

[0085] Data Detection: After receiving a data packet, the drone node performs authentication and integrity verification, discarding unauthenticated and damaged packets and merging authenticated and intact packets. This mechanism effectively prevents the spread of contaminated data in the network and ensures the quality of data transmission.

[0086] Certificateless Signature Mechanism: This solution uses a certificateless signature mechanism, eliminating the need for cumbersome certificate authentication and management operations, saving communication overhead. This makes the system more flexible and efficient, and suitable for resource-limited drone environments.

[0087] In summary, this solution realizes the secure data transmission of drone swarms in collaborative computing through certificateless homomorphic network coding signature technology, with high security, efficiency and flexibility.

Claims

1. A secure collaborative computing method for drones based on certificateless homomorphic network coding signatures, characterized in that: The following steps are involved: A. System initialization: Input the security parameter λ and the dimension of the augmented vector N = N + m to the key generation center KGC, KGC initializes the authentication system and generates a bilinear group (G1, G2, G T ,P,e), from Select an s as the master key and calculate the master public key P pub =(g') s ; Choose four different cryptographic hash functions H1, H2, H3 and H4, which map 0.1* to represents the multiplicative group of integers modulo p; Among them, G1, G2, G T is a cyclic group of order p, where p is a prime number and p ≥ 2 λ , e is a bilinear mapping: G1×G2→G T , g' is the generator of G2\{1}, {1} represents the identity element in group G2, and G2\{1} represents the set of all elements in G2 excluding the identity element 1; B User Registration: When the drone transmits data, it needs to register and obtain part of the private key from KGC The user sets the identity value ID and calculates the secret value X, and sends a registration application (ID, X) to KGC; KGC selects a random number y and calculates Y, which is used to calculate part of the private key. And send it back to the drone, the drone verifies its validity, and if it is valid, calculates the complete private key and the complete public key, where X is (g') x , g' is the generator of G2\{1}, x is Random numbers in ; C. Signature Generation: To defend against contamination attacks, the drone needs to divide the data into vectors and generate a signature before sending the data packet. Specifically: The drone divides the generated data into m vectors And expand each vector to: The drone randomly selects an identifier id∈0,1 for V λ , and run the sign algorithm to generate the signature σ i , where V = span (v1, ..., v m ) is the subspace formed by m augmented vectors, and λ is the security parameter; D. Data detection: Each drone node merges the data packets after receiving the data packets from the channel. The process is as follows: run the verification algorithm to perform integrity check on the received data packets, and perform integrity check on each vector v i and the corresponding signature σ i Verify the equation: Is it true? If so, all undamaged data with the same ID are combined and sent to the downstream drone node. and A data packet consisting of H1, H2, H3, and H4 are the hash functions selected in step A; Y represents a parameter used by KGC to calculate a partial private key in step B; j is an increment, representing the values ​​from g1 to g4. j , taking values ​​from h1 to h m ; X represents a secret value; e(·,·) represents a bilinear mapping; g j 、h j is a random number selected from G1\{1}; v i，j Represents the dimensions of the vector after splitting in step C; v i，n+j Take each dimension of vector V in turn; P pub Represents the master public key; in Represents H3(id,j) and v i，n+j The product of ; H3 represents the third hash function selected in step A; is the coding vector group divided in step C, For 's signature.

2. A method for secure collaborative computing of unmanned aerial vehicles based on certificateless homomorphic network coding signatures according to claim 1, characterized in that: Step A includes: A1. Given the security parameter λ and the augmented vector dimension N = N + m as input, KGC runs the setup algorithm to perform the following operations: A1.

1. Generate a bilinear group tuple in and G T is a cyclic group of prime order p, p ≥ 2 λ , For a bilinear map, choose the generator and random selection where h m Indicates from Randomly select m h, g n Indicates from Randomly select n g; A1.

2. Randomly select an s as the master key and calculate the master public key P pub =(g′) s ; A1.

3. Choose four different {0, 1} λ Map to Cryptographic hash functions H1, H2, H3, H4; A1.

4. KGC publishes parameters params = (λ, p, G1, G2, G T ,e,g′,P pub , h 1， …, h m ,g1,…,g m , H1, H2, H3, H4), and keep the master key msk=s confidential.

3. The method for secure collaborative computing of unmanned aerial vehicles based on certificateless homomorphic network coding signatures according to claim 2, characterized in that: Step B includes: B1. The user sets his unique identity ID∈{0, 1} * And run the set-secret-value algorithm to generate the drone’s secret value X: Choose a random As a secret value calculation, calculate X = (g') x And send a registration application (ID, X) to KGC; B2. After receiving the registration application, KGC runs the partial-private-key algorithm to generate a partial private key: KGC chooses one Calculate Y = (g′) y And k = (y + H1 (ID, Y) · s) mod p and the partial private key d ID =(k, Y), then KGC calculates the hash mask Protecting Part of the Private Key and returns via the public drone communication network For drones, modp represents modular p operation; B3. The drone receives After that, calculate And check the equation Is it true? If so, the drone ID considers k to be valid. After that, the drone sets the complete private key to SK ID ={k, x}, the complete public key is PK ID ={Y,X}.

4. The method for secure collaborative computing of unmanned aerial vehicles based on certificateless homomorphic network coding signatures according to claim 3, characterized in that: Step C includes: C1. The drone divides the collected data into m vectors in Before transmission, the drone sets the vector Expand to V=span(v1,…,v m ) is the subspace spanned by m augmented vectors; C2. The drone randomly selects an identifier id∈0,1 for V λ , and run the Sign algorithm to generate a signature, that is, for each vector v i (i∈[1,m]) calculates the signature:

5. The method for secure collaborative computing of unmanned aerial vehicles based on certificateless homomorphic network coding signature according to claim 4, characterized in that: Step D includes: D1. The drone node uses the verification algorithm to perform integrity verification on the received data packets, that is, for each vector v i and the corresponding signature σ i , check the equation: Is it established, D2. The subset of indices of the packets to be combined, the coding coefficients Randomly selected, the intermediate node combines all undamaged packets with the same identifier id by running the Combine algorithm, and then the intermediate node transmits the packet generated by the combination vector to the downstream node. and signature The data packets that make up the

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