Certificateless signature based cloud data integrity auditing method, system, device, medium and product

Abstract

This application discloses a method, system, device, medium, and product for cloud-based data integrity auditing based on certificate-free signatures, relating to the field of network security technology. The method includes: a key generation center obtaining an anonymous identity identifier for the data owner based on the system's master secret key and the data owner's real identity identifier; obtaining a partial private key for the data owner based on the anonymous identity identifier; the data owner verifying the partial private key based on the anonymous identity identifier, and if verification is successful, secretly selecting a random number as another part of the private key, and obtaining a public key based on the other part of the private key; the data owner obtaining a tag for each data block based on the two parts of the private key; a third-party auditor initiating an integrity challenge to the cloud service provider; the cloud service provider calculating audit evidence; and the third-party auditor verifying the integrity of the audited file stored in the cloud. This application can prevent TPA (Third-Party Awareness Action) from probing privacy, simplify certificate management, achieve efficient and rapid identity authentication, and hide the user's real information.

Description

Technical Field

[0001] This application relates to the field of network security technology, and in particular to a cloud-based data integrity auditing method, system, device, medium, and product based on certificateless signature. Background Technology

[0002] In the Industrial Internet of Things (IIoT), numerous devices and sensors continuously generate massive amounts of data, which is uploaded to the cloud for storage. However, untrusted cloud environments can compromise data security and integrity for various reasons, necessitating technological measures to ensure its integrity. Traditional cloud-based data integrity verification methods typically assume the trustworthiness of the third-party auditor (TPA) performing the audit. While the TPA is trustworthy, they may, for various reasons, secretly probe the private data stored in the cloud by IIoT devices. The data generated by IIoT devices involves core parameters and real-time status information of industrial control systems; leakage could lead to malicious manipulation of the entire industrial control system, production interruptions, or damage to physical equipment. Therefore, to ensure the privacy of IIoT devices stored in the cloud, measures to prevent TPA privacy intrusion must be added to the integrity verification process.

[0003] Furthermore, the development of IIoT relies on the collaborative work of numerous smart devices and industrial sensors, and a reliable identity authentication mechanism is a prerequisite for data interaction between devices. Traditional identity authentication typically uses digital certificates issued by Public Key Infrastructure (PKI). With these certificates, users only need to verify their validity to achieve secure communication globally. However, the PKI mechanism requires users to store certificate configuration information locally and be responsible for subsequent operations such as certificate updates, management, and revocation. This is clearly not user-friendly, and even unbearable, for some resource-constrained IIoT devices. At the same time, in most cases, users do not want their true identity to be known by others, and they are usually unwilling to disclose sensitive data closely related to their true identity.

[0004] Therefore, there is a need for a cloud-based data integrity auditing method that can prevent TPA from probing privacy, simplify certificate management, achieve efficient and fast identity authentication, and hide users' real information. Summary of the Invention

[0005] The purpose of this application is to provide a cloud-based data integrity auditing method, system, device, media, and product based on certificate-free signatures, which can prevent TPA from probing privacy, simplify certificate management, achieve efficient and fast identity authentication, and hide users' real information.

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

[0007] Firstly, this application provides a cloud-based data integrity auditing method based on certificate-free signatures, including:

[0008] The key generation center obtains the system master public key based on the system master secret key, obtains the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtains the data owner's partial private key based on the data owner's anonymous identity identifier, and sends the system master public key, the data owner's anonymous identity identifier, and the data owner's partial private key to the data owner.

[0009] The data owner verifies part of the data owner's private key based on the system's master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key.

[0010] The data owner divides the auditable file stored in the cloud into multiple data blocks, and obtains a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider.

[0011] A third-party auditor launched an integrity challenge against the cloud service provider;

[0012] The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the label of each data block participating in the challenge, and sends the audit evidence to a third-party auditor;

[0013] Third-party auditors verify the integrity of audit files stored in the cloud based on audit evidence, integrity challenges, and the data owner's public key.

[0014] Secondly, this application provides a cloud-based data integrity auditing system based on certificate-free signatures, including: a key generation center, a data owner, a third-party auditor, and a cloud service provider;

[0015] The key generation center is used to obtain the system master public key based on the system master secret key, obtain the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtain the data owner's partial private key based on the data owner's anonymous identity identifier, and send the system master public key, the data owner's anonymous identity identifier and the data owner's partial private key to the data owner;

[0016] The data owner is used to verify part of the data owner's private key based on the system's master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key.

[0017] The data owner is also used to divide the auditable files stored in the cloud into multiple data blocks, and to obtain a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider.

[0018] Third-party auditors are used to initiate integrity challenges to cloud service providers.

[0019] The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the label of each data block participating in the challenge, and sends the audit evidence to a third-party auditor;

[0020] Third-party auditors are also used to verify the completeness of audit documents stored in the cloud based on audit evidence.

[0021] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to implement the cloud-based data integrity auditing method based on certificateless signature as described in any of the preceding claims.

[0022] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the cloud-based data integrity auditing method based on certificateless signature as described in any of the preceding claims.

[0023] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the cloud-based data integrity auditing method based on certificateless signature as described in any of the preceding claims.

[0024] According to the specific embodiments provided in this application, this application has the following technical effects:

[0025] This application provides a cloud-based data integrity auditing method, system, device, medium, and product based on certificateless signatures. To simplify certificate management and achieve efficient and rapid identity authentication, certificateless cryptography has become an ideal alternative in the IIoT environment. Certificateless cryptography is divided into certificateless encryption for confidential transmission and certificateless signing for lightweight identity authentication. This application utilizes certificateless signing to construct a remote data public auditing scheme, achieving lightweight identity authentication and simplifying certificate management. By treating the file to be audited as the message to be signed in the certificateless signature, the audit adds measures to prevent TPAs ​​from secretly probing private information during the public auditing phase, ensuring privacy protection during the public auditing process. Furthermore, based on the system master secret key and the real identity of the data owner, an anonymous identity identifier of the data owner is obtained, and based on the anonymous identity identifier, a portion of the data owner's private key is obtained, thus hiding the user's real information. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 A flowchart illustrating a cloud-based data integrity auditing method based on certificateless signature, provided as an embodiment of this application;

[0028] Figure 2 A schematic diagram of the structure of a cloud-based data integrity auditing system based on certificate-free signatures provided in one embodiment of this application;

[0029] Figure 3 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0030] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] In one exemplary embodiment, such as Figure 1 As shown, a cloud-based data integrity auditing method based on certificate-free signatures is provided, including:

[0033] Step 201: The Key Generation Center (KGC) obtains the system master public key based on the system master secret key, obtains the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtains the data owner's partial private key based on the data owner's anonymous identity identifier, and sends the system master public key, the data owner's anonymous identity identifier, and the data owner's partial private key to the data owner.

[0034] Step 202: The data owner (DO) verifies part of the data owner's private key based on the system master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key.

[0035] Step 203: The data owner divides the auditable file stored in the cloud into multiple data blocks, and obtains a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider (CSP).

[0036] Step 204: The third-party auditor initiates an integrity challenge with the cloud service provider.

[0037] Step 205: The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the label of each data block participating in the challenge, and sends the audit evidence to a third-party auditor.

[0038] Step 206: A third-party auditor verifies the integrity of the audited files stored in the cloud based on audit evidence, integrity challenges, and the data owner's public key.

[0039] In another exemplary embodiment of this application, the key generation center obtains the system master public key based on the system master secret key, specifically as follows:

[0040] KGC randomly selects the master secret key. The master public key mpk is the public mapping of the master secret key s in G1, according to the formula mpk = g s get; Let G1 be the set of all integers modulo p and elements coprime to p, where p represents the order of the multiplicative cyclic group G1 and the multiplicative cyclic group G2.

[0041] KGC will receive the real identity identifier (RID) of the user (data owner) sent by DO, which is ∈ {0,1}. * KGC generates anonymous identity IDs (ID∈{0,1}) based on the user's real identity identifier (RID). * In another exemplary embodiment of this application, the anonymous identity of the data owner is obtained based on the system master secret key and the real identity of the data owner, specifically as follows:

[0042] Randomly select a random number k,

[0043] According to the formula ID1 = g k Obtain the data owner's partially anonymous identity identifier ID1.

[0044] According to the formula Obtain another anonymous identity identifier, ID2, from the data owner.

[0045] The anonymous identity identifier for the data owner is ID = {ID1, ID2}. KGC sends the ID to DO through a secure channel, where g represents the generator of the multiplicative cyclic group G1, and RID represents the real identity identifier of the data owner. This represents a bitwise XOR operation, where s represents the system master secret key, and H1() represents the first hash function.

[0046] In another exemplary embodiment of this application, a portion of the data owner's private key is obtained based on the data owner's anonymous identity identifier, specifically by using the formula psk = H1(ID). s Calculate the data owner's partial private key psk.

[0047] In another exemplary embodiment of this application, after sending the system master public key, the anonymous identity identifier of the data owner, and a portion of the data owner's private key to the data owner, KGC publishes the system public parameter params = (G1, G2, g, p, u, e(), mpk, H1(), H2(), H3(), H4(), ID), but keeps s private.

[0048] After receiving a portion of the private key sent by KGC, DO needs to verify it. In another exemplary embodiment of this application, the data owner verifies the portion of the data owner's private key based on the system master public key and the data owner's anonymous identity identifier, specifically as follows:

[0049] If the formula e(psk,g)=e(H1(ID),mpk) holds true, then the verification passes, where e() represents the bilinear mapping acting on the multiplicative cyclic groups G1 and G2, e(): G1×G1→G2. psk represents a portion of the data owner's private key, g represents the generator of the multiplicative cyclic group G1, H1() represents the first hash function, ID represents the anonymous identity identifier of the data owner, and mpk represents the system master public key. If the verification fails, it means that the key security has been compromised during transmission, and the DO immediately terminates the current process and re-applies for a portion of the private key from the KGC.

[0050] The verification process for the above equation is as follows:

[0051] e(psk,g)=e(H1(ID) s ,g)

[0052] =e(H1(ID),g s )

[0053] =e(H1(ID),mpk)

[0054] If the verification passes, DO accepts a portion of the private key psk generated by KGC and secretly selects a random number. As another part of the private key, the complete private key of DO is represented as sk = (x, psk). DO then calculates and publishes the public key. In another exemplary embodiment of this application, the public key pk of the data owner is obtained from the other part of the data owner's private key, specifically according to the formula pk = g x calculate.

[0055] In another exemplary embodiment of this application, the data owner divides the auditable file F stored in the cloud into multiple data blocks, denoted as F = (m1, ..., m...). t ,…,m n ), where n represents the number of data blocks in file F, m i This represents the i-th data block obtained through block division.

[0056] DO calculates a tag for each data block. In another exemplary embodiment of this application, the tag for each data block is obtained based on part of the data owner's private key and another part of the data owner's private key, specifically:

[0057] According to the formula Calculate the label σ of the t-th data block t Where psk represents the data owner's partial private key, H2() represents the second hash function, and F id File identifier x represents another part of the data owner's private key, u represents a random element in the multiplicative cyclic group G1, and m t This represents the t-th data block. The tag set corresponding to file F is represented as Φ = {σ} t |t∈(1,2,…,n)}.

[0058] In another exemplary embodiment of this application, after DO sends {F,Φ} to CSP, it deletes the local data: file F while retaining the complete private key.

[0059] In another exemplary embodiment of this application, a third-party auditor initiates an integrity challenge to the cloud service provider, specifically including:

[0060] Step 1: TPA determines the number of data blocks to participate in this challenge.

[0061] Step 2: TPA selects a random number

[0062] Step 3: TPA sends an integrity challenge chal = {c, k1} to CSP.

[0063] The CSP calculates audit evidence based on the integrity challenge chal sent by the TPA, using H3() and H4() in the calculation process. In another exemplary embodiment of this application, the audit evidence includes label evidence and data evidence. The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the labels of each data block participating in the challenge, specifically including:

[0064] The challenge weight ω is obtained based on the integrity challenge. Specifically, it is calculated using the formula ω=H4(c||k1).

[0065] Label evidence is calculated based on the challenge weights and the labels of each data block. Specifically, it is calculated using the formula... calculate, Indicates the i-th person participating in the challenge t Labels for each data block.

[0066] Data evidence is calculated based on challenge weights and for each data block. Specifically, it is calculated according to the formula... calculate, Indicates the i-th person participating in the challenge t One data block.

[0067] In another exemplary embodiment of this application, before obtaining the challenge weight based on the integrity challenge, the method further includes: after receiving the challenge request, the CSP uses the formula... Calculate the index set I = {i1,…,u} of the data blocks participating in this challenge. t ,…,i c}, H3() represents the third hash function, k1||t represents concatenating k1 and t, mod represents modulo operation, and i t Indicates the index of the data block participating in the challenge.

[0068] In another exemplary embodiment of this application, the integrity challenge includes the total number of data blocks participating in the challenge, c, and a randomly selected random number, k1; a third-party auditor verifies the integrity of the audited file stored in the cloud based on audit evidence, the integrity challenge, and the data owner's public key, specifically as follows:

[0069] If the formula If true, the audited file stored in the cloud is complete, proving that the cloud data has not been tampered with. e() represents the bilinear mapping applied to the multiplicative cyclic groups G1 and G2, where G1 and G2 are two multiplicative cyclic groups of the same order p. δ represents the tag evidence, g represents the generator of the multiplicative cyclic group G1, ID represents the anonymous identity identifier of the data owner, H1() represents the first hash function, H4() represents the fourth hash function, c||k1 represents concatenating c and k1, mpk represents the system master public key, and F... id Let H1() represent the file identifier, H2() represent the second hash function, pk represent the public key of the data owner, u represent a random element in the multiplicative cyclic group G1, and μ represent the data evidence. H1(): {0,1} * →G1,H2():{0,1} * →G1,H3():{0,1} * →Z n ,

[0070] In another exemplary embodiment of this application, the formula The verification process is as follows:

[0071]

[0072]

[0073] Based on the same inventive concept, this application also provides a cloud data integrity auditing system based on certificateless signature for implementing the aforementioned cloud data integrity auditing method based on certificateless signature. The solution provided by this system is similar to the implementation described in the above method. Therefore, the specific limitations of one or more embodiments of the cloud data integrity auditing system based on certificateless signature provided below can be found in the limitations of the cloud data integrity auditing method based on certificateless signature described above, and will not be repeated here.

[0074] In one exemplary embodiment, such as Figure 2 As shown, a cloud-based data integrity auditing system based on certificate-free signatures is provided, including:

[0075] Key generation centers, data owners, third-party auditors, and cloud service providers.

[0076] The key generation center is used to obtain the system master public key based on the system master secret key, obtain the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtain the data owner's partial private key based on the data owner's anonymous identity identifier, and send the system master public key, the data owner's anonymous identity identifier, and the data owner's partial private key to the data owner.

[0077] The data owner is used to verify part of the data owner's private key based on the system's master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key.

[0078] The data owner also uses the data to divide the auditable files stored in the cloud into multiple data blocks, and obtains a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider.

[0079] Third-party auditors are used to initiate integrity challenges to cloud service providers.

[0080] The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the label of each data block participating in the challenge, and sends the audit evidence to a third-party auditor.

[0081] Third-party auditors are also used to verify the completeness of audit documents stored in the cloud based on audit evidence.

[0082] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 3 As shown, the computer device includes a processor, memory, input / output interfaces (I / O), and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores cloud-based data integrity audit data based on certificate-free signatures. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a cloud-based data integrity audit method based on certificate-free signatures.

[0083] Those skilled in the art will understand that Figure 3 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method embodiments.

[0084] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method embodiments.

[0085] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described method embodiments.

[0086] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0087] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0088] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0089] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A cloud data integrity auditing method based on certificateless signature, characterized in that, The cloud-based data integrity auditing method includes: The key generation center obtains the system master public key based on the system master secret key, obtains the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtains the data owner's partial private key based on the data owner's anonymous identity identifier, and sends the system master public key, the data owner's anonymous identity identifier, and the data owner's partial private key to the data owner. The data owner verifies part of the data owner's private key based on the system's master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key. The data owner divides the auditable file stored in the cloud into multiple data blocks, and obtains a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider; specifically, according to the formula... Calculate the label of the t-th data block ,in, This represents a portion of the data owner's private key. This represents another part of the private key belonging to the data owner. This represents the t-th data block. , where n represents the number of data blocks in the file to be audited. Let p represent the set of all integers modulo p and elements relatively prime to p, where p represents the multiplicative cyclic group. Multiplication Cyclic Group The order of; A third-party auditor initiates an integrity challenge with the cloud service provider; the integrity challenge includes the total number of data blocks participating in the challenge. and randomly selected random numbers ; The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the labels of each data block participating in the challenge, and sends the audit evidence to a third-party auditor. The audit evidence includes label evidence and data evidence. The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the labels of each data block participating in the challenge, specifically including: The challenge weight is obtained based on the integrity challenge. Specifically: ; Label evidence is calculated based on the challenge weights and the labels of each data block participating in the challenge, specifically as follows: according to the formula... calculate, The first to participate in the challenge Labels for each data block; Data evidence is calculated based on the challenge weights and the data blocks participating in the challenge, specifically as follows: according to the formula... calculate, The first to participate in the challenge One data block; Third-party auditors verify the integrity of audit files stored in the cloud based on audit evidence, integrity challenges, and the data owner's public key. Specifically: If the formula If the audit is successful, the auditable files stored in the cloud are complete. Indicates action on the multiplication cyclic group Multiplication Cyclic Group bilinear mapping, Indicates label evidence, Represents the multiplication cyclic group generator, This indicates the anonymous identity of the data owner. ( ) represents the first hash function. () represents the fourth hash function. This means that c and Piecing them together, Indicates the system master public key. The identifier representing the file. ( ) represents the second hash function. The public key representing the data owner. Represents the multiplication cyclic group random elements in This refers to data evidence.

2. The cloud-based data integrity auditing method based on certificateless signatures according to claim 1, characterized in that, Based on the system master secret key and the real identity identifier of the data owner, the anonymous identity identifier of the data owner is obtained, specifically: Randomly select a random number ; According to the formula Obtain partial anonymity of the data owner ; According to the formula Obtain another part of the anonymous identity of the data owner. ; Anonymous identity identifier of data owner ,in, Represents the multiplication cyclic group generator, This indicates the true identity of the data owner. This indicates a bitwise XOR operation. This represents the system's master secret key. () represents the first hash function.

3. The cloud-based data integrity auditing method based on certificateless signatures according to claim 1, characterized in that, The data owner verifies a portion of their private key using the system's master public key and the data owner's anonymous identity identifier, specifically as follows: If the formula If it is true, then it passes verification, where, ( ) indicates an action on the multiplication cyclic group. Multiplication Cyclic Group bilinear mapping, This represents a portion of the data owner's private key. Represents the multiplication cyclic group generator, Indicates the first hash function, This indicates the anonymous identity of the data owner. This represents the system's master public key.

4. A cloud-based data integrity auditing system based on certificate-free signatures, characterized in that, The cloud-based data integrity auditing system based on certificateless signatures includes: a key generation center, a data owner, a third-party auditor, and a cloud service provider; The key generation center is used to obtain the system master public key based on the system master secret key, obtain the data owner's anonymous identity based on the system master secret key and the data owner's real identity identifier, obtain the data owner's partial private key based on the data owner's anonymous identity identifier, and send the system master public key, the data owner's anonymous identity identifier and the data owner's partial private key to the data owner; The data owner is used to verify part of the data owner's private key based on the system's master public key and the data owner's anonymous identity identifier. If the verification is successful, a random number is secretly selected as the other part of the data owner's private key, and the data owner's public key is obtained based on the other part of the data owner's private key. The data owner also uses this information to segment the auditable files stored in the cloud into multiple data blocks, and obtains a tag for each data block based on part of the data owner's private key and another part of the data owner's private key. Then, each data block and its tag are sent to the cloud service provider; specifically, according to the formula... Calculate the label of the t-th data block ,in, This represents a portion of the data owner's private key. This represents another part of the private key belonging to the data owner. This represents the t-th data block. , where n represents the number of data blocks in the file to be audited. Let p represent the set of all integers modulo p and elements relatively prime to p, where p represents the multiplicative cyclic group. Multiplication Cyclic Group The order of; A third-party auditor is used to initiate an integrity challenge to the cloud service provider; the integrity challenge includes the total number of data blocks participating in the challenge. and randomly selected random numbers ; The cloud service provider calculates audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the labels of each data block participating in the challenge, and sends the audit evidence to a third-party auditor. The audit evidence includes label evidence and data evidence. The cloud service provider calculates the audit evidence based on the integrity challenge, the data blocks participating in the challenge, and the labels of each data block participating in the challenge, specifically including: The challenge weight is obtained based on the integrity challenge. Specifically: ; Label evidence is calculated based on the challenge weights and the labels of each data block participating in the challenge, specifically as follows: according to the formula... calculate, The first to participate in the challenge Labels for each data block; Data evidence is calculated based on the challenge weights and the data blocks participating in the challenge, specifically as follows: according to the formula... calculate, The first to participate in the challenge One data block; Third-party auditors also use this information to verify the completeness of audit documents stored in the cloud based on audit evidence, specifically: If the formula If the audit is successful, the auditable files stored in the cloud are complete. Indicates action on the multiplication cyclic group Multiplication Cyclic Group bilinear mapping, Indicates label evidence, Represents the multiplication cyclic group generator, This indicates the anonymous identity of the data owner. ( ) represents the first hash function. () represents the fourth hash function. This means that c and Piecing them together, Indicates the system master public key. The identifier representing the file. ( ) represents the second hash function. The public key representing the data owner. Represents the multiplication cyclic group random elements in This refers to data evidence.

5. A computer device, comprising: A memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement the cloud-based data integrity auditing method based on certificateless signatures as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the cloud-based data integrity auditing method based on certificateless signature as described in any one of claims 1-3.

7. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the cloud-based data integrity auditing method based on certificateless signature as described in any one of claims 1-3.

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