Binary contrast decision based on certificateless digital signature

Abstract

The invention provides a binary comparison decision-making method based on a certificateless digital signature. The binary comparison decision-making method is used for improving the safety and efficiency of a decision-making process. The method comprises initialization of system parameters, user identity verification and private key distribution, generation of a private key and a public key, data signature and verification, and decision analysis by using a binary comparison model. Through the certificateless technology, the method avoids the complexity and security risk of certificate management in the traditional digital signature. In addition, by introducing the binary comparison decision model, the scientificity and objectivity of decision are improved, and the high efficiency of data processing is ensured. The method is widely applicable to decision-making environments requiring rapid and high security assurance.

Description

Technical Field

[0001] The present invention relates to the field of public key cryptography, and in particular to binary comparison decision-making based on certificateless digital signature. Background Art

[0002] In the context of the rapid development of modern information technology, digital signatures, as a key technology to ensure the security of data transmission, have been widely used in various commercial, government and personal data exchange scenarios. Digital signatures can not only verify the integrity and tamper-free status of data, but also confirm the legitimacy of the data source. Traditional digital signature technology often relies on the management of certificates, which are used to bind public keys and identities to ensure the authenticity of public keys. However, the management and distribution of certificates involve complex infrastructure and additional costs, especially in the process of certificate revocation and renewal, which are inconvenient to manage and have security risks. With the evolution of technology, certificateless digital signatures have emerged to address the defects of the certificate system on which traditional digital signatures rely. Certificateless digital signatures eliminate the need for certificates through innovative cryptographic methods. Users only need to use some public parameters and their own private keys to generate signatures, which greatly simplifies the management of public keys and reduces the security risks associated with certificates.

[0003] The core of certificateless digital signature technology is that it uses a special key generation scheme, in which the key generation center (KGC) is responsible for generating and distributing key parameters without issuing and managing certificates for each user. This technology uses complex mathematical constructions, such as bilinear mapping, to achieve a secure signing and verification process. In a certificateless framework, each user's public key is not guaranteed by a certificate issued by a trusted third party, but can be directly calculated from the user's identity information and system parameters, which not only simplifies the key management process, but also enhances the flexibility and scalability of the system. In addition, certificateless digital signature technology supports an implicit authentication mechanism, that is, the verifier can implicitly confirm the identity of the signer by simply verifying the signature of the information without the need for additional certificate verification steps. This mechanism shows its unique advantages in multi-party data exchange and large-scale distributed systems.

[0004] Although certificateless digital signature technology provides many advantages, it still faces some challenges and limitations in practical applications. For example, the security of the key generation center is crucial, and any attack on the KGC may endanger the security of the entire system. In addition, the initial setting and parameter selection of the certificateless system need to be very cautious to prevent potential cryptanalysis attacks. For example, the PDF digital signature method described in patent CN201410356589.9, although it provides an effective protection measure for PDF files, the technology focuses on files of a specific format, lacks wide adaptability, and multiple signatures may lead to inefficient file processing. In addition, although the digital signature technology described in patent CN201010505308.3 improves the security of messages, its complex processing flow and reliance on traditional certificates significantly increase the operating burden of the system.

[0005] The present invention aims to address the limitations and security risks of traditional digital signature technology by introducing a binary comparison decision method based on certificateless digital signature. The present invention is particularly suitable for application scenarios that require fast and secure decision-making, such as online voting, electronic contract signing, etc. Through binary comparison, the method not only simplifies the decision-making process, but also ensures the security and integrity of decision-making data through a powerful encryption algorithm. Summary of the invention

[0006] The present invention provides a binary comparison decision method based on certificateless digital signature. The method integrates advanced certificateless digital signature technology and binary comparison decision model to improve the security, efficiency and accuracy of the decision process. In order to achieve the above improvement effect, the present invention proposes a technical solution including the following implementation steps:

[0007] S1: System parameter generation. During the initialization phase of the key generation center KGC, a set of security parameters is selected. The security parameters include prime number bases, cyclic groups, and bilinear maps. KGC generates the system master key and public parameter set. The public parameter set includes public elements for bilinear maps and other certificateless signature operations.

[0008] S2: User registration and partial private key extraction and verification. The user provides a unique identity to KGC. KGC verifies the user's identity and generates a partial private key based on the user's identity and system parameters. It is sent to the user through a secure channel. The user accepts and verifies the partial private key received from KGC.

[0009] S3: User private key and public key settings. The user generates a random private key locally and calculates and generates his own public key.

[0010] S4: Signature generation and verification. The user uses his private key to sign a specific message. The signing process includes using the user's private key, part of the private key and a random number to generate a digital signature. The verifier uses the master key and the user's public key to verify the signature of the message and confirm the legitimacy of the signature.

[0011] S5: Binary comparison decision-making process, collects and processes relevant factors that affect the decision, and each factor is provided with a relative weight by an expert from the expert group; constructs a judgment matrix based on the binary comparison decision model, and sends it to the end user using a certificateless digital signature to ensure the integrity and tamper-proofness of the decision data; the end user calculates the comprehensive weight of each factor to obtain the final decision.

[0012] As a technical preferred solution of the present invention, the system parameter generation in step S1 specifically includes the following steps:

[0013] S1-1: Set a security parameter L and select a sufficiently large prime number q that satisfies q≥2 L , used to ensure the security and anti-attack strength of the system;

[0014] S1-2: Define an additive cycle group G1 and a multiplicative cycle G2 of order q, and set a bilinear map e:G1×G1→G2;

[0015] S1-3: Introduce two secure hash functions, the hash functions specifically include:

[0016] H1:{0,1} * →G1 , used to map identities to elements in group G1;

[0017] Random number generation for message signing, where It represents the multiplicative group of the priority field of the remainder class modulo q;

[0018] S1-4: The key generation center randomly selects an element s as the system master key, where Select a generator p belonging to G and calculate the system master key P0=sp;

[0019] S1-5: The public parameter set of the published system is params = (G1, G2, e, q, p, p0, g, H1, H2), where g = e(p, p), and the message space M = {0, 1} * , a public parameter set is used by all users to support certificateless signing and verification operations.

[0020] 3. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: the user registration and partial private key extraction and verification in step S2 specifically include the following steps:

[0021] S2-1: User identity submission: The user submits his unique identity ID to the key generation center A ∈{0,1} * , where the identity includes: email address, user ID or any other information that can be used to uniquely identify the user; A represents the user;

[0022] S2-2: Identity verification and partial private key generation: KGC verifies the validity of the submitted identity. After confirmation, it generates the user's partial private key based on the user's identity and pre-set algorithm parameters. The generation of the private key depends on the secure hash function H1 and the system master key. The specific calculation is:

[0023] D A =sH1(ID A )

[0024] Among them, s is the system master key held by KGC, H1 is the hash function that maps the identity to the group G1;

[0025] S2-3: Secure transmission of partial private key: Partial private key D A Transmitted to the user through a secure channel.

[0026] 4. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: the user private key and public key setting in step S3 specifically includes the following steps:

[0027] S3-1: Generation of user private key: The user generates a random secret value x on the local device A As the user's private key, the secret value is selected from the group Right now:

[0028] S3-2: Calculation of public key: The user uses the private key to calculate the user's public key, where the public key P A =x A P.

[0029] 5. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: the signature generation and verification in step S4 comprises the following steps:

[0030] S4-1: Signature generation, specifically including the following steps:

[0031] S4-1-1: Random number generation: The user first generates a random number r locally, selects Right now:

[0032] S4-1-2: Calculate the verification element: Use the generated random number r to calculate the verification element U. The specific calculation formula is: U = g r , where g is the generator of group G1;

[0033] S4-1-3: Message hash calculation: Use the hash function H2 to calculate the hash value h of the message m to be signed. The specific calculation formula is: h = H2 (m, U);

[0034] S4-1-4: Completion of signature: Calculation of signature δ = rP-h(D A +x A V), where x A is the user's private key, V = H1(ID A ), output signature σ=(m,h,δ,);

[0035] S4-2: Verification of signature, including the following steps:

[0036] S4-2-1: Receive the signed message and public information: The signed message is σ=(m,h,δ,), and the public information is (ID A ,P A );

[0037] S4-2-2: Reconstruction of the inspection element: Use the received information to reconstruct the inspection element U'. The specific calculation formula is: U'=e(δ,p)[e(V,P0)e(P A ,V)] h ;

[0038] S4-2-3: Hash verification: Use the same hash function H2 to recalculate the hash value of the original message m and the reconstructed verification element U', and verify whether h'=H2(m,U') is equal to h in the signature;

[0039] S4-2-4: Acceptance or rejection of the signature: If the calculated hash value h′ matches h in the signature, the signature is accepted as valid, otherwise the signature is rejected.

[0040] 6. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: the binary comparison decision in step S5 comprises the following steps:

[0041] S5-1: Determination of decision-making factors: Experts determine the main factors affecting the decision, X1, X2, ..., X n ;

[0042] S5-2: Construction of binary comparison judgment matrix: Experts compare each decision factor pairwise and generate importance index Where f represents the factor x iRelative to x j Importance:

[0043]

[0044] The judgment matrix B is constructed by assigning the matrix B. The calculation formula of matrix B is:

[0045]

[0046] in, Satisfy the constraints:

[0047] S5-3: Compatibility test of the judgment matrix, including two judgment methods:

[0048] S5-3-1: The first step is to use the formula |λ-EB|=0 to find the maximum eigenvalue λ of the matrix B max ; In the second step, C(B) is introduced as a quantitative indicator of incompatibility, where E is the unit matrix and the calculation formula of C(B) is:

[0049]

[0050] If C(B)≤0.10, then the judgment matrix B n×n is compatible; if C(B)>0.01, then the judgment matrix B n×n incompatible;

[0051] When the matrix B=(b ij ) n When the order of is very high, solving the eigenvalues ​​and eigenvectors of the matrix B will be a very time-consuming task. In order to improve the computational efficiency, the following alternative methods can be used:

[0052] S5-3-2: For any i, j, k, let the matrix B' = (b' ij ) n Satisfies: If b' ij ≥1,b' jk ≥1, then b' ik ≥1, then the matrix B' is compatible, and the specific calculation formula is as follows:

[0053]

[0054] Among them, if B' n×n If the transitivity is satisfied, then the matrix B' n×n is consistent; otherwise, it is considered that the matrix B n×n incompatibility;

[0055] S5-4: After the experts obtain the compatible matrix B based on their own opinions, they digitally sign the matrix as a message M and then send it to the end user.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] Enhanced security: The present invention eliminates the management and verification process of traditional digital signatures that rely on certificates through certificateless digital signature technology, thereby reducing security vulnerabilities caused by certificate revocation and expiration. This method enhances the security of the entire system and avoids a series of security risks associated with certificates.

[0058] Simplified system management: Since there is no need to deal with the issuance and management of certificates, the system maintenance cost is significantly reduced, and the user's operation process is simplified. Users do not need to pay attention to the validity period and renewal of certificates, making the system more user-friendly.

[0059] Improve decision-making efficiency and accuracy: The present invention applies a binary comparison decision model, constructs a judgment matrix and calculates factor weights to make the decision-making process more scientific and accurate. At the same time, by automating these processes, the efficiency of decision-making is greatly improved, which is especially suitable for scenarios that require rapid response.

[0060] Wide applicability: Certificateless digital signature technology is not limited to a specific document format or data type, so the present invention is applicable to a variety of data and files. This makes the present invention widely applicable to different industries and fields, such as finance, law, medicine, government, etc., where data security and decision accuracy are extremely high. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A flow chart of the method for binary comparison decision-making based on certificateless digital signature provided by the present invention;

[0062] Figure 2 A schematic diagram of a digital signature system is provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The present invention is further described below in conjunction with the accompanying drawings and examples. However, the present invention can be implemented in many different ways and should not be construed as being limited to the embodiments shown; on the contrary, these embodiments provide those skilled in the art with implementation methods that meet applicable legal requirements.

[0064] Example 1: Figure 1 As shown, the binary comparison decision based on certificateless digital signature described in this embodiment includes the following steps:

[0065] S1: System parameter generation. In the initialization phase of the key generation center KGC, a set of security parameters is selected. The security parameters include prime number bases, cyclic groups, and bilinear mappings. KGC generates a system master key and a public parameter set. The public parameter set includes public elements for bilinear mappings and other cryptographic operations. The specific steps include:

[0066] S1-1: Set a security parameter L and select a sufficiently large prime number q that satisfies q≥2 L , used to ensure the security and encryption strength of the system;

[0067] S1-2: Define the additive cycle group G1 and the multiplicative cycle G2 of order q, and set the bilinear map e:G1×G1→G2;

[0068] S1-3: Introduce three secure cryptographic hash functions, including:

[0069] H1:{0,1} * →G1, used to map identities to group elements;

[0070] Random number generation for message signing, where represents the multiplicative group modulo q;

[0071] S1-4: The key generation center randomly selects an element s as the system master key, where Select a generator p belonging to G and calculate the system master key P0=sp;

[0072] S1-5: The public parameter set of the published system is params = (G1, G2, e, q, p, p0, g, H1, H2), where g = e(p, p), and the message space M = {0, 1} * , a public parameter set is used by all users to support certificateless signing and verification operations.

[0073] S2: User registration and partial private key extraction and verification. The user provides a unique identity to KGC. KGC verifies the user's identity and generates a partial private key based on the user's identity and system parameters, and sends it to the user through a secure channel.

[0074] The user accepts and verifies the partial private key received from KGC; specifically, the following steps are included:

[0075] S2-1: User identity submission: The user submits his unique identity ID to the key generation center A ∈{0,1} * , where the identity includes: email address, user ID or any other information that can be used to uniquely identify the user; A represents the user;

[0076] S2-2: Identity verification and partial private key generation: KGC verifies the validity of the submitted identity. After confirmation, it generates the user's partial private key based on the user's identity and pre-set algorithm parameters. The generation of the private key depends on the secure hash function H1 and the system master key. The specific calculation is:

[0077] D A =sH1(ID A )

[0078] Among them, s is the system master key held by KGC, H1 is the hash function that maps the identity to the group G1;

[0079] S2-3: Secure transmission of partial private key: Partial private key D A Transmitted to the user through a secure channel.

[0080] S3: User private key and public key settings. The user generates a random private key locally and calculates and generates his own public key.

[0081] User private key and public key settings include the following steps:

[0082] S3-1: Private key generation: The user generates a random secret value x on the local device A As the private key, the secret value is selected from the group Right now:

[0083] S3-2: Calculation of public key: The user uses the partial private key received from the key generation center and the self-generated secret value to calculate the user's public key, where the public key P A =x A P.

[0084] S4: Signature generation and verification. The user uses his private key to sign a specific message. The signing process includes using the user's private key, secret value and random number to generate a digital signature. The verifier uses the user's public key to verify the signature of the message and confirm the legitimacy of the signature, including verifying the consistency of the bilinear map and hash function. The specific steps include:

[0085] S4-1: Signature generation, specifically including the following steps:

[0086] S4-1-1: Random number generation: The user first generates a random number r locally, selects Right now:

[0087] S4-1-2: Calculate temporary public key: Use the generated random number r to calculate the temporary public key U. The specific calculation formula is: U = g r, where g is the generator of group G1;

[0088] S4-1-3: Message hash calculation: The hash value of the message m to be signed is calculated using the hash function H2. The specific calculation formula is: h = H2 (m, U);

[0089] S4-1-4: Completion of signature: Calculation of signature δ = rP-h(D A +x A V), where x is the user's secret value, V = H1(ID A ), output signature σ=(m,h,δ,);

[0090] S4-2: Verification of signature, including the following steps:

[0091] S4-2-1: Receive the signed message and public information: The signed message is σ=(m,h,δ,), and the public information is (ID A ,P A );

[0092] S4-2-2: Reconstruction of the inspection element: Use the received information to reconstruct the inspection element U'. The specific calculation formula is: U'=e(δ,p)[e(V,P0)e(P A ,V)] h ;

[0093] S4-2-3: Hash verification: Use the same hash function H3 to recalculate the hash value of the original message m and the reconstructed temporary public key U', and verify whether h'=H3(m,U) is equal to h in the signature;

[0094] S4-2-4: Acceptance or rejection of the signature: If the calculated hash value h′ matches h in the signature, the signature is accepted as valid, otherwise the signature is rejected.

[0095] S5: Binary comparison decision process, collects and processes relevant factors that affect the decision, and each factor is provided with a relative weight by an expert in the expert group; constructs a judgment matrix based on the binary comparison decision model and calculates the comprehensive weight of each factor, and sends it to the end user using a certificateless digital signature to ensure the integrity and tamper-proofness of the decision data; the end user uses a mathematical model to get the final decision, which specifically includes the following steps:

[0096] S5-1: Determination of decision-making factors: According to the specific decision-making problem, determine the main factors affecting the decision, X1, X2, ..., X n ;

[0097] S5-2: Construction of binary comparison judgment matrix: Experts compare each decision factor pairwise and generate importance index Where f represents the factor xi Relative to x j Importance:

[0098]

[0099] The judgment matrix B is constructed by assigning the matrix B. The calculation formula of matrix B is:

[0100]

[0101] in, Satisfy the constraints:

[0102] S5-3: Compatibility verification of the judgment matrix, including two judgment methods:

[0103] S5-3-1: The first step is to use the formula |λE-B|=0 to find the maximum eigenvalue λ of matrix B max ; In the second step, C(B) is introduced as a quantitative indicator of incompatibility, where E is the unit matrix and the calculation formula of C(B) is:

[0104]

[0105] If C(B)≤0.10, then the judgment matrix B n×n is compatible; if C(B)>0.01, then the judgment matrix B n×n are incompatible;

[0106] S5-3-2: For any i, j, k, let the matrix B' = (b' ij ) n Satisfies: If b' ij ≥1,b' jk ≥1, then b' ik ≥1, then the matrix B' is compatible, and the specific calculation formula is as follows:

[0107]

[0108] Among them, if B' n×n If the transitivity is satisfied, then the matrix B' n×n is consistent; otherwise, it is considered that the matrix B n×n incompatibility;

[0109] S5-4: After the experts have derived the compatible matrix B based on their own opinions, they digitally sign the matrix as a message M and send it to the organizer.

[0110] Example 2: Figure 2 As shown in the digital signature system, the signer first applies to KGC for his own partial private key D vAuthorization, then based on the secret value X generated by itself V , forming a complete private key S v , and finally use your own identity information ID v , Public Key PK v and private key S v Sign the information m and generate the signature result σ. The verifier uses the identity information ID v and public key PK v To determine whether σ is a legitimate signature of information m. However, security issues cannot be ignored, and attackers may tamper with a legitimate signature of information m or steal the signer's private key.

[0111] The certificateless signature scheme mainly includes the following steps:

[0112] (1) Generation of system parameters. We set a security parameter L and select a sufficiently large prime number q to satisfy certain security conditions (e.g., prime number q ≥ 2 L ), then we define the additive cycle group G of order q, the multiplication cycle G2 and a bilinear map e:G1×G1→G2; then, we introduce the secure cryptographic hash function H1: The key generation center (KGC) randomly selects an element s as the system master key. Next, select a generator p belonging to G1 and calculate the system master key P0 = sp. Then let g = e(p, p), and finally the public parameter set params = params = (G1, G2, e, q, p, p0, g, H1, H2); message space M = {0, 1} * .

[0113] (2) Extraction and verification of partial private keys. During the user registration process, user A submits his unique ID A ∈{0,1} * After receiving the identity of user A, KGC authenticates the user ID and then calculates the partial private key D of user A. A =sH1(ID A ), and finally transmit D through a secure channel A To user A.

[0114] (3) Set the private key. User A selects the secret value Put x A as your own private key.

[0115] (4) Set the public key. User A calculates P A =x A P, put P A as a public key.

[0116] (5) Signature. User A signs the message m∈{0,1} as follows: * sign.

[0117] (a) Calculate U = g r ;

[0118] (b) Calculate V = H1 (ID A );

[0119] (c) Calculate h = H2(m,U);

[0120] (d) Calculate the complete private key S A =D A +x A V

[0121] (d) Calculation of δ = rP - hS A , and output the signature σ=(m,h,δ)).

[0122] (6) Verification. For the signature message σ=(m,h,δ)) and the public information (ID A ,P A ), the verification process of the verifier is as follows;

[0123] (a) Calculate V = H1 (ID A )

[0124] (b) U'=e(δ,p)[e(V,P0)e(P A ,V)] h ;

[0125] (c) Verify h = H2(m,U). If the equality holds, the signature σ is accepted; otherwise, the signature σ is rejected.

[0126] Taking the land grading process of site A as an example, the organizer needs to determine the weights of each grading factor, and the determination process is as follows.

[0127] The main factors affecting the classification may vary from place to place. Based on experience, we can generally screen out multiple main influencing factors, using X1, X2, ..., X n Indicates the factors that affect the classification of site A. In order to determine the weights of these factors, for the sake of fairness and objectivity, the scheme design needs to invite multiple experts (users in the digital signature scheme in this article) to give quantitative values ​​of the relative superiority relationship between these factors, that is, the factor X in the binary comparison decision scheme in the literature i Relative to factor X j The "importance" indicator for Represents element X j Relative to X i The priority indicators that are "attractive" toi As standard, according to X j The superiority of The value of is as follows, assuming:

[0128]

[0129] This gives us the matrix B:

[0130]

[0131] The specific data are shown in Table 1:

[0132] Table 1 The “importance” index between different influencing factors

[0133]

[0134] And require satisfy: For example, with X i Represents the economic situation of the region, X j Represents the regional environment, It indicates the importance of environmental conditions in affecting regional land classification relative to regional economic conditions.

[0135] Afterwards, the compatibility of the transformation matrix B is determined.

[0136] Generally speaking, there are two ways to determine whether the matrix B is compatible:

[0137] (1) Maximum eigenvalue method of matrix B. The first step is to use the formula |λE-B|=0 (E is the unit matrix) to find the maximum eigenvalue λ of matrix B. max ; The second step is to introduce C(B) as a quantitative indicator of incompatibility, and

[0138]

[0139] When C(B)≤0.10, it can be considered that the judgment matrix B n is compatible; C(B)>0.01 is considered that the judgment matrix B n×n are incompatible.

[0140] (2) When the dimension of matrix B is very high, solving the eigenvalues ​​and eigenvectors of matrix B will be a very time-consuming task. In order to improve the computational efficiency, the following alternative methods can be used:

[0141] For any i, j, k, let the matrix B' = (b' ij ) n Satisfies: If b' ij ≥1,b' jk ≥1, then b'ik ≥1, then the matrix B' is compatible, and the specific calculation formula is as follows:

[0142]

[0143] If B' satisfies transitivity, the matrix B' is considered to be compatible; otherwise, the matrix B' is considered to be incompatible. After the experts obtain the compatible matrix B based on their own opinions, they digitally sign the matrix as a message M and send it to the end user.

[0144] The signing process is as follows:

[0145] Suppose the matrix obtained by k experts is M1,M2,......,M k .

[0146] According to the model in the certificateless signature system, each expert signs the message he or she gives. The expert signs the message M as follows: i ∈{0,1} * Signature (i=1,2,…,k).

[0147] Any Calculate U = g r ;

[0148] Calculate V = H1 (ID A );

[0149] Calculate h = H2(m,U);

[0150] Calculate δ = rP-h(D A +x A V), and output the signature σ=(M i ,h,δ).

[0151] The expert sends the signed information to the receiver, who then verifies the received information.

[0152] For signature σ=(M i ,h,δ) and public information (ID A ,P A ), the receiver performs the following checks:

[0153] Calculate V = H1 (ID A )

[0154] Calculate U'=e(δ,p)[e(V,P0)e(P A ,V)] h ;

[0155] Verify h=H2(m,U). If the equation holds, the receiver accepts the signature σ. Otherwise, if the equation does not hold, the receiver rejects the signature σ and contacts an expert to resend the message and signature.

[0156] Finally, the end user calculates the k-bit expert information M i That is, matrix B determines the factors X1, X2, ..., X n k weight vectors W1,W2,......,W k , we can get W i (i=1,2,……,k) value. Then obtain the corresponding W through the following way i Values:

[0157] Calculate the maximum eigenvalue λ of matrix B max The corresponding eigenvector, then the value of the eigenvector is the value of the weight vector W.

[0158] Finally, the weights obtained by each expert are averaged to obtain the final, relatively fair weight.

[0159] Let the weight of the i-th expert be W i1 ,W i2 ,......,W in , then the final weight given by the k experts is

[0160] The embodiment of the present invention elaborates on the binary comparison decision method based on certificateless digital signature, covering the generation of system parameters, user registration and private key extraction, verification of some private keys, user private key and public key settings, signature generation and verification, and binary comparison decision process. This method adopts certificateless digital signature technology, effectively avoiding the complexity and security risks of traditional digital signatures relying on certificates, and improving the security and efficiency of the system. The binary comparison decision part uses expert input and judgment matrix to ensure the scientificity and objectivity of the decision process and improve the quality of decision. In addition, the detailed steps of the whole process ensure the operability and accuracy of the implementation, so that the method is not only suitable for business and financial decision-making, but also can be widely used in fields that require high data security and decision accuracy.

[0161] The above embodiments only express the implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for those of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention.

Claims

1. A binary comparison decision method based on certificateless digital signature, characterized by: The method comprises the following steps: S1: System parameter generation. During the initialization phase of the key generation center KGC, a set of security parameters is selected. The security parameters include prime number bases, cyclic groups, and bilinear maps. KGC generates the system master key and public parameter set. The public parameter set includes public elements for bilinear maps and other certificateless signature operations. S2: User registration and partial private key extraction and verification. The user provides a unique identity to KGC. KGC verifies the user's identity and generates a partial private key based on the user's identity and system parameters. It is sent to the user through a secure channel. The user accepts and verifies the partial private key received from KGC. S3: User private key and public key settings. The user generates a random private key locally and calculates and generates his own public key. S4: Signature generation and verification. The user uses his private key to sign a specific message. The signing process includes using the user's private key, part of the private key and a random number to generate a digital signature. The verifier uses the master key and the user's public key to verify the signature of the message and confirm the legitimacy of the signature. S5: Binary comparison decision-making process, collects and processes relevant factors that affect the decision, and each factor is provided with a relative weight by an expert from the expert group; constructs a judgment matrix based on the binary comparison decision model, and sends it to the end user using a certificateless digital signature to ensure the integrity and tamper-proofness of the decision data; the end user calculates the comprehensive weight of each factor to obtain the final decision.

2. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: The system parameter generation in step S1 specifically includes the following steps: S1-1: Set a security parameter L and select a sufficiently large prime number q that satisfies q≥2 L , used to ensure the security and anti-attack strength of the system; S1-2: Define an additive cycle group G1 and a multiplicative cycle G2 of order q, and set a bilinear map e:G1×G1→G2; S1-3: Introduce two secure hash functions, the hash functions specifically include: H1:{0,1} * →G1 , used to map identities to elements in group G1; Random number generation for message signing, where It represents the multiplicative group of the priority field of the remainder class modulo q; S1-4: The key generation center randomly selects an element s as the system master key, where Select a generator p belonging to G and calculate the system master key P0=sp; S1-5: The public parameter set of the published system is params = (G1, G2, e, q, p, p0, g, H1, H2), where g = e(p, p), and the message space M = {0, 1} * , a public parameter set is used by all users to support certificateless signing and verification operations.

3. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: The user registration and partial private key extraction and verification in step S2 specifically include the following steps: S2-1: User identity submission: The user submits his unique identity ID to the key generation center A ∈{0,1} * , where the identity includes: email address, user ID or any other information that can be used to uniquely identify the user; A represents the user; S2-2: Identity verification and partial private key generation: KGC verifies the validity of the submitted identity. After confirmation, it generates the user's partial private key based on the user's identity and pre-set algorithm parameters. The generation of the private key depends on the secure hash function H1 and the system master key. The specific calculation is: D A =sH1(ID A ) Among them, s is the system master key held by KGC, H1 is the hash function that maps the identity to the group G1; S2-3: Secure transmission of partial private key: Partial private key D A Transmitted to the user through a secure channel.

4. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: The user private key and public key setting in step S3 specifically includes the following steps: S3-1: Generation of user private key: The user generates a random secret value x on the local device A As the user's private key, the secret value is selected from the group Right now: S3-2: Calculation of public key: The user uses the private key to calculate the user's public key, where the public key P A =x A P.

5. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: The signature generation and verification in step S4 includes the following steps: S4-1: Signature generation, specifically including the following steps: S4-1-1: Random number generation: The user first generates a random number r locally, selects Right now: S4-1-2: Calculate the verification element: Use the generated random number r to calculate the verification element U. The specific calculation formula is: U = g r , where g is the generator of group G1; S4-1-3: Message hash calculation: Use the hash function H2 to calculate the hash value h of the message m to be signed. The specific calculation formula is: h = H2 (m, U); S4-1-4: Completion of signature: Calculation of signature δ = rP-h(D A +x A V), where x A is the user's private key, V = H1(ID A ), output signature σ=(m,h,δ,); S4-2: Verification of signature, including the following steps: S4-2-1: Receive the signed message and public information: The signed message is σ=(m,h,δ,), and the public information is (ID A ,P A ); S4-2-2: Reconstruction of the inspection element: Use the received information to reconstruct the inspection element U'. The specific calculation formula is: U'=e(δ,p)[e(V,P0)e(P A ,V)] h ; S4-2-3: Hash verification: Use the same hash function H2 to recalculate the hash value of the original message m and the reconstructed verification element U', and verify whether h'=H2(m,U') is equal to h in the signature; S4-2-4: Acceptance or rejection of the signature: If the calculated hash value h′ matches h in the signature, the signature is accepted as valid, otherwise the signature is rejected.

6. The binary comparison decision method based on certificateless digital signature according to claim 1 is characterized in that: The binary comparison decision in step S5 includes the following steps: S5-1: Determination of decision-making factors: Experts determine the main factors affecting the decision, X1, X2, ..., X n ; S5-2: Construction of binary comparison judgment matrix: Experts compare each decision factor pairwise and generate importance index Where f represents the factor x i Relative to x j Importance: The judgment matrix B is constructed by assigning the matrix B. The calculation formula of matrix B is: in, Satisfy the constraints: S5-3: Compatibility test of the judgment matrix, including two judgment methods: S5-3-1: The first step is to use the formula |λ-EB|=0 to find the maximum eigenvalue λ of the matrix B max ; In the second step, C(B) is introduced as a quantitative indicator of incompatibility, where E is the unit matrix and the calculation formula of C(B) is: If C(B)≤0.10, then the judgment matrix B n×n is compatible; if C(B)>0.01, then the judgment matrix B n×n incompatible; When the matrix B=(b ij ) n When the order of is very high, solving the eigenvalues ​​and eigenvectors of the matrix B will be a very time-consuming task. In order to improve the computational efficiency, the following alternative methods can be used: S5-3-2: For any i, j, k, let the matrix B' = (b' ij ) n Satisfies: If b' ij ≥1,b' jk ≥1, then b' ik ≥1, then the matrix B' is compatible, and the specific calculation formula is as follows: Among them, if B' n×n If the transitivity is satisfied, then the matrix B' n×n is consistent; otherwise, it is considered that the matrix B n×n incompatibility; S5-4: After the experts obtain the compatible matrix B based on their own opinions, they digitally sign the matrix as a message M and then send it to the end user.

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