Post-quantum digital signature method of QC-LDPC code based on perforation and random insertion

Abstract

The invention discloses a post-quantum digital signature method of a QC-LDPC code based on perforation and random insertion, and relates to the technical field of information security, the method comprises the following steps: step 1, generating a secret key, including generating a public key and a private key based on the QC-LDPC code; step 2, generating a signature, including generating a digital signature according to a text to be signed and the private key; and 3, verifying the signature, namely verifying whether the digital signature is valid or not.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to a post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes. Background Art

[0002] Digital signature is an important technology used in modern information security to ensure data integrity, authenticate information sources and prevent tampering. It is widely used in finance, communications, e-government and other fields. With the development of quantum computing, traditional digital signature schemes based on public key encryption face potential security threats. Quantum computers can efficiently crack the currently popular public key cryptography systems, such as RSA and elliptic curve encryption. Therefore, it is necessary to develop new cryptographic algorithms that adapt to the quantum computing environment, namely post-quantum cryptography.

[0003] At present, post-quantum digital signature schemes based on coding theory have received widespread attention. The CFS (Courtois-Finiasz-Sendrier) signature scheme is a typical post-quantum digital signature scheme based on coding theory, and its security is based on the difficulty of the comprehensive decoding problem. This makes the CFS signature scheme effectively resistant to attacks brought by quantum computing. However, although the CFS signature scheme has strong quantum resistance, it still faces some problems in practical applications, mainly in the following aspects: 1. The length of the public key and signature is too large: The CFS signature scheme uses a public key encryption system based on Goppa code, which makes its public key and signature very large. As the key length increases, the cost of public key storage and transmission increases sharply, making it unsuitable for use on devices with limited resources, especially in application scenarios such as the Internet of Things (IoT).

[0004] 2. Low efficiency of signature generation: In the traditional CFS signature scheme, the decoding process requires multiple attempts to generate a valid signature, resulting in low efficiency of signature generation. Especially at a high security level, the decoding process may require a large number of attempts, increasing the computational overhead.

[0005] 3. Security needs to be improved: With the development of attack technology, the CFS signature scheme has gradually exposed some potential security issues. For example, the existing scheme may be vulnerable to structured attacks, Stern attacks, and OTD attacks. These attacks may infer private keys or forge signatures by analyzing the structure of the signature generation matrix or the public key matrix.

[0006] 4. Resistance to quantum attacks: Although the CFS signature scheme still maintains a certain resistance to attacks by quantum computers, with the deepening of cryptographic research, quantum attack technology is also constantly developing. It is necessary to further enhance the security of post-quantum digital signature schemes based on coding theory to ensure that they can resist more complex quantum attacks.

[0007] In order to overcome the above problems, there have been some attempts to improve the CFS signature scheme in recent years. Most of these improvements focus on the following two aspects: 1. Improve the public key structure: For example, replace Goppa code with low-density parity check (LDPC) code, RM code, etc. to reduce the size of public key and signature. By introducing new encoding methods, the efficiency of key storage is improved and the bandwidth consumption of public key transmission is reduced.

[0008] 2. Improve signature generation efficiency: By introducing parallel computing and optimizing the decoding algorithm, the computational efficiency in the signature generation process is improved, the number of decoding attempts is reduced, and the signature generation time is shortened.

[0009] Although the above improvements have solved the shortcomings of the CFS signature scheme to a certain extent, there is still a trade-off between the size of the public key, the efficiency of signature generation, and security. Traditional improvement methods either sacrifice signature efficiency and security when reducing the size of the public key, or increase the complexity of the public key when improving the efficiency of signature generation.

[0010] Therefore, technicians in this field are committed to developing a new post-quantum digital signature method to solve the above-mentioned defects in the prior art. Summary of the invention

[0011] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is how to enhance the security of the signature scheme while ensuring efficient signature generation and miniaturization of public keys, and solve the problems of too large public keys, low signature efficiency and insufficient security in the prior art.

[0012] To achieve the above objectives, the present invention provides an improved digital signature scheme based on punctured quasi-cyclic low-density parity-check code (QC-LDPC) and random insertion technology. By utilizing the quasi-cyclic structure of QC-LDPC code and combining puncturing and random insertion technology, not only the storage and transmission costs of the public key are significantly reduced, but also the efficiency of signature generation is improved, and the scheme's anti-quantum attack capability and structural attack defense capability are enhanced.

[0013] The present invention provides a post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes, comprising the following steps: Step 1: Generate keys, including generating public keys and private keys based on QC-LDPC codes; Step 2: Generate a signature, including generating a digital signature based on the text to be signed and the private key; Step 3: Verify the signature, including verifying whether the digital signature is valid.

[0014] Furthermore, the step 1 includes the following sub-steps: Step 1.1, select the initial encoding parameters, that is, select a parameter QC-LDPC code, where is the codeword length, is the number of information bits, and the codeword space is , generating the matrix for Matrix, parity check matrix and the generator matrix Satisfaction relationship ; Step 1.2: Generate a new generator matrix through puncture operation ; Step 1.3, perform a random insertion operation, in the generator matrix Insert several new columns into the matrix to get the generated matrix after insertion , where the inserted column is inserted by randomly selecting the column index; according to the relationship between the generator matrix and the parity check matrix, the parity check matrix after puncturing and random insertion is obtained ; Step 1.4: Parity check matrix As the private key, and on this basis generate the public key , where the public key is obtained by Obtained by disturbance.

[0015] Furthermore, the step 1.2 includes the following sub-steps: Step 1.2.1: From the codeword space Select the codeword with the smallest Hamming weight , and determine the codeword Support set , wherein the codeword The support is defined as Index The set of ; Step 1.2.2: In the support set Select a codeword with minimum Hamming weight based on ,in, Represents the codeword space The specific definition of codeword projection is as follows: Given a codeword and index set , then the codeword In the index set The projection on , is the code word The index in the index set A sub-codeword composed of the components in , in the index set The projection onto is defined as: set up satisfy ,in, express Hamming weight of; randomly select an index set , so that and ; Step 1.2.3. Remove the generator matrix Zhongyou Index the columns to form a new generator matrix .

[0016] Furthermore, in step 1.3, a column index set is randomly selected ,satisfy , and insert the new column into the generator matrix The generated matrix after insertion is obtained .

[0017] Further, in step 1.4, it is assumed that For one A random matrix, For one The permutation matrix, the public key The formula for generating is: in, is the parity check matrix after puncturing and random insertion.

[0018] Furthermore, the step 2 includes the following sub-steps: Step 2.1: Calculate the text to be signed The hash value of Step 2.2: Calculate the error vector ; Step 2.3: Generate the digital signature.

[0019] Furthermore, in step 2.1, the text to be signed Use counter and hash functions Sign and define the checksum as ,in, The text to be signed The hash processing result of Indicates connection and the counter Generate a new hash value, Represents a join operation.

[0020] Furthermore, in step 2.2, the error vector satisfy: in, is the public key, satisfying ; is the error vector to be solved; make and , then , the error vector is obtained by solving , the error vector will be used as a part of the digital signature during the signature generation process; The BP algorithm is used to The decoding process aims to find an error vector that meets the following conditions through iterative calculation : ; Since the parity check matrix The parity check matrix has been punctured and randomly inserted , need to be replaced The End elements, defined as: Make , and meet ;make in, and Respectively Before Elements and elements; Therefore, we can Rewritten as: in, Indicates a The binary random submatrix of , the index range is and ; Representation Matrix Remove the last The form after the column; therefore, we get: thereby, .

[0021] Further, in step 2.3, if the step 2.2 obtains The Hamming weight Exceeds the specified error threshold , then Increase by 1 and restart the signing process; when When , and generate the following digital signature : in, is the text to be signed, is the error vector, is the counter.

[0022] Furthermore, the step 3 includes the following sub-steps: Step 3.1. Calculate the hash value , and used with the public key Perform signature verification, where is the text to be signed, is the counter; Step 3.2: Use the public key and the error vector The digital signature Verify and calculate , determine whether the following equation holds: If true, it means the digital signature valid; otherwise, the digital signature invalid.

[0023] The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes provided by the present invention has at least the following technical effects: 1. The technical solution provided by the present invention significantly reduces the size of the public key and signature by adopting QC-LDPC code combined with perforation and random insertion technology. Compared with the traditional post-quantum digital signature scheme based on Goppa code, the public key size of the technical solution provided by the present invention is reduced from 6283256 bytes to 6144 bytes, and the signature generation time and storage requirements are also greatly reduced, which greatly improves the storage and transmission efficiency of the signature, making the technical solution of the present invention particularly suitable for resource-constrained devices, such as Internet of Things devices, embedded systems, etc.

[0024] 2. The technical solution provided by the present invention reduces the number of decoding attempts required for signature generation from factorial level to constant multiple by combining the quasi-cyclic structure of QC-LDPC code and BP decoding algorithm, thereby greatly shortening the signature generation time and significantly improving the efficiency of signature generation.

[0025] 3. The technical solution provided by the present invention provides enhanced resistance to quantum computing attacks. Due to the structure of the QC-LDPC code and the introduced puncture and random insertion technology, the complexity and unpredictability of the codeword structure are increased, thereby improving the ability to resist quantum computing attacks. Traditional Goppa code-based solutions may face certain risks under quantum attacks, while the technical solution adopted by the present invention can effectively resist attacks based on quantum algorithms and ensure security in the era of quantum computing.

[0026] 4. The technical solution provided by the present invention makes the generator matrix and the parity check matrix more irregular through perforation and random insertion technology, greatly increasing the difficulty of attack, thereby significantly enhancing the defense capability against structured attacks (such as Stern attack, OTD attack, etc.). Existing solutions often allow attackers to crack by analyzing the matrix structure due to the regularity of the matrix.

[0027] 5. The technical solution provided by the present invention provides flexible key storage and computing requirements. After adopting QC-LDPC code, the key storage requirements are greatly optimized. By reducing storage requirements and improving signature generation efficiency, it can not only reduce computing overhead, but also adapt to large-scale applications, especially when used on low computing power and low power consumption devices, it can effectively reduce the resource consumption of the device.

[0028] 6. The technical solution provided by the present invention is highly adaptable and suitable for a variety of post-quantum cryptographic application scenarios. It has a wide range of applicability, especially for application requirements in post-quantum cryptography. By optimizing the storage and generation process of public keys and signatures, the technical solution provided by the present invention not only has broad application potential in resource-constrained scenarios such as the Internet of Things and embedded systems, but can also be used in other post-quantum cryptographic systems that require efficient and secure signatures.

[0029] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of signature generation and signature verification of a preferred embodiment of the present invention; Figure 2 It is a schematic diagram of a generator matrix of a QC-LDPC code modified by puncturing and random insertion according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0031] The following describes several preferred embodiments of the present invention with reference to the drawings in the specification, so that the technical content is clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0032] The embodiments of the present invention relate to a post-quantum cryptographic technology based on coding theory, and in particular, a digital signature method optimized using a quasi-cyclic low-density parity-check code (QC-LDPC) with puncturing and random insertion, which is suitable for the field of cryptography that resists quantum computing attacks, especially for realizing efficient digital signatures in resource-constrained devices (such as IoT devices). Specifically, a post-quantum digital signature method proposed in an embodiment of the present invention optimizes the traditional CFS signature scheme by combining puncturing technology and random insertion technology, which not only significantly reduces the size of the public key and improves the efficiency of signature generation, but also enhances the security against quantum attacks, Stern attacks, OTD attacks, etc. This method combines the advantages of the quasi-cyclic structure, puncturing, and random insertion of QC-LDPC codes, and provides an efficient and secure digital signature solution with the following technical features: 1. Puncture technology: By selecting the codeword with the minimum Hamming weight, a specific column is removed from the generator matrix to form a punctured generator matrix, thereby enhancing the structural irregularity of the parity check matrix; 2. Random insertion technology: randomly insert rows or columns into the perforated matrix to increase the complexity of the matrix and improve the ability to resist attacks; 3. Quasi-cyclic structure: The quasi-cyclic matrix characteristics are used to reduce the key storage requirements, while supporting efficient BP decoding algorithms and improving the success rate of signature generation; 4. Optimize the signature process: significantly reduce the number of decoding attempts required for signature generation, from the original factorial level to a constant multiple.

[0033] Compared with the existing technical solutions, the technical solution provided by the embodiment of the present invention can significantly reduce the size of the public key and improve the ability to resist quantum attacks.

[0034] Example 1 like Figure 1 As shown, an embodiment of the present invention provides a post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes, comprising the following steps: Step 1: Generate keys, including generating public keys and private keys based on QC-LDPC codes; Step 2: Generate a signature, including generating a digital signature based on the text to be signed and the private key; Step 3: Verify the signature, including verifying whether the digital signature is valid.

[0035] Example 2 like Figure 2 As shown, based on Example 1, step 1 includes the following sub-steps: Step 1.1, select the initial encoding parameters, that is, select a parameter QC-LDPC code, where is the codeword length, is the number of information bits, and the codeword space is , generating the matrix for Matrix, parity check matrix and the generator matrix Satisfaction relationship ; Step 1.2: Generate a new generator matrix through puncture operation The puncturing operation is to form a new generator matrix by selecting the codeword with the minimum Hamming weight and removing some columns from the generator matrix. The punctured generator matrix is ​​still capable of error correction, but by removing some columns, the matrix becomes more unpredictable and more difficult to attack. Step 1.3: Perform random insertion operations to generate the matrix Insert several new columns into the matrix to get the generated matrix after insertion , where the inserted columns are inserted by randomly selecting column indexes, which increases the complexity of the matrix and prevents structured attacks; the parity check matrix after puncturing and random insertion is obtained according to the relationship between the generator matrix and the parity check matrix ; Step 1.4: Parity check matrix As a private key, and generate a public key based on it , where the public key is obtained by Obtained by disturbance.

[0036] Example 3 Based on Example 2, step 1.2 includes the following sub-steps: Step 1.2.1: From the codeword space Select the codeword with the smallest Hamming weight , and determine the codeword Support set , where the codeword The support is defined as Index The set of ; Step 1.2.2: In the support set Select a codeword with minimum Hamming weight based on ,in, Represents the codeword space The specific definition of codeword projection is as follows: Given a codeword and index set , then the codeword In the index set The projection on , is the codeword The index of A sub-codeword composed of the components in , in the index set The projection onto is defined as: set up satisfy ,in, express Hamming weight of; randomly select an index set , so that and ; Step 1.2.3. Remove the generator matrix Zhongyou Index the columns to form a new generator matrix .

[0037] In step 1.3, randomly select a set of column indexes ,satisfy , and insert the new column into the generator matrix The generated matrix after insertion is obtained .

[0038] In step 1.4, assume For one A random matrix, For one The permutation matrix, public key The formula for generating is: in, is the parity check matrix after puncturing and random insertion.

[0039] Example 4 Based on Example 3, step 2 includes the following sub-steps: Step 2.1: Calculate the text to be signed The hash value of Step 2.2: Calculate the error vector ; Step 2.3: Generate a digital signature.

[0040] In particular, in step 2.1, treat the signed text Use counter and hash functions Sign and define the checksum as ,in, The text to be signed The hash processing result of Indicates connection and counter Generate a new hash value, Represents a join operation.

[0041] In particular, in step 2.2, the error vector satisfy: in, is a public key, satisfying ; is the error vector to be solved; make and , then , the error vector is obtained by solving , error vector It will be used as a part of the digital signature during the signature generation process; Use BP algorithm to correct the error vector The decoding process aims to find an error vector that meets the following conditions through iterative calculation : ; Since the parity check matrix The parity check matrix has been punctured and randomly inserted , need to be replaced The End elements, defined as: Make , and meet ;make in, and Respectively Before Elements and elements; Therefore, we can Rewritten as: in, Indicates a The binary random submatrix of , the index range is and ; Representation Matrix Remove the last The form after the column; therefore, we get: thereby, .

[0042] In particular, in step 2.3, if the value obtained in step 2.2 is The Hamming weight Exceeds the specified error threshold , then Increase by 1 and restart the signing process; when When , and generate the following digital signature : in, is the text to be signed, is the error vector, It's a counter.

[0043] Example 5 Based on Example 4, step 3 includes the following sub-steps: Step 3.1. Calculate the hash value , get data bit 1, and use it with the public key Perform signature verification, where is the text to be signed, For counter; Step 3.2: Use the public key and the error vector Digital Signature Verify and calculate , get data bit 2, and determine whether data bit 1 is equal to data bit 2, that is, whether the following equation holds: If true, it means digital signature Valid; otherwise, the digital signature invalid.

[0044] Example 6 The embodiment of the present invention is about the device identity authentication in the Industrial Internet based on the post-quantum digital signature method of QC-LDPC code with puncturing and random insertion. In the Industrial Internet of Things (IIoT), multiple sensors and devices need to communicate with each other while ensuring the authenticity of the device identity and the integrity of data transmission. Traditional digital signature methods are difficult to resist quantum computing attacks, so a post-quantum signature scheme is urgently needed.

[0045] Specifically, the implementation steps of the embodiment of the present invention include: Step 1: Key distribution: Step 1.1: During the device manufacturing phase, each device generates a private key and a public key, and registers the public key with the cloud authentication server; Step 1.2: The private key is stored in the device’s security chip. Step 2: Signature generation: Step 2.1: When the device sends a data packet to the cloud server, the device uses any of the methods provided in Embodiments 1 to 5 of the present invention to process the data packet. Sign and generate signature ; Step 2.2: During the signing process, the optimized QC-LDPC code is used to generate a check matrix to improve the signing efficiency and anti-attack capability; Step 3: Signature verification: Step 3.1: After receiving the device data, the cloud server verifies the signature using the public key registered with the device to ensure that the data packet has not been tampered with; Step 3.2: If the signature verification passes, the data is accepted and used for subsequent analysis; if the verification fails, the server will reject the data packet and issue an alarm.

[0046] The advantages of the embodiments of the present invention are: 1. QC-LDPC codes optimized with puncturing and random insertion techniques can significantly reduce signature size and computation time; 2. Ensure the security of device authentication, which is difficult to crack even in a quantum computing environment.

[0047] Example 7 The embodiment of the present invention is about the communication security guarantee of the post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes in the Internet of Vehicles. In the Internet of Vehicles (V2X), vehicles and vehicles and infrastructure (such as traffic lights and traffic control centers) need to exchange information in real time, such as location, speed, road conditions, etc., requiring efficient and low-latency encrypted communication.

[0048] Specifically, the implementation steps of the embodiment of the present invention include: Step 1: Initialize the vehicle public key infrastructure (VPKI): Step 1.1: Each car generates a pair of keys (public key and private key) when it leaves the factory, and uploads the public key to the authentication system of the traffic management center; Step 1.2: The private key is securely stored by the car’s onboard unit (OBU); Step 2: Real-time message signing: Step 2.1: When the vehicle sends traffic information or a lane change signal, the OBU signs the message using the private key of the present invention to generate a signature. ; Step 2.2: The signing process is fast, ensuring that the low latency requirement of real-time vehicle communication is not affected; Step 3: Signature verification and trust propagation: Step 3.1: The receiver (other vehicle or traffic control center) verifies the signature using the public key issued by the traffic management center to ensure the authenticity of the message and the legitimacy of the sender's identity. Step 3.2: If the verification is successful, the trust relationship is propagated in the Internet of Vehicles, otherwise the message is marked as abnormal and filtered.

[0049] The advantages of the embodiments of the present invention are: 1. Provide post-quantum secure communication guarantees to prevent quantum computing from destroying traditional encryption; 2. Efficient signature generation and verification algorithm to meet the stringent requirements of the Internet of Vehicles for low latency.

[0050] The preferred specific embodiments of the present invention are described in detail above. It should be understood that ordinary technicians in the field can make many modifications and changes based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by technicians in the technical field based on the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes, characterized in that: The method comprises the following steps: Step 1: Generate keys, including generating public keys and private keys based on QC-LDPC codes; Step 2: Generate a signature, including generating a digital signature based on the text to be signed and the private key; Step 3: Verify the signature, including verifying whether the digital signature is valid.

2. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes according to claim 1, characterized in that: The step 1 includes the following sub-steps: Step 1.1, select the initial encoding parameters, that is, select a parameter QC-LDPC code, where is the codeword length, is the number of information bits, and the codeword space is , generating the matrix for Matrix, parity check matrix and the generator matrix Satisfaction relationship ; Step 1.2: Generate a new generator matrix through puncture operation ; Step 1.3, perform a random insertion operation, in the generator matrix Insert several new columns into the matrix to get the generated matrix after insertion , where the inserted column is inserted by randomly selecting the column index; according to the relationship between the generator matrix and the parity check matrix, the parity check matrix after puncturing and random insertion is obtained ; Step 1.4: Parity check matrix As the private key, and on this basis generate the public key , where the public key is obtained by Obtained by disturbance.

3. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 2, characterized in that: The step 1.2 includes the following sub-steps: Step 1.2.1: From the codeword space Select the codeword with the smallest Hamming weight , and determine the codeword Support set , wherein the codeword The support is defined as Index The set of ; Step 1.2.2: In the support set Select a codeword with minimum Hamming weight based on ,in, Represents the codeword space The specific definition of codeword projection is as follows: Given a codeword and index set , then the codeword In the index set The projection on , is the code word The index in the index set A sub-codeword composed of the components in , in the index set The projection onto is defined as: set up satisfy ,in, express Hamming weight of; randomly select an index set , so that and ; Step 1.2.

3. Remove the generator matrix Zhongyou Index the columns to form a new generator matrix .

4. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 3, characterized in that: In step 1.3, a column index set is randomly selected ,satisfy , and insert the new column into the generator matrix The generated matrix after insertion is obtained .

5. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 4, characterized in that: In step 1.4, it is assumed that For one A random matrix, For one The permutation matrix, the public key The formula for generating is: in, is the parity check matrix after puncturing and random insertion.

6. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 5, characterized in that: The step 2 includes the following sub-steps: Step 2.1: Calculate the text to be signed The hash value of Step 2.2: Calculate the error vector ; Step 2.3: Generate the digital signature.

7. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 6, characterized in that: In step 2.1, the text to be signed Use counter and hash functions Sign and define the checksum as ,in, The text to be signed The hash processing result of Indicates connection and the counter Generate a new hash value, Represents a join operation.

8. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 7, characterized in that: In step 2.2, the error vector satisfy: in, is the public key, satisfying ; is the error vector to be solved; make and , then , the error vector is obtained by solving , the error vector will be used as a part of the digital signature during the signature generation process; The BP algorithm is used to The decoding process aims to find an error vector that meets the following conditions through iterative calculation : ; Since the parity check matrix The parity check matrix has been punctured and randomly inserted , need to be replaced The End elements, defined as: Make , and meet ;make in, and Respectively Before Elements and elements; Therefore, we can Rewritten as: in, Indicates a The binary random submatrix of , the index range is and ; Representation Matrix Remove the last The form after the column; therefore, we get: thereby, .

9. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 8, characterized in that: In step 2.3, if the The Hamming weight Exceeds the specified error threshold , then Increase by 1 and restart the signing process; when When , and generate the following digital signature : in, is the text to be signed, is the error vector, is the counter.

10. The post-quantum digital signature method based on punctured and randomly inserted QC-LDPC codes as claimed in claim 9, characterized in that: The step 3 includes the following sub-steps: Step 3.

1. Calculate the hash value , and used with the public key Perform signature verification, where is the text to be signed, is the counter; Step 3.2: Use the public key and the error vector The digital signature Verify and calculate , determine whether the following equation holds: If true, it means the digital signature valid; otherwise, the digital signature invalid.

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