Data storage integrity verification system and method based on special polynomial ring

Abstract

The invention discloses a data storage integrity verification system and method based on a special polynomial ring, and relates to the technical field of network security. The system comprises a data coding module, a base generation module, a standard value library and a measurement module, the data coding module, the base generation module and the standard value library are respectively connected with the measurement module; the data coding module is used for converting input data into a ring polynomial; the base generation module generates bases in a random selection mode; the measurement module completes integrity verification of the data by calling the base generation module and the standard value library; and the standard value library is used for storing a standard integrity check value of the input data. According to the method, an integrity verification mechanism is designed based on a special polynomial ring, the ring takes input data as polynomial coefficients, various password attacks based on artificial intelligence and quantum computing are resisted by utilizing random selection of polynomial independent variables, and the security of the method only depends on the mathematical principle and does not depend on any mathematical problem, so that the security of the system is greatly improved. The method has the property of unconditional safety.

Description

Technical Field

[0001] The present invention relates to a data storage integrity verification system and method based on a special polynomial ring, belonging to the technical field of network security. Background Art

[0002] Artificial intelligence and quantum computing, the core forces of a new generation of technological change, are profoundly transforming human society. While driving social progress, these two technologies are also having a profound impact on cybersecurity. AI has enhanced the automated defense capabilities of information systems, while quantum computing has driven a computing revolution and enabled secure key distribution. However, while these technologies are driving advancements in cybersecurity, they also pose significant challenges. In the field of cryptography, AI and quantum computing will reshape the landscape of cryptanalysis. AI, through deep learning, is pushing the boundaries of cryptanalysis, enabling autonomous identification of encryption mechanisms and automated discovery of vulnerabilities in cryptographic protocols. Quantum computing significantly reduces the security of classical cryptographic systems. The quantum Shor algorithm exploits the parallelism and superposition properties of quantum computing to directly crack RSA and elliptic curve cryptography (ECC). The quantum Grover algorithm can directly halve the security strength of symmetric encryption and hashing algorithms. A global wave of post-quantum cryptography (PQC) is sweeping the globe. The United States will fully transition to PQC by 2035. The China National Institute of Commercial Cryptography Standards officially launched a call for proposals for a new generation of quantum-resistant cryptographic algorithms in February 2025.

[0003] The country is currently striving to develop a trusted data space. Trusted data storage is the foundation for ensuring data security and building a trusted data space. Because data faces numerous security threats during storage, such as forgery and tampering, it is crucial to establish a highly reliable integrity verification algorithm for data storage and verify the credibility of stored data in real time.

[0004] In light of the significant threats posed by artificial intelligence and quantum computing to cryptographic systems, this paper proposes a data storage integrity verification system and method based on a special polynomial ring. Unlike a binary polynomial ring, the polynomial coefficients and independent variables in this ring all belong to a finite field, resulting in a richer internal structure. This ring uses input data as polynomial coefficients and utilizes random selection of polynomial independent variables to resist cryptanalysis. Its security relies solely on mathematical principles and is unconditionally secure. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a data storage integrity verification system and method based on a special polynomial ring. Different from the conventional cryptographic design based on mathematical problems, the integrity verification mechanism is designed only based on mathematical principles to resist various cryptographic attacks based on artificial intelligence and quantum computing, thereby improving the security of data integrity verification to resist security threats from artificial intelligence and quantum computing, and having unconditional security.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows: the system includes a data encoding module, a base generation module, a standard value library and a measurement module; the data encoding module, the base generation module and the standard value library are respectively connected to the measurement module; the data involved refers to the data stored in the computing device and the network communication data;

[0007] The data encoding module is used to convert the input data to be integrity-checked into a polynomial in a ring to prepare for the subsequent integrity check by the measurement module; the basis generation module uses a random selection method to generate a basis for the measurement module to perform subsequent measurements; the measurement module completes the integrity check of the data to be integrity-checked by calling the basis generation module and the standard value library to ensure that the data is not tampered with; the standard value library is used to store the standard integrity check value of the input data to be integrity-checked.

[0008] The function of the data encoding module is to convert the input data to be checked for integrity into a polynomial ring. Elements in . The number of elements in is not less than Assume that the input data to be checked for integrity is ,in is the data label of the data to be checked for integrity, The length of the data to be checked for integrity, the data content of the data to be checked for integrity The data encoding module will Convert to Chinese elements . Now the element group , is an element-wise polynomial.

[0009] The base generation module is responsible for the generation of the base, randomly selecting Elements in As a basis, the basis generation module randomly selects a finite field As a base.

[0010] The standard value library stores the standard integrity check values ​​of the input data to be checked, stored by entry. The specific structure of each entry is as follows:

[0011]

[0012] The data tag is the standard integrity check value, The data length of the standard integrity check value, The base and standard check value selected for the standard integrity check value respectively. is the number of data entries in the standard value library. All data in the reference value library are stored confidentially and are only used internally by the integrity verification system of the present invention.

[0013] The metrics module receives element groups ,examine Whether it is in the standard value library.

[0014] 1) If If it is not in the standard value library, the base generation module is called. The base generation module randomly selects As a basis, and returned to the measurement module. The measurement module calculates

[0015]

[0016] Will Stored in the benchmark library. At the same time, the output data T=2 indicates that the input data to be checked for integrity is new data, and the standard integrity check value of the data to be checked for integrity has been generated and stored.

[0017] 2) If In the standard value library, the measurement module reads The corresponding standard integrity check value. In order to distinguish the symbols, it is assumed that The corresponding standard integrity check value is .if , then the output data T=0, indicating that the input data to be integrity checked has changed relative to the standard integrity check value. , then calculate the new standard calibration value

[0018]

[0019] if , then the output data T=1, indicating that the input data to be checked for integrity has not changed relative to the standard integrity check value. Otherwise, the output data T=0, indicating that the input data to be checked for integrity has changed relative to the standard integrity check value.

[0020] The method comprises the following steps:

[0021] Initialization phase: Select a finite field The standard value library data is empty and the number of data entries is 0.

[0022] Step 1: Input the data to be checked for integrity. The data encoding module converts the data content of the input data to be checked for integrity into a polynomial ring. , and generate element groups, which are sent to the measurement module.

[0023] Step 2: After receiving the element group, the measurement module checks whether the data label of the data to be integrity-checked in the element group exists in the standard value library; if so, go to step 5;

[0024] Step 3: If the data label in the element group does not exist in the standard value library, call the basis generation module to generate the basis.

[0025] Step 4: The measurement module substitutes the basis into the element polynomial to obtain the standard integrity check value. The data tag, data length, basis, and standard check value of the standard integrity check value are stored in the standard value library, and the number of entries in the standard value library is increased by 1. At the same time, the data T=2 is output, indicating that the input data to be checked is new data and the standard integrity check value for the new data has been generated and stored.

[0026] Step 5: If the data tag of the data to be integrity checked in the element group exists in the standard value library, the measurement module uses the data tag of the data to be integrity checked as an index to read the standard integrity check value corresponding to this data tag from the standard value library.

[0027] Step 6: Check whether the data length of the data to be checked in the element group is equal to the data length of the standard integrity check value. If they are not equal, output data T=0, indicating that the input data to be checked has changed relative to the standard integrity check value.

[0028] Step 7: If the length of the data to be checked in the element group is equal to the length of the standard integrity check value, substitute the basis into the element polynomial to obtain a new standard check value. Compare the new standard check value with the standard check value. If they are equal, output data T = 1, indicating that the input data to be checked has not changed relative to the standard integrity check value.

[0029] Step 8: If the new standard check value is not equal to the standard integrity check value, then output data T=0, indicating that the input data to be checked for integrity has been changed relative to the standard integrity check value.

[0030] The beneficial effects of this invention are: unlike conventional cryptography, which is designed based on mathematical problems and is vulnerable to cryptanalysis based on artificial intelligence and quantum computing, this invention relies solely on mathematical principles (the mathematical properties of a special polynomial ring) to design an integrity verification mechanism. This special polynomial ring uses input data as polynomial coefficients and utilizes random selection of polynomial arguments to resist various cryptographic attacks based on artificial intelligence and quantum computing. The security of this invention relies solely on mathematical principles, not on any mathematical problems, and is therefore unconditionally secure. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Integrity check system based on special polynomial ring;

[0032] Figure 2 Workflow diagram of the integrity verification system based on special polynomial rings. DETAILED DESCRIPTION

[0033] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0034] The framework diagram of the system of the present invention is as follows: Figure 1 As shown in the figure, the workflow of the integrity verification system based on the special polynomial ring is as follows Figure 2 shown.

[0035] The following is the background mathematics of the inventive method:

[0036] Polynomial ring Based on finite fields The following are two common finite fields: .

[0037] 1. Finite fields ( is a prime number): set In the model The four arithmetic operations form a domain.

[0038] 2. Finite fields Operation in First Irreducible polynomial.

[0039] The technical solution of the present invention is described in detail below with reference to two specific examples.

[0040] Example 1: Integrity Verification of Data Storage in a Cloud Environment

[0041] Assume that in a cloud computing environment, users need to transfer a large amount of encrypted data from local terminals to the cloud environment for storage. In order to ensure that the data is not maliciously tampered with or damaged after storage or during subsequent use, an integrity verification method is required. The method of the present invention focuses on solving the problem of integrity verification after data storage.

[0042] Initialization phase: cloud environment selects finite domain = , is a prime number. The cloud environment initializes its standard value library. The standard value library is used to store the verification information of the data block. The initial state is empty, does not contain any data entries, and the data entry counter is set to 0.

[0043] Step 1: The cloud environment receives a data block as input data. The data encoding module converts the data content of the input data into a polynomial ring For example, if the data content is 25600 bits of binary data, the data content is mapped to every 256 bits of data. The elements in , map the data content as a whole to . Here the data length is required If the data length is not divisible by 256, the data is padded according to the standard algorithm until the data content length is a multiple of 256. The data encoding module generates an element group for the data block. , respectively representing the data block ID, data length, and the converted element polynomial. The generated element group is then sent to the measurement module of the cloud environment.

[0044] Step 2: The measurement module in the cloud environment receives the element group sent by the user terminal. The measurement module first checks whether the data block ID in the element group exists in the standard value library.

[0045] Step 3: If the data label in the element group does not exist in the standard value library, call the basis generation module to generate the basis.

[0046] Step 4: The metric module substitutes the basis into the element polynomial to obtain the check value. It then stores the data tag, data length, basis, and check value in the standard value library, incrementing the number of entries in the standard value library by 1. It also outputs data T=2, indicating to the user terminal or other system that the received data block is new and that its integrity check value has been generated and securely stored.

[0047] Step 5: When the cloud environment receives new data, the process of steps 1 to 4 is repeated. When the cloud environment needs to verify the integrity of stored data (for example, before the data is used or periodically), the measurement module will perform the following steps.

[0048] Step 6: The measurement module uses the ID of the data block as an index to read the corresponding stored data entry from the standard value library of the cloud environment. To distinguish, the data entry read from the standard value library is recorded as ,in is the length of the stored data, is the base of storage, Is the stored checksum. The cloud environment's measurement module compares the length of the retrieved data block The length of the data in the corresponding data entry read from the standard value library .if , the measurement module outputs data T = 0, indicating that the length of the retrieved data block has changed compared with the previously stored data block, which usually means that the data may have been tampered with.

[0049] Step 7: If the data length in the element group is equal to the data length in the entry, substitute the basis into the element polynomial to obtain a new check value. , compare the new checksum to the standard checksum in this entry A comparison is performed, and if they are equal, the output data T=1, indicating that the retrieved data block is exactly the same as the previously stored data block and no changes have occurred.

[0050] Step 8: If the new check value is not equal to the check value in the entry, the output data T=0 indicates that the content of the retrieved data block has changed compared with the previously stored data block, which usually means that the data may have been tampered with.

[0051] Example 2: Data integrity check based on TPCM

[0052] The following describes a trusted boot scheme based on TPCM and a special polynomial ring. TPCM stands for integrity verification system.

[0053] Initialization phase: TPCM selects a finite field = , is a prime number. TPCM initializes its standard value library. The standard value library is used to store the checksum information of the data block. The initial state is empty and does not contain any data entries. The data entry counter is set to 0.

[0054] Step 1: In the verification information generation phase, key startup components such as BIOS firmware, boot loader, operating system kernel, etc. are divided into different data blocks. Each data block is regarded as an input data The data encoding module converts the data content of the input data into a polynomial ring Elements in BIOS, for example, assuming the data content is 25600000 bits of binary data, then the data content is mapped to every 256 bits of data The elements in , map the data content as a whole to . Here the data length is required If the data length is not divisible by 256, the data is padded according to the standard algorithm until the data content length is a multiple of 256. The data encoding module generates an element group for the data block. , respectively representing the data block ID, data length, and converted element polynomial.

[0055] Step 2: In the verification information generation phase, the measurement module calls the base generation module to generate the base The measurement module calculates the checksum of the BIOS firmware , and stored in the standard value library, the entry value is , respectively representing the data tag, data length, base, and check value. At the same time, the data T=2 is output to indicate to the user terminal or other system that the received data is new data and its integrity check value has been generated and securely stored.

[0056] Step 3: During the trusted boot phase, the integrity of each key boot component data block to be loaded and executed is verified in turn. Taking BIOS as an example, the data encoding module receives Encode BIOS data as a polynomial ring For the elements in , perform the same operation as step 1.

[0057] Step 4: The measurement module accepts the results of the data encoding module , according to the data label Take the corresponding entry from the standard value library. To distinguish, the data entry read from the standard value library is recorded as ,in is the original length of the data, Is the checksum of the original data. If the data length is inconsistent, the measurement module outputs data T = 0, indicating that the length of the retrieved data block has changed compared with the previously stored data block, and the trusted boot process is terminated.

[0058] Step 5: If the input data length is equal to the data length in the standard value library entry, recalculate the checksum of the input data , the new check value and the standard checksum in this entry The calculated checksum is compared with the stored checksum. If they are equal, the output data T=1 indicates that the retrieved data block is exactly the same as the previously stored data block and has not been changed. The trusted chain continues to transmit. If the calculated checksum is not equal to the stored checksum, the output data T=0 indicates that the content of the retrieved data block has changed compared to the previously stored data block, and the trusted boot process terminates.

[0059] The method of the present invention was implemented on a Xilinx FPGA 100MHZ. Without using pipelines, a comparative experiment was conducted with the mainstream SM3, SHA2-256, and SHA3-256 methods. The results are as follows:

[0060] The present invention SM3 SHA2-256 SHA3-256 Throughput 8Gbps 3.5Gbps 3Gbps 4Gbps

[0061] It can be seen that the throughput of the present invention is far superior to that of existing algorithms. The data involved in this technical solution refers to any record of information in electronic or other ways, especially the data stored in computing devices and network communication data.

[0062] The above are only preferred specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A data storage integrity verification system based on a special polynomial ring, characterized in that: The special polynomial ring is constructed based on a finite field. The integrity verification system includes a data encoding module, a basis generation module, a standard value library, and a measurement module. The data involved refers to data stored in computing devices and network communication data. The data encoding module, basis generation module, and standard value library are connected to the measurement module respectively. The data encoding module converts the input data to be integrity-checked into a polynomial in a ring, preparing for the subsequent integrity check by the measurement module. The basis generation module uses a random selection method to generate a basis for the measurement module to perform subsequent measurement. The measurement module completes the integrity check of the data to be checked by calling the base generation module and the standard value library; The standard value library is used to store the standard integrity check values ​​of the input data to be checked for integrity; The data to be checked for integrity is data stored in a computer.

2. The data storage integrity verification system based on a special polynomial ring according to claim 1, characterized in that: The data encoding module converts the input data to be checked for integrity into a polynomial ring Elements in, F is a finite field; let the input data to be checked for integrity be ,in is the data label of the data to be checked for integrity, is the length of the data to be checked for integrity, The data content of the data to be checked for integrity; The data encoding module will Convert to Chinese elements , constituting the element group , is an element-wise polynomial.

3. The data storage integrity verification system based on a special polynomial ring according to claim 1, characterized in that: The basis generation module randomly selects a finite field As a base.

4. The data storage integrity verification system based on a special polynomial ring according to claim 1, characterized in that: The standard value library stores the standard integrity check values ​​of the data to be checked by entry. The specific structure of each entry is as follows: The data tag is the standard integrity check value, The data length of the standard integrity check value, The base and standard check value selected for the standard integrity check value respectively; is the number of data entries in the standard value library; all data in the benchmark value library are stored confidentially and used within the integrity verification system.

5. The data storage integrity verification system based on a special polynomial ring according to claim 1, characterized in that: The metrics module receives element groups ,examine Whether it is in the standard value library; 1) If If it is not in the standard value library, the base generation module is called; the base generation module randomly selects As a basis, and returned to the measurement module; the measurement module substitutes the basis into the element polynomial to generate a standard check value ,Will It is stored in the benchmark database and outputs data T=2, indicating that the input data to be checked for integrity is new data and the standard integrity check value of the data to be checked for integrity has been generated and stored. 2) If In the standard value library, the measurement module reads The corresponding standard integrity check value; suppose it is read from the standard value library The corresponding standard integrity check value is ;if , then the output data T=0, indicating that the input data to be integrity checked has changed relative to the standard integrity check value; if , then substitute the basis into the element polynomial to generate a new standard check value , if , the output data T=1, indicating that the input data to be checked for integrity has not changed relative to the standard integrity check value; otherwise, the output data T=0, indicating that the input data to be checked for integrity has changed relative to the standard integrity check value.

6. A data storage integrity verification method based on a special polynomial ring for implementing the system according to any one of claims 1 to 5, characterized in that: The following steps are involved: Initialization phase: Selecting domain , the standard value library data is empty, and the number of data entries is 0; Step 1: Input the data to be checked for integrity. The data encoding module converts the data content of the data to be checked for integrity into a polynomial ring. , and generate element groups, and send the element groups to the measurement module; Step 2: After receiving the element group, the measurement module checks whether the data label of the data to be integrity-checked in the element group exists in the standard value library; if so, go to step 5; Step 3: If the data label in the element group does not exist in the standard value library, the base generation module is called to generate the base; Step 4: The measurement module substitutes the basis into the element polynomial to generate a standard integrity check value. It then stores the data tag, data length, basis, and standard check value of the standard integrity check value in the standard value library, and increments the number of entries in the standard value library by 1. At the same time, the output data T=2 indicates that the input data to be integrity checked is new data, and the standard integrity check value for the new data has been generated and stored. Step 5: If the data tag of the data to be integrity-checked in the received element group exists in the standard value library, the measurement module uses the data tag of the data to be integrity-checked as an index to read the standard integrity check value corresponding to the data tag from the standard value library; Step 6: Check whether the length of the data to be checked in the element group is equal to the length of the standard integrity check value. If not, output data T=0, indicating that the input data to be checked has been changed relative to the standard integrity check value. Step 7: If the data length of the data to be integrity-checked in the element group is equal to the data length of the standard integrity check value, substitute the basis into the element polynomial to obtain a new standard check value; Compare the new standard check value with the standard integrity check value. If they are equal, output data T=1, indicating that the input data to be checked has not changed relative to the standard integrity check value. Step 8: If the new standard check value is not equal to the standard check value, then output data T=0, indicating that the input data to be checked for integrity has been changed relative to the standard integrity check value.

Images