A method for authenticating a UAV cluster based on zero-knowledge proof

Abstract

This invention proposes a drone swarm authentication method based on zero-knowledge proof, belonging to the field of drone swarm secure communication technology. Its technical solution includes the following steps: S1, system initialization; S2, secondary drone registration before takeoff; S3, bidirectional authentication and key negotiation between secondary drones during flight; S4, dynamic networking of secondary drones. This invention combines zero-knowledge proof and elliptic curve cryptography to achieve drone swarm identity authentication. Through a two-stage design of pre-registration and online authentication, it significantly reduces the computational and communication overhead of in-flight authentication while ensuring drone identity privacy and communication security. It effectively resists typical threats such as man-in-the-middle attacks, impersonation attacks, replay attacks, and message tampering, avoiding single points of failure and communication bottlenecks caused by the central node.

Description

Technical Field

[0001] This invention relates to the field of secure communication technology for unmanned aerial vehicle (UAV) swarms, and in particular to a UAV swarm authentication method based on zero-knowledge proof. Background Technology

[0002] In recent years, with continuous breakthroughs in key areas such as flight control, environmental perception, and autonomous navigation, UAV swarm technology has become an important development direction for intelligent collaborative mission systems. By constructing a real-time communication network among multiple UAVs, UAV swarms can achieve efficient information sharing, distributed task decision-making, and dynamic allocation, thereby significantly improving the flexibility of mission execution, system robustness, and spatial coverage. With its collaborative flexibility, strong mission adaptability, and good scalability, UAV swarms have shown broad application prospects in many important fields such as military reconnaissance, disaster relief, logistics distribution, agricultural monitoring, and public safety, driving related industries towards intelligent and networked development.

[0003] In unmanned aerial vehicle (UAV) swarm systems, secure, reliable, and efficient communication between nodes is the cornerstone of ensuring overall collaborative effectiveness and mission success. However, unlike wired or controlled closed environments on the ground, UAV swarms operate in highly open, dynamically changing airspace that may face malicious attacks. They are often deployed in scenarios with complex terrain and variable electromagnetic environments, and may even be directly exposed to hostile cyberattacks. This environmental characteristic makes each node in the swarm vulnerable to various security threats such as identity spoofing, data eavesdropping, and message tampering. More seriously, attackers may physically capture legitimate nodes and launch infiltration and sabotage from within. These threats not only endanger the security of individual UAVs but may also undermine the trust foundation and collaborative logic of the entire swarm. Therefore, the issues of UAV identity security and trusted authentication are becoming increasingly prominent, becoming a key bottleneck restricting the large-scale reliable application of UAV swarms.

[0004] To address the authentication problem of drone swarms, academia has conducted multi-path research. Existing solutions can be broadly categorized into three types: those based on Physically Unclonable Functions (PUFs), those based on Elliptic Curve Cryptography (ECC), and those based on blockchain. Physically Unclonable Functions (PUFs) utilize physical variations in semiconductor manufacturing processes to generate unique responses, providing drones with uncopyable physical identifiers and effectively resisting physical attacks. The paper "APUF and Fuzzy Extractor-Based UAV-Ground Station and UAV-UAV Authentication MechanismWith Intelligent Adaptation of Secure Sessions" by Raja Karmakar et al. proposes a UAAS scheme that combines PUF with a fuzzy extractor, achieving two-way authentication between drones and ground stations, as well as between drones themselves. It also introduces the Thompson sampling algorithm to dynamically adjust session duration to reduce idle time windows. However, the introduction of the fuzzy extractor introduces significant computational overhead, resulting in an overall efficiency lower than similar PUF schemes. The paper "Lightweight Security Authentication Method for Drones Based on Fuzzy Extractor" proposed by Chen Ruizheng et al. designs a lightweight security authentication scheme for drones that combines PUF and fuzzy extractor, achieving bidirectional authentication and key negotiation between drones through base station registration and pseudonym mechanism. However, in this scheme, all authentication interactions between drones need to be forwarded through the base station, which not only introduces significant communication latency and overhead, but also makes the base station a single point of failure, causing the entire cluster authentication service to collapse if it fails. The paper "Lightweight Drone-to-Ground Station and Drone-to-Drone Authentication Scheme for Internet of Drones" proposed by Qi Xie et al. designs a PUF authentication protocol that does not require the ground station to store drone information, supporting direct mutual authentication between drones and reducing the storage pressure on the ground station. However, this scheme does not consider cross-trust domain scenarios; when drones need to authenticate with ground stations in different domains or other drones, the protocol cannot be directly extended.

[0005] Elliptic Curve Cryptography (ECC), with its advantages of short keys, high security, and high computational efficiency, is widely used in the design of drone authentication protocols in resource-constrained environments. The paper "Provably Secure and Reliable Privacy-Preserving Authentication Scheme for Drone-to-Drone Communications in Internet of Autonomous Things" by Mohd Shari et al. proposes a provably secure and privacy-preserving authentication protocol, PSRS-D2D, for inter-drone communication in autonomous IoT. This scheme, based on ECC and hash functions, maintains lightweight characteristics while achieving two-way authentication and privacy protection. However, it only supports pairwise authentication and lacks an efficient group authentication mechanism, limiting its scalability in large-scale cluster scenarios. The paper "Certificate-Free Group Authentication Key Negotiation Protocol in Drone Networks" by Wang Yuecheng et al. proposes a group authentication key negotiation protocol based on certificate-free cryptography, employing a "head-slave" architecture to achieve lightweight authentication and dynamic node management for drone groups. However, this protocol relies excessively on the head node as a central node; the failure of the head node will prevent the entire group from completing key negotiation, posing a single point of failure risk. The paper "Research on Identity Authentication Scheme for UAV Communication Network" by Tao Xia et al. designs a lightweight authentication scheme based on ECC and message authentication codes, using a ground station as a trusted intermediary to achieve bidirectional identity authentication and session key negotiation between UAVs and the ground station, as well as between UAVs themselves. However, this scheme also relies on forwarding by the ground station and cannot support direct authentication between UAVs in wide-area cluster environments without ground station coverage.

[0006] Blockchain technology, with its decentralized, immutable, and traceable characteristics, offers a new approach to solving the single point of failure problem in centralized architectures. The paper "A blockchain authentication scheme for UAV-aided fog computing" by Xiaoyu Du et al. proposes a drone identity authentication scheme based on a fog node-assisted blockchain, registering drone information to the blockchain and using smart contracts and reputation mechanisms to achieve trusted authentication of drones across regions. However, this scheme is highly dependent on the reliability and performance of fog nodes, and the introduction of blockchain brings additional computational overhead and economic costs. Security vulnerabilities still exist in the design of reputation mechanisms and the handling of node failures. The paper "Identity Management and Authentication of a UAV Swarm Based on a Blockchain" by Pengbin Han et al. proposes a drone swarm identity management model based on Distributed Identifiers (DIDs), combining blockchain technology to achieve distributed authentication and secure communication across institutions. However, this scheme uses the PBFT consensus algorithm, and as the network scales up, the communication complexity increases significantly, potentially leading to performance bottlenecks. Furthermore, the computational latency introduced by encryption and authentication mechanisms may affect real-time performance when the number of drones is large.

[0007] In addition to the mainstream technologies mentioned above, some researchers have explored other lightweight authentication methods. The paper "A Low-Consumption Security Authentication Protocol for UAVs based on Embedded Message Authentication Code" by Rong Wei et al. proposes a low-power authentication protocol based on embedded message authentication codes. By reversibly embedding authentication information into encrypted data, it reduces transmission overhead while ensuring security. However, this scheme relies on complex data hiding and encryption / decryption operations, increasing the computational burden on resource-constrained UAVs; its security excessively depends on the collision resistance of hash functions and strict time synchronization, and it lacks signature protection for key fields, making it vulnerable to replay and forgery attacks, and lacking forward security. The paper "ARandom Label and Lightweight Hash-Based Security Authentication Mechanism for a UAV Swarm" by Feng Hu et al. designs an authentication scheme based on random labels and lightweight hash functions. It uses RC4 stream ciphers to protect the database and combines SHA-256 and SPONGENT-128 to generate irreversible random labels for authentication. Although the scheme performs well in terms of energy consumption, its security relies heavily on the key strength of the RC4 stream cipher and the collision resistance of the hash function. It is not strong enough to defend against replay attacks, man-in-the-middle attacks and label forgery, and is at risk of being cracked and impersonated.

[0008] In summary, existing drone authentication schemes each have their trade-offs in terms of security, efficiency, and decentralization. While PUF-based schemes offer hardware-level security, they are susceptible to environmental noise and require additional error correction mechanisms. ECC-based schemes offer high computational efficiency but often employ centralized architectures, creating single points of failure. Blockchain-based schemes achieve decentralized trust but face performance bottlenecks and resource consumption challenges. Other lightweight schemes often have security shortcomings. Of particular concern is that most schemes, when enabling direct mutual authentication between drones, still rely on central nodes such as ground stations, lead drones, or base stations as intermediaries or trust anchors, failing to truly achieve independent authentication and key negotiation between secondary drones. Summary of the Invention

[0009] To address the technical problems of existing UAV swarm authentication schemes, such as the risk of single point of failure of the central node, excessive computing and communication overhead during flight, insufficient protection of identity privacy, and difficulty in ensuring the security of dynamic networking, this invention provides a UAV swarm authentication method based on zero-knowledge proof. This method enables direct mutual authentication and session key negotiation between secondary machines, effectively resists various typical network attacks, and significantly reduces resource consumption during flight while ensuring identity privacy and communication security, thereby improving the security protection level and operational efficiency of UAV swarm authentication.

[0010] Based on a thorough investigation of current drone swarm authentication schemes and an in-depth analysis of their shortcomings, this invention proposes a partially decentralized authentication and key negotiation method that integrates zero-knowledge proofs and elliptic curve cryptography. This invention combines non-interactive zero-knowledge proofs, elliptic curve cryptography (ECC), and a pseudonym mechanism. Through a two-stage design of pre-registration and online authentication, it is applied to resource-constrained drone swarm environments, effectively addressing the technical drawbacks of existing schemes, such as reliance on a central node, high computational and communication overhead, and insufficient privacy protection.

[0011] Because this invention uses underlying cryptographic techniques, in order to clearly explain the principles and steps of this invention, relevant cryptographic knowledge will be explained first:

[0012] 1. Elliptic Curve Cryptography (ECC)

[0013] Elliptic Curve Cryptography (ECC) is based on the algebraic structure of elliptic curve point groups over finite fields. Let p be a prime number. For a finite field, defined in The equation of the non-singular elliptic curve on is: ,in And satisfy This is to ensure the curve is smooth. All points on the curve, together with the point at infinity, form an additive group, denoted as . For any two points Based on this, scalar multiplication can be defined as follows: ,in .

[0014] (1) Elliptic Curve Discrete Logarithm Problem (ECDLP)

[0015] Given the elliptic curve group Two points P and ,in Solving for the integer k is computationally infeasible. The difficulty of this problem forms the security foundation of ECC.

[0016] 2. Pedersen commitment

[0017] Pedersen commitment is a cryptographic commitment scheme based on the discrete logarithm hard problem. It uses two independent generators to combine the message with a random masking factor to generate a commitment value, ensuring concealment (the message cannot be inferred from the commitment) and binding (the content of the commitment cannot be tampered with), and supports additive homomorphic operations, that is, the product of commitments corresponds to the commitment of the sum of messages.

[0018] (1) Pedersen commitment

[0019] Assume the secret value to be promised is The specific steps are as follows:

[0020] Blinding factor: randomly selected. As a blinding factor, it ensures that even if m is the same, the result of each commitment is different, thus hiding the secret value.

[0021] Compute the commitment: In the elliptic curve additive group, where G and H are two cardinal points of the group, compute the commitment: .

[0022] 3. Zero-knowledge proof

[0023] Zero-knowledge proof (ZKP) is a cryptographic protocol that allows a prover to demonstrate the correctness of a statement to a verifier without revealing secret information. Its security is characterized by completeness (an honest prover can convince an honest verifier), reliability (a malicious prover cannot deceive), and zero-knowledge property (no additional information is revealed). Based on the interaction method, it is divided into interactive and non-interactive types. This paper adopts a non-interactive zero-knowledge proof based on the Sigma protocol and the Fiat-Shamir transform.

[0024] The Sigma protocol is a three-round interactive proof protocol that includes the following steps: Commitment: The prover is randomly selected. Calculate commitment Send to the validator. Challenge: The validator sends the challenge. Response: The prover calculates the response: (w is the prover's secret information) and send it to the verifier. Verification: The verifier verifies. (h is the public commitment or public key corresponding to the prover's secret evidence w) Whether it is true or not.

[0025] The Fiat-Shamir transformation can convert it into a non-interactive protocol. The transformation steps are as follows:

[0026] (1) Proofreader calculates commitment .

[0027] (2) Generate the challenge e = H(R) using a hash function, where e is the hash value of the commitment R.

[0028] (3) Calculate the response z = r + ew

[0029] (4) Send proof π = (R,z)

[0030] (5) After receiving π, the verifier recalculates e = H(a) and verifies it. .

[0031] Non-interactive zero-knowledge proofs maintain the security of the Sigma protocol while avoiding the interactive process, making them suitable for communication-constrained environments such as drone swarms.

[0032] For ease of understanding, the symbols and their meanings involved in this invention are first given in Table 1 below:

[0033] Table 1. Symbols and their meanings

[0034]

[0035] This invention is achieved through the following measures: a method for authenticating drone swarms based on zero-knowledge proofs, comprising the following steps:

[0036] S1, System initialization;

[0037] S2, Pre-flight registration of the secondary aircraft;

[0038] S3, In-flight secondary inter-aircraft two-way authentication and key negotiation;

[0039] S4, dynamic networking of secondary machines;

[0040] Further, step S1 includes:

[0041] S11, Head unit initialization;

[0042] S111, Head Machine The order is defined as a large prime number. Elliptic curve group G, generator P, select head machine master key The public key corresponding to the computing head machine ;

[0043] S112, Head Machine Choose a one-way collision-resistant hash function Public parameters Secretly store the master key .

[0044] Further, step S2 includes:

[0045] S21, secondary machine Kana generation;

[0046] S211, secondary machine Heading machine Submission includes real identity Registration application, head machine Calculate part of the kana after receiving. And send to the secondary machine Secondary machine Generate pseudonym secret value Based on secret value and some kana The secondary machine is calculated. kana ;

[0047] S22, secondary machine Voucher generation;

[0048] S221, secondary unit Generate random numbers Use the private key to calculate the corresponding public key. Randomly select secret value This is the credential key. Secondary machine. based on and Calculation vouchers ;

[0049] S222, secondary unit For private key and credentials private key Generate random blinding factors respectively , Calculate commitment and challenges And based on the blinding factor and and challenges Calculate the response and Output knowledge signature ;

[0050] S223, Generate current timestamp Using the head unit public key Regarding the message Encrypt the message Send to head unit .

[0051] S23, Head Machine Credential verification;

[0052] S231, Head Machine By message Extract message And verify its timestamp The validity of the function is then calculated, and the generated pseudonyms are then generated. ,judge If true, calculate the challenge value. Then judge the equation. Whether the equation holds true or not, if the equation holds true, then the secondary machine can be determined. A trusted entity;

[0053] S232, Head Machine Calculation generation identity document , correspondence Record to mapping table In the middle, and temporarily store the secondary machine credentials Remove from local storage;

[0054] S233, Head Machine After completing the credential verification and information registration for all secondary machines, use its own private key. For mapping table Obtain by signing And send the signature through a secure channel Send to secondary machine .

[0055] S234, secondary machine Use the head machine's public key Verify signature The validity of the signature is checked; if the signature is valid, the mapping table is saved. To local storage, otherwise the drone Registration failed, and you will be unable to join the drone cluster.

[0056] Further, step S3 includes:

[0057] S31, secondary unit in drone swarm To the secondary machine Send a two-way authentication request;

[0058] S311, secondary unit Generate secret value and from the mapping table Searching for secondary machines identity document Then based on , and Calculate the generated parameters ;

[0059] S312, secondary unit To construct a two-way authentication request, the method is as follows: generate the current timestamp. and calculate the signature. Then, the authentication request message Send to ;

[0060] S32, secondary machine With secondary machine Complete two-way authentication and negotiate with it to generate a session key:

[0061] S321, secondary unit Upon receiving the authentication request message, first check the timestamp. Whether it is valid, and then from the local mapping table. Find the secondary machine identity document and calculate Determine the equation Check if it is true. If it is true, proceed to the next step; otherwise, determine... Illegal node, authentication failed;

[0062] S322, secondary unit Choose a random secret value and calculate Then generate a session key. ;

[0063] S323, Calculation parameters and signature and the authentication request message Send to ;

[0064] S324, After receiving the authentication request message, the secondary machine first checks the timestamp. Whether it is valid, and then from the local mapping table. Find the secondary machine identity document and calculate Determine the equation Is it true? If it is true, then... and Two-way authentication complete; otherwise, a decision will be made. Illegal node, authentication failed;

[0065] Further, step S4 includes:

[0066] S41, secondary unit added;

[0067] S411, drone swarm led by the head unit and a set of secondary machines Composition, if there is a secondary machine To join a drone swarm, this secondary machine Follow steps S211, S221, S222, and S223 to execute the registration request;

[0068] S412, Head Machine Upon receiving the request, refer to steps S231 and S232 to complete the mapping table. The update then uses its own private key. For mapping table Obtain by signing And send the signature through a secure channel Send to secondary machine Secondary machine Use the head machine's public key Verify signature The validity of the signature is checked; if the signature is valid, the mapping table is saved. To local storage, otherwise the drone Registration failed, and you will be unable to join the drone cluster.

[0069] S413, all secondary machines according to the updated mapping table Referring to steps S311, S312, S321, S322, S323 and S324, complete the mutual authentication protocol and establish a new session key to achieve secure cluster communication after the new secondary machine joins.

[0070] S42, Secondary machine exit;

[0071] S421, drones After submitting the request to leave the group, the remaining secondary and primary machines... Joint deletion mapping table middle Correspondence Then generate the updated mapping table. At the same time, all session keys associated with the secondary machine to be exited within the cluster will be... Mark it as invalid and clear this type of session key locally from each secondary machine;

[0072] S422, Remaining Secondary Machine Update Mapping Table Then, referring to steps S311, S312, S321, S322, S323 and S324, complete the mutual authentication between the remaining secondary machines and re-establish the session key to realize secure cluster communication after the secondary machine to be exited leaves.

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] (1) In view of the problems that existing solutions mostly adopt centralized architecture and rely too much on the head unit or ground station as trust intermediary, resulting in single point of failure risk and communication bottleneck, this invention adopts a partially decentralized design. The head unit only participates in the credential verification and mapping table distribution in the pre-flight registration stage. During the flight, the secondary units directly complete the two-way identity authentication and session key negotiation without the intervention of the head unit. This eliminates the hidden danger of authentication service paralysis caused by the failure of the central node and improves the robustness, scalability and task adaptability of the system. At the same time, by dividing the two stages of pre-registration and online authentication, the computationally intensive operations such as credential generation and zero-knowledge proof construction are completed before takeoff. The authentication stage during flight only requires lightweight hash operation and a small amount of elliptic curve multiplication, which greatly reduces the computing burden and energy consumption in the air and realizes lightweight authentication with low latency and low overhead. It is suitable for large-scale UAV swarm scenarios with limited resources.

[0075] (2) To address the problems of insufficient identity privacy protection and susceptibility to tracking and correlation analysis in existing inventions, this invention introduces a pseudonym mechanism and non-interactive zero-knowledge proof technology. The secondary machine uses a pseudonym jointly generated with the head machine to identify itself during communication, and the pseudonym can be updated with the task. There is no mathematical correlation between different pseudonyms, so attackers cannot associate pseudonyms with real identities or track the same node through multiple communications. At the same time, zero-knowledge proof ensures that the secondary machine proves the validity of the credentials to the verifier without disclosing any private key information, thereby achieving identity anonymity, non-correlation, and private key confidentiality, and eliminating the risk of identity privacy leakage from the source.

[0076] (3) To address the weakness of existing inventions in resisting common network attacks, this invention designs credentials and authentication signatures based on the difficulty assumption of the Elliptic Curve Discrete Logarithm Problem (ECDLP) and a collision-resistant hash function. The credentials and their knowledge signatures are unforgeable. The authentication signature is bound to a pseudonym, a timestamp, and part of the communication key. Any tampering with the message will be detected by the receiver. The timestamp in the authentication message effectively resists replay attacks. The signature verification mechanism can resist impersonation attacks, man-in-the-middle attacks, and message tampering attacks, while also meeting the non-repudiation requirement, providing comprehensive security for UAV swarm communication.

[0077] (4) To address the insufficient forward / backward security of existing inventions in dynamic networking scenarios, this invention designs a complete secondary machine joining and leaving protocol. When a new node joins, it needs to re-register and obtain the updated mapping table, and renegotiate the session key with other nodes in the group; when a node leaves, the leader and remaining nodes synchronously update the mapping table, delete the leaving node entry, and re-establish the session key. This mechanism ensures that the leaving node cannot continue to use the original key to participate in communication, and the new node cannot decrypt the historical communication content, achieving strict forward and backward security, and adapting to the actual needs of dynamic changes in UAV swarm topology. Attached Figure Description

[0078] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0079] Figure 1 The present invention provides an overall flowchart of a drone swarm authentication method based on zero-knowledge proof.

[0080] Figure 2 This is a system overview diagram of a drone swarm authentication method based on zero-knowledge proof provided by the present invention.

[0081] Figure 3 The system model diagram of a drone swarm authentication method based on zero-knowledge proof provided by the present invention is shown.

[0082] Figure 4 The flowchart shows the registration phase of a drone swarm authentication method based on zero-knowledge proof provided by this invention.

[0083] Figure 5 The flowchart illustrates the authentication phase of a drone swarm authentication method based on zero-knowledge proof provided by this invention.

[0084] Figure 6 A comparison chart showing the computational overhead of different inventions for different numbers of secondary machines in a drone swarm authentication method based on zero-knowledge proof provided by this invention.

[0085] Figure 7 A comparison chart of communication overhead between different numbers of secondary machines and different inventions for a drone swarm authentication method based on zero-knowledge proof provided by this invention. Detailed Implementation

[0086] To make the objectives, technical features, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0087] Example 1: To verify the security of the present invention, this Example 1 focuses on a proposed drone swarm authentication method based on zero-knowledge proof, such as... Figure 1 , Figure 2 , Figure 4 , Figure 5 As shown, the present invention includes the following steps:

[0088] S1, System initialization;

[0089] S2, Pre-flight registration of the secondary aircraft;

[0090] S3, In-flight secondary inter-aircraft two-way authentication and key negotiation;

[0091] S4, dynamic networking of secondary machines;

[0092] like Figure 3 As shown, the UAV swarm authentication method based on zero-knowledge proof includes a leader UAV and secondary UAVs. Its functional and security assumptions are described below:

[0093] 1. Header Node: The uniquely deployed trusted central node in each drone swarm, possessing strong computing and storage capabilities. The head node undertakes the following core responsibilities during the registration phase:

[0094] 1) Receive and verify the identity credential information submitted by the secondary machine;

[0095] 2) Construct and maintain a global identity credential mapping table;

[0096] 3) After signing and encrypting the mapping table, distribute it to all secondary machines.

[0097] The head unit is considered a fully trusted entity, but it does not participate in the interaction between secondary units during the authentication phase, thereby avoiding becoming a communication bottleneck or a single point of failure.

[0098] 2. Secondary UAV: ​​A drone node that performs specific tasks and possesses basic computing and storage capabilities. Before takeoff, the secondary UAV registers, obtains and decrypts the encrypted mapping table distributed by the lead drone, and stores it. During the flight mission, the secondary UAV can independently complete mutual authentication and key negotiation with other secondary UAVs based on this mapping table, without relying on the lead drone in real time. Secondary UAVs communicate using pseudonyms to protect their identity privacy.

[0099] 1. Safety Objectives

[0100] This invention proposes a drone swarm authentication method based on zero-knowledge proof. It adopts a two-stage design of pre-registration and online authentication. The lead drone only participates in pre-flight registration, while the secondary drones directly complete two-way authentication and session key negotiation during flight. This method significantly reduces computation and communication overhead while ensuring identity privacy and communication security, and effectively resists various typical attacks.

[0101] 2. Security Model

[0102] The security model of this invention is defined through an interactive game between challenger C and adversary A. Adversary A can query the credential key of the secondary machine and replace credentials, but cannot obtain the private key of the secondary machine. and pseudonym private key If the advantage of opponent A in winning the game is negligible, this invention satisfies the requirement of unforgeability in terms of identity authentication. Opponent A is allowed to perform the following oracle queries:

[0103] 1) Secondary machine generates a query: Enemy A enters their identity. When an inquiry is made, Challenger C queries the identity according to the dimensional series table. If the identity exists in the list, the secondary machine pseudonym is returned to the adversary A. If the identity does not exist in the list, the pseudonym secret value of the secondary machine is generated, the pseudonym and key pair are recorded in the list, and the pseudonym and public key are returned to the adversary.

[0104] 2) Hash Query: The opponent inputs any value to perform a hash query. Challenger C queries the corresponding hash value according to the maintained list. If it exists, the hash value is returned to the opponent; if it does not exist, the hash value is calculated, stored in the list, and returned to the opponent.

[0105] 3) Credential key query: Adversary A queries identity. The challenger C requests the credential key from the list. If the corresponding credential key exists, return it; otherwise, generate a credential key. Record it in a list and return it to opponent A.

[0106] 4) Credential Replacement Inquiry: Opponent A enters their identity. Challenger C performs a voucher replacement query, replacing the voucher based on the list in the maintenance table. The corresponding voucher.

[0107] 5) Private Key Query: Adversary A enters their identity Challenger C performs a private key query and replaces the key based on the list in the maintenance table. If the corresponding private key exists, it is returned to the adversary; otherwise, a private key is generated and returned to the adversary A.

[0108] 6) Verification Signature Request: Opponent A enters their identity. Inquire about its knowledge signature. Challenger C's query list. Corresponding vouchers Generate a knowledge signature according to the knowledge signature algorithm. And return.

[0109] Definition 1: If the advantage of opponent A in winning the game is negligible, this invention satisfies the unforgeability requirement for adaptive selection message attacks during the registration phase, thereby ensuring that the identity cannot be forged during the registration phase.

[0110] Game: Challenger C and opponent A play a game.

[0111] 1) System initialization phase: Challenger C runs step S1 to generate common parameters. And send the public parameters to adversary A.

[0112] 2) Inquiry Phase: The adversary A adaptively performs the above-mentioned oracle inquiries.

[0113] 3) Forgery Phase: Opponent A outputs information about their identity. Forged certificates and knowledge signature If the following conditions are met, then opponent A is said to have won the game:

[0114] a) Signature The algorithm was validated.

[0115] b) Opponent A did not reveal his identity. A credential key query was initiated;

[0116] c) Opponent A did not reveal his identity. voucher A knowledge signature query was initiated.

[0117] 3. Formal security proof

[0118] According to the definition of the security model, this section will demonstrate the security of the invention in terms of identity authentication through a game played between challenger C and adversary A.

[0119] Theorem 1 If the Elliptic Curve Discrete Logarithm Problem (ECDLP) is difficult, then under the random oracle model, this invention satisfies the existence of unforgeability against adaptive selection message attacks during the registration phase, thereby guaranteeing the unforgeability of the authenticated identity.

[0120] Proof: Assume there exists a probabilistic multinomial-time adversary A that can achieve a non-negligible advantage. Forging credentials and knowledge signatures during the registration phase of this scheme would allow challenger C to solve the ECDLP problem using A, i.e., given a random ECDLP instance. C's goal is to calculate its corresponding private key k.

[0121] The interaction process between A and C is as follows:

[0122] 1. System initialization phase: C selects challenge identity. Run step S1 to generate common parameters C will The public keys of all secondary machines are sent to adversary A. C maintains the list. It is used to record response information when the adversary inquires.

[0123] 2. Inquiry stage:

[0124] 1) Secondary machine generates an inquiry: Enemy A's identity When questioned, Challenger C checks the identity against the maintained list L. If the identity is found in the list, a secondary machine pseudonym is returned. Give the identity to the adversary A; if the identity does not exist in list L, generate the pseudonym secret value for the secondary machine. ,pseudonym key pair ,Will Record the data in list L and return the pseudonym. and public key To the enemy.

[0125] 2) Credential key query: Adversary for identity verification C queries the credential key, and C queries the maintained list L. Corresponding credential key If the credential key exists, it is returned to the adversary; otherwise, C selects a random number. As the credential key, Record in table L, and Return it to the enemy.

[0126] 3) Voucher Replacement Prompt: When opponent A enters... When performing a voucher replacement query, Challenger C queries list L. If a corresponding item exists, the voucher is calculated. ,Will Record in table L, and Return it to A.

[0127] 4) Secondary machine private key query: Adversary A enters identity Challenger C performs a private key query and replaces the key based on the list in the maintenance table. corresponding private key If it exists, return the private key. Give it to the adversary; if it does not exist, generate a private key. ,Will Store it in list L, and add the private key. Return it to opponent A.

[0128] 5) Knowledge signature query: When adversary A queries the identity... When performing a signature query, Challenger C queries list L. If a corresponding item exists, and... Then return Give it to opponent A, otherwise end the game; if no corresponding item exists, use the private key. and credentials private key Generate random blinding factors respectively , Calculate commitment and challenges And based on the blinding factor and and challenges Calculate the response and Generate knowledge signature ,Will Record the data in list L and return it. Give it to opponent A;

[0129] 3. Forgery Stage: Through the above inquiries, the adversary ultimately generates a forgery profile regarding their identity. signature , like C terminates the game; if And signature Verification was successful, and adversary A did not reveal their identity. The credential key was requested, and adversary A did not verify their identity. If a knowledge signature query has been initiated, then adversary A has successfully forged a valid signature. By the bifurcation lemma, adversary A can forge another valid knowledge signature. The corresponding challenges are as follows: and Therefore:

[0130]

[0131]

[0132] Subtracting the two equations, we get:

[0133]

[0134]

[0135]

[0136] Challenger C Output As a solution to the ECDLP problem. Since the ECDLP problem is difficult to solve, the knowledge signature is unforgeable against adversary A. Therefore, the adversary cannot forge valid credentials and thus cannot pass the identity authentication.

[0137] 4. Informal Security Analysis

[0138] This section takes a cryptographic primitives and protocol design perspective and conducts an informal analysis of the security attributes satisfied by the scheme, covering identity integrity, private key confidentiality, identity anonymity, non-associability, partial decentralization, non-repudiation, and the ability to resist common attacks.

[0139] 1) Identity Integrity: Under the ECDLP assumption, an adversary cannot forge the knowledge signature of the secondary machine in polynomial time. Therefore, attackers cannot forge the secondary machine's identity to register. During the authentication phase, the authentication signature generated by the secondary machine... Thanks to the collision-resistant hash function, any modification to the message will result in a change in the hash value, which will be detected by the verifier; moreover, attackers cannot complete registration at the head machine, so secondary machines cannot access the mapping table. Obtain the attacker's identity verification Thus verifying the signature Therefore, the invention ensures the integrity of identity information.

[0140] 2) Private Key Confidentiality: During the registration phase, a non-interactive zero-knowledge proof based on the Sigma protocol and Fiat-Shamir transformation is used. This proof satisfies the zero-knowledge property, meaning that the verifier can only be certain that the prover knows the private key, but cannot obtain any valid information about the private key.

[0141] 3) Anonymity: The secondary machine uses pseudonyms in communication. It identifies itself, but its true identity is known only to the primary and secondary units. (Pseudonym) pseudonym secret value generated by the secondary machine and headphone private key And the hash value of the secondary machine's true identity. Together they constitute the whole. Because the secret value of the pseudonym cannot be obtained. and headphone private key Furthermore, the real identity has been hashed, so attackers cannot associate the pseudonym with the real identity, thus achieving identity anonymity protection.

[0142] 4) Unassociability: Furthermore, before each mission takeoff, the secondary machine regenerates the pseudonym secret value. The pseudonyms are updated to ensure that there is no mathematical correlation between them. Since there is no mathematical correlation between different pseudonyms, attackers cannot trace the behavior of the same secondary machine by analyzing pseudonyms from multiple communications, thus satisfying the non-correlation requirement.

[0143] 5) Partial Decentralization: During the authentication phase, if no secondary machines dynamically join, the head machine does not participate in the mutual authentication and key negotiation process between secondary machines. The secondary machines can independently complete the authentication process based solely on the mapping table distributed before takeoff, thus achieving decentralization of the authentication process and effectively preventing the head machine from becoming a communication bottleneck or a single point of failure.

[0144] 6) Non-repudiation:

[0145] a) Registration Phase: The pseudonym for the secondary machine is jointly generated by the secondary machine and the head machine. When the head machine receives the registration message... At that time, the kana equation will be verified. Whether it is true or not, thus making a preliminary judgment on the message. Is it from a secondary machine? Moreover, knowledge signatures The challenge value generated in The signature contains pseudonyms. This proves that the message came from the secondary machine. If the secondary machine subsequently denies ever registering the credential, the primary machine can use the credential to sign. It makes it impossible for them to deny;

[0146] b) During the authentication phase, the secondary machine uses credentials. Authentication signature generated The signature is bound to a pseudonym, a timestamp, and part of the communication key. If a secondary machine denies participating in key negotiation or denies sending parameters... The other party can provide As a basis for verification, it achieves non-repudiation.

[0147] 7) Resist attacks

[0148] a) Impersonation attack: During the registration phase, impersonators need to forge credentials from a legitimate secondary machine. and its knowledge signature According to Theorem 1, under the ECDLP assumptions, knowledge signatures... Unforgeable, therefore, an attacker registers at the client machine and records the forged credentials in the mapping table; during the authentication phase, an imposter needs to forge the authentication signature. Because of the authentication signature The calculation depends on Furthermore, the attacker's credentials cannot be registered in the mapping table, therefore the victim cannot find the attacker's identity verification in the mapping table. Thus verifying Therefore, attackers cannot forge authentication signatures. In summary, this invention can effectively resist spoofing attacks.

[0149] b) Replay attack: The registration request message and authentication message contain timestamps. The recipient first checks The system prioritizes freshness and rejects expired messages. Due to the uniqueness and real-time nature of timestamps, attackers cannot pass verification by replaying old messages.

[0150] c) Man-in-the-middle attack: During the registration phase, the difficulty of ECDLP ensures that credentials are unforgeable; during the authentication phase, the authentication signature... Mapping table required In and one's own credentials In combination, if an attacker attempts to insert or tamper with a message during the authentication phase, they will fail the signature verification, thus the invention is resistant to man-in-the-middle attacks.

[0151] d) Tampering attack: Challenge value and authentication signature in the knowledge signature during the registration phase. Generated by a collision-resistant hash function, any hash field (such as...) , Any alteration (such as falsification of hash values) will result in a recalculated hash value that differs from the original value, allowing the verifier to detect it immediately. Therefore, this invention possesses the ability to resist message tampering.

[0152] 4. Proof of correctness

[0153] This section provides proof of the correctness of the relevant formulas in this invention.

[0154] (1) During the registration phase, the head machine Verify secondary machine The correctness of the equation for knowledge signature:

[0155] Equation 1:

[0156]

[0157]

[0158]

[0159]

[0160] Example 2: To verify the performance of the present invention, Example 2 compares and analyzes it with four representative existing UAV swarm authentication schemes, including Scheme 1 proposed by Chen Ruizheng et al. in "Lightweight Security Authentication Method for UAVs Based on Fuzzy Extractor", Scheme 2 proposed by Mohd Shari et al. in "Provably Secure and Reliable Privacy-Preserving Authentication Scheme for Drone-to-Drone Communications in Internet of Autonomous Things", Scheme 3 proposed by Tao Xia et al. in "Research on Identity Authentication Scheme for UAV Communication Network", and Scheme 4 proposed by QiXie et al. in "Lightweight Drone-to-Ground Station and Drone-to-Drone Authentication Scheme for Internet of Drones". Since the above schemes are highly consistent with the application background and security objectives of the present invention in UAV swarms, they have good comparability.

[0161] 1. Calculation cost analysis

[0162] In the performance analysis of this invention, the experimental setup of the existing literature "Lightweight Security Authentication Method for Unmanned Aerial Vehicles Based on Fuzzy Extractor" was referenced. To obtain the baseline runtime for each cryptographic operation, this paper used the hashlib library in Python to implement hash functions and the pycrypto library to implement elliptic curve dot multiplication and symmetric encryption / decryption operations on a test platform with an Intel Core i5-6300U 2.4GHz processor and 8GB of memory. 1000 independent tests were performed on each operation, and the average value was taken as the baseline runtime. Addition and XOR operations on the elliptic curve group are ignored in this paper due to their extremely short execution time. Details of the computational overhead for each participating entity are shown in Table 2.

[0163] Table 2 Average execution time of cryptographic operations

[0164]

[0165] Table 3 compares the computational overhead of various schemes in a scenario where the drone swarm size is n (excluding base stations or leader drones) and mutual authentication and session key generation are required between any two drones. In this invention, the computational overhead of a single drone involves only a small number of elliptic curve scalar dot multiplications and hash operations, and the authentication process does not require the participation of the leader drone, thus the additional computational burden of the leader drone is not considered. In contrast, the scheme of Chen Ruizheng et al. introduces a Physically Unclonable Function (PUF) and performs multiple symmetric encryption and decryption operations, while also considering the computational overhead of the base station; the scheme of Mohd Shari et al. also involves multiple symmetric encryption and decryption operations; the scheme of Tao Xia et al. requires drones to first complete mutual authentication with the base station, and then establish authentication with other drones through the base station and generate keys, increasing the interaction and computation links; the scheme of Qi Xie et al. also relies on multiple PUF calls and symmetric encryption and decryption. The above schemes all have higher computational overhead than this invention, indicating that this invention has a significant advantage in computational efficiency and is more suitable for the lightweight authentication requirements of resource-constrained drone swarms.

[0166] Table 3 Computational cost of a swarm of n drones

[0167]

[0168] like Figure 6 As shown in the figure, the computational overhead of each scheme is clearly compared when the number of drones is 5, 10, 15, 20, and 25. The data shows that when the number of drones reaches 20, the computational overhead of this invention is reduced by 94.50% compared to the scheme of Chen Ruizheng et al., and by 91.77% compared to the scheme of Qi Xie et al., demonstrating a significant efficiency advantage. Compared to the schemes of Mohd Shari et al. and Tao Xia et al., the computational overhead of this invention is reduced by 65.77% and 55.30% respectively, also showing a significant efficiency advantage. In lightweight scenarios, this invention consistently maintains the lowest computational overhead, further verifying its applicability and lightweight advantages in resource-constrained drone swarm environments.

[0169] 2. Communication Overhead Analysis

[0170] This section analyzes the communication overhead of this invention. At an 80-bit security level, elements in the elliptic curve group... The length is 256 bytes, and the hash function output is an integer. The length of each timestamp is 160 bytes. The length is 4 bytes, PUF challenge response pair The length is 160 bytes, and the output is symmetrically encrypted. The length is 128 bytes. Consider a cluster of drones (excluding base stations or lead drones), where any two drones must authenticate each other and generate a session key. Based on the above parameter settings, the total communication overhead of this invention and existing related solutions under the same cluster size is compared in Table 4. The results show that the communication overhead of this invention is lower than other comparative solutions, exhibiting superior performance.

[0171] Table 4. Communication overhead of a swarm of n drones

[0172]

[0173] like Figure 7 As shown, when the drone swarm size is 5, 10, 15, 20, and 25 drones, the comparison results of the proposed scheme with those of Chen Ruizheng et al., Qi Xie et al., Mohd Shari et al., and Tao Xia et al. in terms of communication overhead are clearly visible. Figure 7 Data shows that the communication overhead of this invention is lower than that of the other four comparative schemes at all scales, and the advantage becomes more significant as the number of drones increases. When the drone swarm size reaches 20 drones, the communication overhead of this invention is reduced by 75.36%, 59.57%, 62.39%, and 43.70% respectively compared with the schemes of Chen Ruizheng et al., Qi Xie et al., Mohd Shari et al., and Tao Xia et al. Therefore, this invention has a significant advantage in communication efficiency and can better meet the needs of large-scale drone swarms for low-overhead authentication.

[0174] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof, characterized in that, Includes the following steps: S1, System initialization; S2, Pre-flight registration of the secondary aircraft; S3, In-flight secondary inter-aircraft two-way authentication and key negotiation; S4, dynamic networking of secondary machines.

2. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 1, characterized in that, S1 includes head unit initialization; including the following steps: S111, Head Machine The order is defined as a large prime number. Elliptic curve group G, generator P, select head machine master key The public key corresponding to the computing head machine ; S112, Head Machine Choose a one-way collision-resistant hash function Public parameters Secretly store the master key .

3. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 1, characterized in that, S2 includes the following steps: S21, secondary machine Kana generation; S22, secondary machine Voucher generation; S23, Head Machine Credential verification; In step S21, the head unit initialization includes the following steps: S211, secondary machine Heading machine Submission includes real identity Registration application, head machine Calculate part of the kana after receiving. And send to the secondary machine Secondary machine Generate pseudonym secret value Based on secret value and some kana The secondary machine is calculated. kana .

4. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 3, characterized in that, In step S22, the secondary machine The voucher generation process includes the following steps: S221, secondary unit Generate random numbers Use the private key to calculate the corresponding public key. Randomly select secret value For the credential key, the secondary machine based on and Calculation vouchers ; S222, secondary unit For private key and credentials private key Generate random blinding factors respectively , Calculate commitment and challenges And based on the blinding factor and and challenges Calculate the response and Output knowledge signature ; S223, secondary unit Generate current timestamp Using the head unit public key Regarding the message Encrypt the message and then encapsulate it. Send to head unit .

5. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 3, characterized in that, In step S23, the head machine The credential verification process includes the following steps: S231, Head Machine By message Extract message And verify its timestamp The validity of the generated pseudonyms is calculated. ,judge If true, calculate the challenge value. Then judge the equation. Whether the equation holds true or not; if the equation holds true, then determine whether the secondary machine is valid. A trusted entity; S232, Head Machine Calculation generation identity document , correspondence Record to mapping table In the middle, and temporarily store the secondary machine credentials Remove from local storage; S233, Head Machine After completing the credential verification and information registration for all secondary machines, use its own private key. For mapping table Obtain by signing And send the signature through a secure channel Send to secondary machine ; S234, secondary machine Use the head machine's public key Verify signature The validity of the signature is checked; if the signature is valid, the mapping table is saved. To local storage, otherwise the drone Registration failed, and you will be unable to join the drone cluster.

6. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 1, characterized in that, S3 includes the following steps: S31, secondary unit in drone swarm To the secondary machine Send a two-way authentication request; S32, secondary machine With secondary machine Complete two-way authentication and negotiate with it to generate a session key.

7. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 6, characterized in that, In step S31, the secondary drone in the drone cluster To the secondary machine Sending a two-way authentication request includes the following steps: S311, secondary unit Generate secret value and from the mapping table Searching for secondary machines identity document Then based on , and Calculate the generated parameters ; S312, secondary unit To construct a two-way authentication request, the method is as follows: generate the current timestamp. and calculate the signature. Then, the authentication request message Send to .

8. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 6, characterized in that, In step S32, the secondary machine With secondary machine Complete two-way authentication and negotiate the generation of a session key, including the following steps: S321, secondary unit Upon receiving the authentication request message, first check the timestamp. Whether it is valid depends on the local mapping table. Find the secondary machine identity document and calculate Determine the equation Check if it is true. If it is true, proceed to the next step; otherwise, determine... Illegal node, authentication failed; S322, secondary unit Choose a random secret value and calculate Generate session key ; S323, Calculation parameters and signature and the authentication request message Send to ; S324, After receiving the authentication request message, the secondary machine first checks the timestamp. Whether it is valid, and then from the local mapping table. Find the secondary machine identity document and calculate Determine the equation Is it true? If it is true, then... and Two-way authentication complete; otherwise, a decision will be made. The node is invalid; authentication failed.

9. The UAV swarm authentication method based on zero-knowledge proof according to claim 1, characterized in that, S4 includes the following steps: S41, secondary unit added; In S41, the secondary machine joining process includes the following steps: S411, drone swarm led by the head unit and a set of secondary machines Composition, if there is a secondary machine To join a drone swarm, this secondary machine Refer to S211, S221, S222, and S223 to execute the registration request; S412, Head Machine Upon receiving the request, refer to S231 and S232 to complete the mapping table. The update then uses its own private key. For mapping table Obtain by signing And send the signature through a secure channel Send to secondary machine The secondary machine uses the public key of the head machine. Verify signature The validity of the signature is checked; if the signature is valid, the mapping table is saved. To local storage, otherwise the drone Registration failed; you will be unable to join the drone cluster. S413, all secondary machines according to the updated mapping table Referring to steps S311, S312, S321, S322, S323 and S324, complete the mutual authentication protocol and establish a new session key to achieve secure cluster communication after the new secondary machine joins. S42, Secondary machine exit.

10. The method for authenticating unmanned aerial vehicle (UAV) swarms based on zero-knowledge proof according to claim 1, characterized in that, In S42, the secondary machine exit process includes the following steps: S421, drones After submitting the request to leave the group, the remaining secondary and primary machines... Joint deletion mapping table middle Correspondence Then generate the updated mapping table. This will transfer all session keys associated with the secondary machine to be exited within the cluster. Mark it as invalid and clear this type of session key locally from each secondary machine; S422, Remaining Secondary Machine Update Mapping Table Then, steps S311, S312, S321, S322, S323 and S324 complete the mutual authentication between the remaining secondary machines and re-establish the session key to realize secure cluster communication after the secondary machine to be exited leaves.

Images