Multi-factor group authentication and key agreement protocol method based on certificateless aggregation signature

Abstract

The invention discloses a multi-factor group authentication and key agreement protocol method based on certificateless aggregation signature. A trusted authentication mechanism generates system parameters and distributes a key to initialize a system; the user and the intelligent equipment node register to the gateway node through a public channel, so that extra overhead caused by establishment of a secure channel is avoided; in an authentication and key negotiation stage, a user only needs to send an authentication request to a gateway node to realize bidirectional authentication and session key negotiation with a group of intelligent device nodes; the protocol adopts an aggregation signature mechanism, so that a user can verify the authenticity and integrity of keys returned by all devices at one time, a negotiated session key has uniqueness, and even if a gateway node key is broken, the key security can still be ensured, and perfect forward secrecy is supported; meanwhile, the protocol dynamically updates the key in the group through the Chinese remainder theorem to realize forward security and backward security; the method has higher safety and efficiency in an industrial internet scene, and is particularly suitable for a multi-device environment.

Description

Technical Field

[0001] This invention relates to the field of information security technology, specifically to a multi-factor group authentication and key negotiation protocol method based on certificateless aggregate signatures. Background Technology

[0002] With the widespread application of Industrial Internet of Things (IIoT) and Internet of Things (IoT) technologies, an increasing number of terminal devices are collaborating and exchanging data through networks. In this process, inter-device authentication and key negotiation have become crucial foundations for ensuring system security. Traditional authentication methods often employ point-to-point authentication mechanisms, supporting only one pair of communicating entities for identity verification and key generation per authentication. This often fails to meet performance and efficiency requirements in industrial scenarios with large-scale device access and high-frequency communication requests.

[0003] Meanwhile, to enhance authentication security, multi-factor authentication mechanisms are gradually becoming mainstream, but their unified coordination and key management in group authentication scenarios still face many challenges. Existing solutions, when handling batch authentication of multiple devices, are prone to problems such as lengthy authentication processes, high computational overhead, and high communication costs, making them unsuitable for the efficiency and scalability requirements of the Industrial Internet. Furthermore, to reduce the burden of public key certificate management, Certificateless Public Key Cryptography (CL-PKC) is widely used.

[0004] However, traditional certificateless authentication methods (such as those in references [1] ZHANG J, CUI J, ZHONG H, et al. PA-CRT: Chinese Remainder Theorem Based Conditional Privacy-Present Authentication Scheme in Vehicular Ad-Hoc Networks[J / OL]. IEEE Trans. Dependable Secur. Comput., 2021, 18(2): 722-735. https: / / doi.org / 10.1109 / TDSC.2019.2904274. DOI:10.1109 / TDSC.2019.2904274; [2] HARN L. Group Authentication[J / OL]. IEEE Trans.Computers,2013,62(9):1893-1898.https: / / doi.org / 10.1109 / TC.2012.251.DOI:10.1109 / TC.2012.251;[9]LI J,WEN M,ZHANGT.Group-Based Authentication and Key Agreement With Dynamic Policy Updating for MTC in LTE-A Networks[J / OL].IEEE Internet Things J., 2016,3(3):408-417.https: / / doi.org / 10.1109 / JIOT.2015.2495321.DOI:10.1109 / JIOT.2015.2495321;

[10] YANG Z,LAI J,SUN Y,et al.A Novel Aut henticated Key Agreement ProtocolWith Dynamic Credential for WSNs[J / OL].ACM Trans.Sens.Networks,2019,15(2):22:1-22:27.https: / / doi.org / 10.1145 / 3303704.DOI:10.1145 / 3303704. etc.) usually do not fully consider the efficiency of aggregate processing of authentication requests and key negotiation in group authentication. On the other hand, although existing research (such as (

[11] HED,KUMAR N,CHILAMKURTI N K.)A secure temporal-credential-based mutu alauthentication and key agreement scheme with pseudo identity for wireles ssensor networks[J / OL].Inf.Sci.,2015,321:263-277.https: / / doi.org / 10.1016 / j.ins.2015.02.010.DOI:10.1016 / J.INS.2015.02.010;[6]JIANG Q,MA J,WEI F,etal.An untraceable temporal-credential-based two-factor authenticatio n schemeusing ECC for wireless sensor networks[J / OL].J.Netw.Comput.Appl.,2016,76:37-48.https: / / doi.org / 10.1016 / j.jnca.2016.10.001.DOI:10.1016 / J.JNCA.2016.10.001;[4]VINOTH R,DEBORAH L J,VIJAYAKUMAR P,et al.Secure Multifactor AuthenticatedKey Agreement Scheme for Industri al IoT[J / OL].IEEE Internet Things J.,2021,8(5):3801-3811.https: / / doi.org / 10.1109 / JIOT.2020.3024703.DOI:10.1109 / JIOT.2020.3024703;[8]LI J,ZHA NG W,KUMARI S,et al.Security analysis andimprovement of a mutual authentication and key agreement solution forwireless sensor networks using chaotic maps[J / OL].Trans.Emerg.Telecommun.Technol.,2018,29(6).https: / / doi.org / 10.1002 / ett.3295.DOI:10.1002 / ETT.3295.While methods like aggregation signatures have been introduced into authentication protocols to improve verification efficiency, the security and integrity guarantees in the combination of group authentication and dynamic key management are still imperfect. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide a multi-factor group authentication and key negotiation protocol method, system, electronic device and computer storage medium based on certificateless aggregate signature, which supports multi-factor authentication, can efficiently complete group authentication and key negotiation, and has forward security, backward security and low communication and computing overhead, so as to meet the security requirements of multi-device application environments such as the Industrial Internet.

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] A multi-factor group authentication and key negotiation protocol method based on certificateless aggregate signatures is applied to a data aggregation signature authentication system in the Industrial Internet. The method includes the following steps:

[0008] 1) The gateway node initializes the system and sets the necessary system parameters;

[0009] 2) Before a smart device node is deployed to the target area, the gateway will select a unique identifier for it and store it in the smart device's memory. After that, the smart device will register on the public channel.

[0010] 3) Users must first register with the gateway node of the industrial internet system in order to authenticate and negotiate keys with smart device nodes;

[0011] 4) Users need to log in successfully before they can send authentication and key negotiation requests to the gateway node;

[0012] 5) Users authenticate with a group of smart device nodes and negotiate session keys at a time;

[0013] 6) Users can update their local passwords and biometric identifiers, and add or delete smart devices.

[0014] Step 1) includes:

[0015] The gateway node selects an elliptic curve over a finite field and a generator over an additive cyclic group as its base point;

[0016] The gateway node selects a random number as the system private key and calculates the system public key;

[0017] Gateway node selects master key;

[0018] Gateway node selects hash function;

[0019] The gateway node pre-sets the maximum capacity, group key threshold, and group key for each group;

[0020] The gateway node exposes system parameters.

[0021] Step 2) includes:

[0022] Smart devices select messages related to random number calculation;

[0023] The gateway node checks whether the smart device is a legitimate smart device node identity and is not registered. If not, the session is terminated.

[0024] The gateway stores the information in the registry of the smart device node.

[0025] Step 3) includes:

[0026] Users insert their smart cards into the industrial internet terminal, select their identity identifier, and send registration request information to the gateway;

[0027] After receiving a user's registration message, the gateway determines whether the identity is valid and not registered. If not, the session is terminated; otherwise, the gateway registers the user information.

[0028] Step 4) includes:

[0029] The user inserts the smart card into the corresponding terminal, enters their identity and password, and records their biometric identifier.

[0030] The smart card verifies the user's identity. If the user successfully passes the verification, the authentication and key negotiation phase continues.

[0031] Step 5) includes:

[0032] The gateway verifies the legitimacy of the user's identity, and all smart device nodes verify the identity of the gateway device.

[0033] If the verification passes, the gateway calculates the aggregate signature, and the smart device node and the user calculate the session key.

[0034] Step 6) includes:

[0035] Users insert smart cards into industrial internet terminals and enter their identity identifier, current password, and biometric identifier to verify their identity.

[0036] If the verification is successful, the smart card requests a new password and biometric identifier from the user. The user can also provide the old biometric identifier or password to update the password or biometric identifier separately.

[0037] When a smart device node requests to join or leave a group, the gateway updates the group key.

[0038] A data aggregation signature authentication system for the Industrial Internet, implementing the aforementioned multi-factor group authentication and key negotiation protocol method based on certificateless aggregation signature, includes:

[0039] Intelligent device nodes: Deployed in the target production area to sense and collect real-time data in the industrial production environment;

[0040] User: Industrial system operators, equipped with smart cards for authentication and session negotiation;

[0041] Gateway node: As the central control module, it is responsible for system initialization, user and device registration, authentication coordination and key negotiation.

[0042] During system operation, users log in to the system using smart cards. After successful login, a secure communication connection is established with multiple smart device nodes through the gateway. During the authentication phase, the gateway generates an aggregate signature, and the smart device nodes interact securely with the user based on the shared group key.

[0043] An electronic device, comprising:

[0044] One or more processors;

[0045] A storage device on which one or more programs are stored;

[0046] When the program is executed, it causes the processor to implement the aforementioned method for multi-factor group authentication and key negotiation protocol based on certificateless aggregate signature.

[0047] A computer storage medium storing a computer program that, when executed by a processor, implements a multi-factor group authentication and key negotiation protocol method based on certificateless aggregate signature.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] This invention provides a multi-factor group authentication and key negotiation protocol method based on certificateless aggregate signatures, which has the following advantages: combining aggregate signatures and multi-factor authentication mechanisms to improve security and authentication efficiency; supporting users to authenticate and negotiate keys with multiple smart devices at once, reducing system overhead; supporting smart devices to dynamically join and leave groups, providing high flexibility and scalability; improving the security of the identity verification process through collaborative management of smart cards and gateways; and being applicable to various industrial internet scenarios such as industrial control, smart grids, and edge computing, effectively alleviating problems such as difficulties in device security management and data leakage risks. Attached Figure Description

[0050] Figure 1This is a flowchart of a multi-factor group authentication and key negotiation method based on certificateless aggregate signature in an embodiment of the present invention.

[0051] Figure 2 This is a network model diagram of a multi-factor group authentication and key negotiation method based on certificateless aggregate signature in an embodiment of the present invention.

[0052] Figure 3 This is a diagram illustrating the smart device node registration phase of a multi-factor group authentication and key negotiation method based on certificateless aggregate signatures, according to an embodiment of the present invention.

[0053] Figure 4 This is a user registration phase diagram of the multi-factor group authentication and key negotiation method based on certificateless aggregate signature in an embodiment of the present invention.

[0054] Figure 5 This diagram illustrates the login, authentication, and key negotiation stages of a multi-factor group authentication and key negotiation method based on certificateless aggregate signatures, as described in an embodiment of the present invention.

[0055] Figure 6 This is a comparison chart of the computational overhead between the multi-factor group authentication and key negotiation method based on certificateless aggregate signature in this embodiment of the invention and existing technologies.

[0056] Figure 7 This is a comparison chart of the communication overhead between the multi-factor group authentication and key negotiation method based on certificateless aggregate signature in this embodiment of the invention and existing technologies.

[0057] Figure 8 This is a comparison chart showing the end-to-end latency between the multi-factor group authentication and key negotiation method based on certificateless aggregate signature in this embodiment of the invention and existing technologies.

[0058] Figure 9 This is a comparison chart of throughput between the multi-factor group authentication and key negotiation method based on certificateless aggregate signature in this embodiment of the invention and existing technologies.

[0059] Figure 10 This is a schematic diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] In this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0062] Furthermore, in this invention, relational terms such as first and second are used merely to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0063] like Figure 1 As shown in the figure, this embodiment presents a multi-factor group authentication and key negotiation protocol method based on certificateless aggregate signature, applied to a data aggregation signature authentication system in the Industrial Internet. The method specifically includes:

[0064] S101, System Initialization: The trusted authentication authority generates system parameters and distributes keys;

[0065] The industrial internet data aggregation signature authentication system in this embodiment is as follows: Figure 2 As shown, it includes users, the Internet, gateway nodes, smart device nodes, and factories;

[0066] Users are staff members in the Industrial Internet and possess a smart card. Users register with the gateway node using the smart card. After registration, the smart card will store the user's verification information and authentication credentials. During the login phase, the smart card can use the verification information to verify the user's password and biometric identifier. If the verification is successful, the smart card will assist the user in sending an authentication and key negotiation request to the gateway node.

[0067] The Internet is used to transmit messages;

[0068] The gateway node is responsible for registering users and smart device nodes, as well as assisting users and smart device nodes in performing two-way authentication and negotiating session keys. After registration, users and smart device nodes will share authentication credentials with the gateway node. Users can send a request to the gateway node to execute the AKA protocol with the target smart device node. After success, they can use the negotiated session key to communicate with the smart device node and obtain real-time production data.

[0069] The types of smart device nodes are diverse, such as sensors, smart meters, and industrial cameras, which are deployed in the target production environment to monitor the industrial production status and collect real-time production data.

[0070] The factory is used to collect and process data;

[0071] The gateway node is responsible for initializing the system and setting necessary system parameters, assisting user and smart device nodes in generating and distributing random numbers, and assisting in the authentication and key negotiation process after completing the above parameter generation and distribution operations during the initialization phase.

[0072] Step S101 includes:

[0073] (1) The gateway GWN is selected from large prime numbers p and q, and a finite field. Elliptic curve on Finally, the gateway GWN selects an addition cyclic group. A generator P on the graph is used as the base point;

[0074] (2) The set of gateways GWN selected over a finite field random numbers in Used as the system private key and used to calculate the system public key P. pub =sP;

[0075] (3) Gateway GWN selects a 1024-bit master key msk;

[0076] (4) Gateway GWN selects hash function and h4(·):{0,1} * →{0,1} l Where 'l' represents a fixed length, such as 256 bits. Represents a set over a finite field;

[0077] (5) The gateway GWN pre-sets the maximum capacity N for each group. (When the number of smart device nodes in a group exceeds the maximum capacity N, the group members need to re-register, and the gateway GWN needs to reset the maximum capacity. For example, let the newly set maximum capacity N be N.) * =λN, (1<λ<5), select the group key threshold ρ for each group, and select N coprime integers z. k >ρ(k∈[N]); Gateway GWN calculates N coprime integers z. k The product of the products α k =Z / z k Calculate β k Make α k β k ≡1 mod z k and γ k =α k β k Gateway GWN selects a group key for each group. Satisfying k g<ρ, and calculate the corresponding group public key K. g =k g P; For each group, the gateway GWN initializes the list value γ = 0, and stores the information sequence in the verification table.

[0078] (6) Finally, the gateway GWN publicly discloses the system parameter information sequence.

[0079] S102, Device Registration and Initiation of Authentication Request: Users and smart devices register with the gateway node through a public channel, eliminating the overhead of a secure channel; users send group authentication requests to the gateway node, such as... Figure 3 , Figure 4 As shown;

[0080] Step S102 includes:

[0081] (1) Smart device SD j Select random number Calculate the hash value x j =h0(s j ||SID j ), X j =x j P, K j =k j P and session key SK j =k j P pub Calculate the encrypted value {K j E1} is sent to the gateway GWN via a public channel;

[0082] (2) Gateway GWN calculates session key SK j =sK j And decrypt Check the SD card of smart devices j Is the device a legitimate smart device node identity and not registered? If not, terminate the session; the gateway GWN selects a random number. Calculate Y j =y j P, PK j =X j +Y j hash value hid j =h1(SID) j ‖PK j ||P pub ), private key psk j =hid j *s+y j Select random number RN j Calculate the hash value mk j =h4(SID)j msk RN j Gateway GWN is the SD card for smart devices. j Select a group from SD in the middle j Randomly select a random number z j Set γ = γ + γ j Finally, the gateway GWN will assign {SID} j ,z j ,γ j ,RN j PK j Store to smart device SD card j Calculate the encrypted value in the node registry. And send E2 to the smart device SD via a public channel. j ;

[0083] (3) After receiving the reply message from the gateway GWN, the smart device SD j Decryption And store the information sequence {x j ,psk j ,z j ,k g ,mk j PK j};

[0084] (4) User U i Insert your own smart card (SC) into the industrial internet terminal. i Select Identity ID i and random number RN i Calculate anonymous identity DID i =h4(ID) i RN i Select random numbers; Calculate K i =k i P, Session Key SK i =k i P pub and encrypted value User U i The information sequence {K i E3} is sent to the gateway GWN via a public channel;

[0085] (5) Received user U i After receiving the registration message, the gateway GWN calculates the session key SK. i =sK i Decryption value Gateway GWN determines identity ID iIs the session valid and unregistered? If not, terminate the session; otherwise, the gateway GWN selects a random number N. i Calculate the hash value S i =h4(DID) i ||msk||N i ), for user U i Generate random kana TID i Set the first kana Second kana The counter is initialized to 0 (ctr = 0). The information sequence includes pseudonyms, the counter value, the anonymous identity, and a random number. Stored in the user authentication table; finally, the gateway GWN calculates the encrypted value. And send the encrypted value E4 to user U via a public channel. i ;

[0086] (6) After receiving the message, user U i Calculate the decryption value Select password PW i And random numbers n0∈{0,1} 8 Enter your biometric identifier (BIO) i The biometric key and reconstruction parameters (BK) are generated using a fuzz extractor. i ,P i = Gen(BIO) i ), calculate verification information V i =h4(ID) i ||BK i PW i )mod n0 and verification information The information sequence {TID i ,P i A i V i Store n0} into smart card SC i ;

[0087] S103, Group Authentication and Key Negotiation: The gateway and each smart device node jointly complete group authentication and session key negotiation; the user verifies the validity of the keys returned by all devices at once through the aggregate signature mechanism, such as... Figure 5 As shown;

[0088] Step S103 includes:

[0089] (1) User U i Smart Card SC i Insert the corresponding terminal and enter your identity. and password PW i * Enter biometric identifiers

[0090] (2) Smart Card SC i Calculate reconstruction parameters and verification information Determine the verification information V i and V i * If the keys are not equal, the session is terminated; otherwise, the user has successfully passed the authentication and can continue with the authentication and key negotiation phase.

[0091] (3) Smart Card SC i Calculate the XOR value Select a random number N u Generate the current timestamp TS1 and calculate the hash value. A u =a u P, K u =a u P pub and verification value Finally, the smart card SC i Send message M1 = {TID} to gateway GWN i A u ,V1,TS1};

[0092] (4) After receiving message M1, the gateway GWN first checks that the timestamp difference is less than the threshold. If the condition is not met, terminate the session; otherwise, the gateway GWN determines the appropriate option based on the pseudonym TID. i Search for the second kana If the search fails, continue searching for the first kana. If the session fails again, the gateway GWN will terminate the session based on the pseudonym TID. i Extract the anonymous identity DID from the user registry. i and random number N i Calculate the hash value S i =h4(DID) i ||msk||N i ), K u =sA u and verification value V1 * =h4(A u ‖S i ‖K u ‖TS1); Gateway GWN determines and verifies information V1 and V1 * If the values ​​are not equal, terminate the session and set the counter value ctr = ctr + 1. If the counter value is greater than the threshold ctr ≥ t, the gateway GWN suspends the smart card SC. i If they are equal, then the two kana are equal. Setting a second pseudonym in the gateway GWN

[0093] (5) For all smart device serial numbers j∈[n], the gateway GWN calculates the hash value mk. j =h4(SID) j msk RN j Generate the current timestamp TS2 and calculate the verification message V. 2j =h4(A u ‖mk j (TS2), finally calculate and verify the summation messages. Message M2 = {A u The broadcast, V2, TS2} is sent to all smart device nodes in the group;

[0094] (6) After receiving message M2, each smart device node SD j Check if the timestamp difference is less than or equal to the threshold If the condition is not met, terminate the session; otherwise, access the smart device SD card. j Calculate verification message Verify verification information Check if the condition is met; if not, terminate the session.

[0095] (7) Smart device SD j Select a random number N j Calculate hash value

[0096] B j =b j P and session key sk u-j =b j A u Subsequently, smart device SD j Calculate the hash value h j =h2(B j ‖sk u-j ||SID j ‖K g ), sgk j =psk j +x j +k g and signature σ j =b j +h j *sgk j Finally, smart device SD j Send message M 3j ={σ j B j SID j} to gateway GWN;

[0097] (8) After receiving all messages M 3jAfter (j∈[n]), the gateway GWN calculates the aggregate signature. And send a message Give U i Finally, the gateway GWN calculates the new pseudonym. And set kana

[0098] (9) After receiving message M4, for the smart device index j∈[n], the smart card SC i Calculate the private key sk u-j =a u B j hash value hid j =h1(SID) j ‖PK j ||P pub ) and h j =h2(B j ‖sk u-j ||SID j ‖K g Smart Card SC i verify Does it hold true? If it does, for all smart device indexes j∈[n], user U i Accept sk u-j As with smart devices SD j The session key; finally, the smart card SC i Calculate new kana and TID i Updated to

[0099] S104. Generate a unique key: The user generates an independent session key with each device node, which is unique and forward confidential.

[0100] Step S104 includes: after receiving message M4, for the smart device sequence index j∈[n], the smart card SC i Calculate session key sk u-j =a u B j hash value hid j =h1(SID) j ‖PK j ||P pub ) and hash value h j =h2(B j ‖sk u-j ||SID j ‖K g Smart Card SC i verify Does it hold true? If it does, for all smart device indexes j∈[n], user U iAccept sk u-j As with SD j Session key;

[0101] S105. Dynamic Key Update: When a smart device joins or leaves the group, the group key is updated using the Chinese Remainder Theorem to ensure forward and backward security.

[0102] Step S105 includes:

[0103] (1) User U i Smart Card SC i Insert the industrial internet terminal and enter your identity. The current password is PW i * and biometric identifiers Smart Card SC i Calculate reconstruction parameters and verification information Determine the verification information V i and V i * Check if they are equal; if not, reject this request.

[0104] (2) Smart Card SC i Request a new password PW from the user i new and biometric identifiers Note that users can also provide old biometric identifiers or passwords to update their passwords or biometric identifiers individually; Smart Card SC i Generate refactoring parameters Select random number Calculate verification information XOR value and Then delete the old information P. i A i V i n0, store the information sequence Ultimately, the smart card SC i Includes information sequence

[0105] In the group authentication and key negotiation protocol, forward security means that when a new member joins a group, it cannot obtain the group's previously private information; backward security means that when a member leaves a group, it cannot continue to obtain the group's subsequently private information. The protocol achieves forward and backward security by updating the group key.

[0106] When the smart device node SD k When a request is made to join a group, the gateway GWN updates the group key through the following steps:

[0107] (1) Gateway GWN selects a new group private key Calculate the new group public key Set the sum value γ = γ + γ k ,calculate Finally, the gateway GWN generates the current timestamp TS. g And calculate the value of d g Group public key and timestamps (TS) g signature Message Broadcast to all smart device nodes within the group;

[0108] (2) SD of each smart device node j Verify signature upon receiving message. If verification fails, terminate the session; otherwise, calculate a new group private key.

[0109] As can be seen, on the smart device node SD k After joining, the gateway GWN updates γ = γ + γ k Therefore, γ mod z k =1, Smart Device SD k A new group private key can be calculated. Due to the smart device node SD k I don't know the previous group private key k g It cannot calculate the corresponding signature key sgk k =psk k +x k +k g This prevents access to the group's previous private information, thus achieving forward security.

[0110] When the smart device node SD k When a request is made to leave a group, the gateway GWN updates the group key through the following steps:

[0111] (1) Gateway GWN selects a new group private key Calculate the new group public key Set γ = γ - γ k ,calculate Finally, the gateway GWN generates the current timestamp TS. g And calculate the value of d g , and TS g signature The message Broadcast to all smart device nodes within the group;

[0112] (2) SD card for each smart device jVerify signature upon receiving message. If verification fails, the session will be terminated; otherwise, the smart device SD card will be accessed. j Calculate the new group private key

[0113] As can be seen, on the smart device node SD k Upon departure, the gateway GWN updates γ = γ - γ k Therefore, γ mod z k =0, Smart device node SD k The new group private key cannot be calculated, therefore the new signing key cannot be calculated either. This prevents access to private information within the group, thus achieving backward security.

[0114] In the data aggregation signature authentication system of the Industrial Internet, the gateway node is responsible for the initialization and publication of system parameters, including generating elliptic curve parameters, public-private key pairs, master keys, and hash functions, and setting group capacity and group key thresholds. Before deployment, smart device nodes are assigned a unique identifier by the gateway and stored in the device's memory; after deployment, they can register via a public channel. Users register by inserting a smart card into an industrial terminal and entering their identity information and biometric identifier; the smart card stores the user's authentication credentials. After logging in, the user performs local identity verification via the smart card; upon successful verification, the user initiates a group authentication and key negotiation request to the gateway. After verifying the user's legitimacy, the gateway generates an aggregation signature. The system identifies and assists users in completing the authentication process with a group of target smart device nodes. After authentication, the user and each device node calculate a session key based on the negotiated information to achieve secure communication. In addition, the system supports updates to user passwords and biometrics, and smart device nodes can be dynamically added or deleted. The gateway updates the group key in real time to ensure communication security and system scalability. Thus, this invention utilizes certificateless aggregate signature technology and a multi-factor mechanism to achieve efficient, flexible, and secure group authentication and key negotiation, significantly reducing computational and communication overhead, improving the overall security and robustness of the system, and solving the problems of low authentication efficiency and insufficient security in high-concurrency industrial scenarios in existing technologies.

[0115] To verify the usability of this invention, the following will demonstrate and illustrate the test results and related operational overhead of the designed multi-factor group authentication and key negotiation method under simulation. The relevant configuration is as follows:

[0116] Windows 10 (64-bit, CPU@3.20GHz, RAM: 16GB, Inter(R)Core(TM)i7-8700), VMwareWorkstation 16Pro, Ubuntu 18.04.6LTS (64-bit), NS 3.28.

[0117] like Figure 6 As shown, the computation time for basic operations is as follows:

[0118] logo meaning Runtime (ms) <![CDATA[T h ]]> Hash operation 0.025 <![CDATA[T ecm ]]> Elliptic curve multiplication 8.412 <![CDATA[T eca ]]> Elliptic curve addition 0.051 <![CDATA[T s ]]> Symmetric encryption / decryption operations 0.078 <![CDATA[T mm ]]> Modular multiplication 0.004 <![CDATA[T puf ]]> Physically Unclonable Function Operations 0.120 <![CDATA[T fe ]]> Fuzzy extraction operation 8.412

[0119] When a user performs authentication and key negotiation with n smart device nodes, the computation time of the method of this invention is (4T). ecm +2T eca +2T mm +5T h )*n+4T ecm +T fe +9Th = (33.883n + 42.285) ms; When the number of smart device nodes is 10, 20, 30, 40, and 50 respectively, the computational overhead of the relevant protocols is as follows: Figure 6Released,Released[3],[4],[5],

[20] ,

[23] Released[3]MING Y,YANG P,MAHDIKHANI H,et al.A Secure One-to-Many Authentication and KeyAgreement Scheme for Industrial IoT[J / OL].IEEE Syst.J.,2023,17(2):2225-2236.https: / / doi.org / 10.1109 / JSYST.2022.3209868.[4]VINOTH R,DEBORAH LJ,VIJAYAKUMAR P,et al.SecureMultifactor Authenticated Key Agreement Scheme for Industrial IoT[J / OL].IEEEInternet of Things [5]VINOTH R,DEBORAH LJ.An efficient key agreement and authentication protocol for secure communicationin industrial IoT applications[J / OL].J.Ambient Intell.Humaniz.Comput.,2023,14(3):1431-1443.https: / / doi.org / 10.1007 / s12652-021-03167-z al.Practical Threshold Multi-Factor Authentication[J / OL].IEEE Trans.Inf.Forensics Secur.,2021,16:3573-3588.3081263;

[23] SAHOO SS,MOHANTY S,SAHO OKS,et al.A Three-Factor-Based Authentication Scheme of 5G Wireless Sensor Networks for IoT System[J / OL].IEEE InternetThings J.,2023,10(17):15087-15099.https: / / doi.org / 10.1109 / JIOT.2023.3264565.DOI:10.1109 / JIOT.2023.3264565. With the increase in the number of smart devices, the computation time of this protocol increases significantly compared to the protocol (

[23] SAHOO SS,MOHANTY S,SAHOO KS,et al.A Three-Factor-Based Authentication Scheme of 5G Wireless Sensor Networks for IoT System[J / OL].IEEE Internet Things J., 2023,10(17):15087-15099.https: / / doi.org / 10.1109 / JIOT.2023.3264565.DOI:10.1109 / JIOT.2023.3264565), protocol (

[27] GUO P,LIANGW,XU SA privacy preserving four-factor authentication protocol for internet of medical things[J / OL].Comput.Secur.,2024,137:103632.https: / / doi.org / 10.1016 / j.cose.2023.103632.DOI:10.1016 / J.COSE.2023.Compared to protocols like 103632, which are also group authentication and key negotiation protocols, the computational overhead of this invention is higher. However, compared to the one-to-one AKA protocol, the computational overhead of this invention is significantly reduced, and the advantage in computational overhead becomes more pronounced as the number of smart device nodes increases. Mainstream protocols such as Ming cannot achieve perfect forward secrecy and three-factor security, resulting in weak security. Furthermore, they require secure channels during user and smart device node registration, leading to resource waste in scenarios with a large number of smart device nodes. Therefore, this invention can reduce computational overhead while ensuring security, achieving a better balance between computational overhead and security.

[0120] like Figure 7 As shown, assuming the timestamp, hash function, random number and identity identifier, elliptic curve element, and symmetric encryption ciphertext lengths are 4 bytes, 32 bytes, 20 bytes, 32 bytes, and 16 bytes respectively, the communication overhead of the relevant methods when a user authenticates and negotiates keys with n smart device nodes is as follows:

[0121] method Total number of messages Communication overhead (bytes) Ming et al. 2n+2 172n+136 Vinoth et al. 4n+2 200n+184 Vinoth et al. 2n+2 104n+200 Sahoo et al. 4n 336n Guo et al. 4n 432n Method of the present invention 2n+2 188n+116

[0122] When the number of smart device nodes is 10, 20, 30, 40, and 50 respectively, the total message length transmitted by the relevant methods is as follows: Figure 7As shown, in the figure, [3], [4], [5],

[20] ,

[23] refer to [3] MING Y, YANG P, MAHDIKHANI H, et al. A Secure One-to-Many Authentication and Key Agreement Scheme for Industrial IoT [J / OL]. IEEE Syst. J., 2023, 17(2): 2225 - 2236. https: / / doi.org / 10.1109 / JSYST.2022.3209868. DOI: 10.1109 / JSYST.2022.3209868; [4] VINOTH R, DEBORAH L J, VIJAYAKUMAR P, et al. Secure Multifactor Authenticated Key Agreement Scheme for Industrial IoT [J / OL]. IEEE Internet Things J., 2021, 8(5): 3801 - 3811. https: / / doi.org / 10.1109 / JIOT.2020.3024703. DOI: 10.1109 / JIOT.2020.3024703; [5] VINOTH R, DEBORAH L J. An efficient key agreement and authentication protocol for secure communication in industrial IoT applications [J / OL]. J. Ambient Intell. Humaniz. Comput., 2023, 14(3): 1431 - 1443. https: / / doi.org / 10.1007 / s12652-021-03167-z. DOI: 10.1007 / S12652-021-03167-Z;

[20] LI W, CHENG H, WAN G P, et al. Practical Threshold Multi-Factor Authentication [J / OL]. IEEE Trans. Inf. Forensics Secur., 2021, 16: 3573 - 3588. https: / / doi.org / 10.1109 / TIFS.2021.3081263. DOI: 10.1109 / TIFS.2021.3081263;

[23] SAHOO SS,MOHANT YS,SAHOO KS,et al.A Three-Factor-Based Authentication Scheme of 5G WirelessSensor Networks for IoT System[J / OL].IEEE Internet Things J.,2023,10(17):15087-15099.https: / / doi.org / 10.1109 / JIOT.2023.3264565.DOI:10.1109 / JIOT.2023.3264565. As the number of smart device nodes increases, the message length of this protocol grows more slowly than that of protocols

[20] and

[23] . It can be seen that the communication overhead of the method of this invention is low, and as the number of smart device nodes increases, the advantage of the communication overhead of the method of this invention relative to some mainstream methods becomes more and more significant. Although Ming et al. ([3] MING Y, YANG P, MAHDIKHAN IH, et al. A Secure One-to-Many Authentication and KeyAgreement Scheme for Industrial IoT [J / OL]. IEEE Syst.J.,2023,17(2):2225-2236.https: / / doi.org / 10.1109 / JSYST.2022.3209868.DOI:10.1109 / JSYST.2022.3209868.) and Vinoth et al ([5]VINOTH R,DEBORAH L J.An efficient keyagreement and authentication pro protocol for secure communication in industrialIoT applications[J / OL].J.Ambient Intell.Humaniz.Comput.,2023,14(3):1431-1443.http The communication overhead of the method described in (s: / / doi.org / 10.1007 / s12652-021-03167-z.DOI:10.1007 / S12652-021-03167-Z.) is less than that of the method of this invention, but the method of this invention is more secure. Therefore, the method of this invention achieves lower communication overhead while ensuring security.

[0123] like Figure 8 and Figure 9As shown, the end-to-end latency and network throughput of the method of this invention and mainstream protocols were simulated using the NS-3 tool, with the experimental environment described above; the simulation results are as follows. Figure 8 and Figure 9As shown, in the figure, [3], [4], [5],

[23] ,

[27] refer to [3] MING Y, YANG P, MAHDIKHANI H, et al. A Secure One-to-Many Authentication and Key Agreement Scheme for Industrial IoT [J / OL]. IEEE Syst. J., 2023, 17(2): 2225 - 2236. https: / / doi.org / 10.1109 / JSYST.2022.3209868. DOI: 10.1109 / JSYST.2022.3209868; [4] VINOTH R, DEBORAH L J, VIJAYAKUMAR P, et al. Secure Multifactor Authenticated Key Agreement Scheme for Industrial IoT [J / OL]. IEEE Internet Things J., 2021, 8(5): 3801 - 3811. https: / / doi.org / 10.1109 / JIOT.2020.3024703. DOI: 10.1109 / JIOT.2020.3024703; [5] VINOTH R, DEBORAH L J. An efficient key agreement and authentication protocol for secure communication in industrial IoT applications [J / OL]. J. Ambient Intell. Humaniz. Comput., 2023, 14(3): 1431 - 1443. https: / / doi.org / 10.1007 / s12652-021-03167-z. DOI: 10.1007 / S12652-021-03167-Z;

[23] SAHOO S S, MOHANTY S, SAHOO K S, et al. A Three-Factor-Based Authentication Scheme of 5G Wireless Sensor Networks for IoT System [J / OL]. IEEE Internet Things J., 2023, 10(17): 15087 - 15099. https: / / doi.org / 10.1109 / JIOT.2023.3264565. DOI: 10.1109 / JIOT.2023.3264565;

[27] GUO P, LIANG W, XU S. Aprivacy preserving four-factor authentication protocol for internet ofmedicalthings[J / OL].Comput.Secur.,2024,137:103632.https: / / doi.org / 10.1016 / j.cose.2023.103632.DOI:10.1016 / J.COSE.2023.103632. As the number of simulation scenarios increases, the network latency of this protocol increases more slowly, and the throughput decrease is also better than that of the protocol[5],

[27] . It can be seen that the end-to-end latency of the method of this invention is only higher than that of the one-to-many AKA protocol proposed by Ming et al.[3] and Vinoth et al.[5], which has higher communication efficiency; at the same time, the throughput of the method of this invention is larger, indicating that the communication performance of the method of this invention is better. Therefore, the method of this invention can ensure better communication performance when the number of smart device nodes is large, and is more suitable for large-scale IIoT.

[0124] This invention combines certificateless public-key cryptography (CL-PKC) with aggregated signature mechanisms to effectively ensure the security and efficiency of device group authentication and key negotiation processes in the Industrial Internet. By introducing aggregated signature technology, the method enables users to perform one-time batch authentication of multiple smart device nodes, significantly reducing computational and communication overhead and improving system scalability. During authentication, user identity verification relies on a multi-factor mechanism, including password and biometric information, combined with the local verification capabilities of smart cards to prevent identity forgery and authentication bypass. To further enhance security, this invention introduces a certificateless cryptography system (CL-PKC), avoiding the complexity and security vulnerabilities of certificate management in traditional public-key infrastructures, simplifying the key distribution process, and effectively preventing key substitution attacks. After successful authentication, users and devices negotiate and generate a group session key, supporting forward and backward security to ensure that historical and future communication content is not leaked. Furthermore, the system supports dynamic management of smart devices, including adding and deleting devices, and the gateway can synchronously update the group key to maintain communication security. User passwords and biometric identifiers can also be updated as needed, enhancing the long-term reliability of identity verification. This invention introduces a timestamp mechanism in authentication messages, which can effectively resist active attacks such as replay attacks, delay attacks, and man-in-the-middle attacks; at the same time, it has a certain fault tolerance capability, supporting rapid recovery and renegotiation when terminal devices or gateways fail, ensuring high availability and robustness of the system.

[0125] In summary, this invention utilizes aggregate signatures and certificateless encryption mechanisms to establish an efficient, secure, and flexible multi-factor authentication and key negotiation protocol, meeting the comprehensive requirements for security, real-time performance, and scalability in multi-device access scenarios within the industrial internet environment.

[0126] An electronic device, such as Figure 10 As shown, it specifically includes:

[0127] One or more processors 701;

[0128] Storage device 702, on which one or more programs are stored;

[0129] When one or more programs are executed by one or more processors 701, the one or more processors 701 implement the multi-factor group authentication and key negotiation protocol method described above, including: system initialization, user registration, smart device registration, user login, group authentication and session key negotiation, user information update and device dynamic management and other operation processes.

[0130] A computer storage medium storing a computer program, which, when executed by a processor, implements the multi-factor authentication and key negotiation protocol method described above.

[0131] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the embodiments have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the invention.

Claims

1. A method of multi-factor group authentication and key agreement protocol based on certificateless aggregate signature, characterized in that, The application relates to a data aggregation signature authentication system applied to an industrial internet, and the method comprises the following steps: 1) a gateway node initializes a system and sets necessary system parameters; 2) before intelligent device nodes are deployed to a target area, the gateway selects unique identities for the intelligent device nodes and stores the identities in memories of the intelligent devices, and then the intelligent devices are registered on a public channel; 3) a user must be registered with a gateway node of the industrial internet system to be authenticated and key negotiated with the intelligent device nodes; 4) the user needs to be successfully logged in to send an authentication and key negotiation request to the gateway node; 5) the user is authenticated and session keys are negotiated with a group of intelligent device nodes at a time; 6) the user updates a local password and a biological feature identifier, and the intelligent device adds and deletes.

2. The method of claim 1, wherein, Step 1) comprises: The gateway node selects an elliptic curve on a finite field and a generator on an additive cyclic group as a base point; The gateway node selects a random number as a system private key and calculates a system public key; The gateway node selects a master key; The gateway node selects a hash function; The gateway node pre-sets a maximum capacity of each group, a group key threshold and a group key; The gateway node discloses system parameters.

3. The method of claim 1, wherein, Step 2) comprises: The intelligent device selects a random number to calculate related messages; The gateway node checks whether the intelligent device is a legal intelligent device node identity and is not registered, and if not, the session is terminated; The gateway stores the information into an intelligent device node register.

4. The method of claim 1, wherein, Step 3) comprises: The user inserts his / her smart card into an industrial internet terminal, selects his / her identity, and sends a registration request message to the gateway; After receiving the registration message of the user, the gateway judges whether the identity is legal and is not registered, and if not, the session is terminated; otherwise, the gateway registers the user information.

5. The method of claim 1, wherein, Step 4) comprises: The user inserts the smart card into the corresponding terminal, inputs the identity and password, and inputs the biological feature identifier; The smart card verifies whether the user identity is legal, and if the user passes the verification, the authentication and key negotiation phase is continued.

6. The method of claim 1, wherein, Step 5) comprises: The gateway verifies the user identity, and all the intelligent device nodes verify the gateway device identity; If the verification is passed, the gateway calculates an aggregation signature, and the intelligent device nodes and the user calculate session keys.

7. The method of claim 1, wherein, Step 6) comprises: The user inserts the smart card into the industrial internet terminal, inputs the identity, the current password and the biological feature identifier to verify the user identity; If the verification is passed, the smart card requests a new password and a biological feature identifier from the user, and the user can also provide the old biological feature identifier or password to update the password or the biological feature identifier separately; When the intelligent device node requests to join or leave a group, the gateway updates the group key. 8.A data aggregation signature authentication system in an industrial internet, characterized by, The application realizes a multi-factor group authentication and key negotiation protocol method based on a certificateless aggregation signature, and the method comprises: The intelligent device node: deployed in a target production area, used for sensing and collecting real-time data in an industrial production environment; The user: an industrial system operator, equipped with a smart card for identity verification and session negotiation; The gateway node: as a central control module, responsible for system initialization, user and device registration, authentication coordination and key negotiation tasks; In the system running process, the user uses the smart card to log in the system, and successfully establishes the secure communication connection with multiple smart device nodes through the gateway; the authentication stage generates the aggregate signature by the gateway, and the smart device node interacts with the user based on the shared group key.

9. An electronic device, comprising: Comprise: One or more processors; Storage device, which has one or more programs stored thereon; When the program is executed, the processor implements the multi-factor group authentication and key agreement protocol method based on the certificateless aggregate signature according to any one of claims 1-7.

10. A computer storage medium, characterized in that, The computer program is stored on the storage device, and when the program is executed by the processor, the multi-factor group authentication and key agreement protocol method based on the certificateless aggregate signature according to any one of claims 1-7 is implemented.

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