Identity-based signature method supporting multi-message aggregation

Abstract

The invention discloses an identity-based signature method supporting multi-message aggregation. The identity-based signature method comprises the steps of system initialization and key generation, user signature key generation, message signature construction, single signature verification, signature aggregation and aggregation signature verification. Due to the fact that the linear homomorphic signature technology is adopted, the identity-based aggregation signature method is provided, and the technical problems of signature after aggregation, key size expansion and the like in the existing aggregation signature technology are solved. Through the method, a verifier can safely and efficiently merge a plurality of signatures into a signature with a compact size, efficient data source authentication can be realized while the data integrity is guaranteed, and the verification efficiency is remarkably improved. The method has the advantages of high security, low communication cost, small calculation overhead and the like, can be applied to the technical fields of large-scale data authentication, distributed system security, lightweight cryptographic protocols and the like, and is particularly suitable for mobile terminals or Internet of Things equipment scenes with limited calculation resources.

Description

Technical Field

[0001] This invention belongs to the field of privacy protection technology, specifically relating to an identity-based signature method for achieving data integrity and provenance authentication in a multi-message environment. Background Technology

[0002] In today's digital age, ensuring the authenticity and integrity of information is of paramount importance. As a core application of public-key cryptography, digital signature technology is a crucial foundation for identity authentication and data integrity verification. Among these, identity-based signatures, as an important digital signature mechanism, demonstrate significant advantages in simplifying system architecture and improving authentication efficiency due to their key management method, which does not rely on digital certificates. In this mechanism, each user is associated with a unique identity identifier (ID), and a trusted key generation center generates a corresponding user-signing private key based on this identifier.

[0003] As the number of signatures increases, the storage and verification process places a heavy computational and communication burden on the verifier. To address this issue, identity-based aggregation signature methods have emerged, which effectively reduce transmission costs and alleviate the computational pressure on the verifier. Specifically, this method allows multiple signers to generate independent signatures for different messages and aggregate them into a single compact signature. This enables the verifier to authenticate all original signatures with only one verification operation, greatly improving verification efficiency. However, existing identity-based aggregation signature methods still have certain limitations: some methods are only applicable to signature aggregation in multi-identity-single-message scenarios, lacking flexibility in practical applications; others, while supporting multi-identity-multi-message scenarios, still result in large aggregated signature lengths, introducing significant communication and computational overhead. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned technical problems and provide an identity-based signature method that supports multi-message aggregation, which has data integrity, high computational efficiency, low communication cost, and high verification efficiency.

[0005] The technical solution adopted to solve the above technical problems consists of the following steps:

[0006] (1) System initialization and key generation

[0007] 1) Construct a bilinear group system

[0008] Construct a bilinear group system F using the following formula:

[0009] F=

[0010] in, Is the order as cyclic group , The parameter q takes the value of a finite number of positive integers. for Group elements, It is a bilinear mapping.

[0011] 2) Construct the group elements and determine the hash function

[0012] Random selection indivual The elements of the group { }, indivual Group elements and define the hash function. .

[0013] in, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector is represented by n and m, where n and m are finite positive integers.

[0014] 3) Generate the master private key and public key

[0015] from Group of integers of order Randomly select the master private key According to the master private key Calculate the public key .

[0016] Calculate the public key u using the following formula:

[0017] ;

[0018] Where h is An element in the group.

[0019] (2) Generate user signature key

[0020] Generate user signature key using the following formula ;

[0021] ;

[0022] in, Indicates the first indivual Group elements, Represents identity vector The bit , Represents identity vector The Bits; for An element in the group, Represents identity vector The last bit as The index.

[0023] (3) Construct message signature

[0024] The user's signature key is generated by the Key Generation Center (KGC). Sign the message M.

[0025] 1) Calculate the hash function value

[0026] Calculate the hash function value using the following formula :

[0027] ;

[0028] in, express Group elements, Represents the message vector M's first... bit ; From the group One of the elements, Represents the message vector Each bit is exponentially multiplied, then multiplied by the sum of the results. As the value of the hash function.

[0029] 2) Calculate the signature value

[0030] Calculate the signature value using the following formula :

[0031]

[0032]

[0033] ;

[0034] in, It is a signature The first part, It is a signature Part Two; yes Group elements, Indicates the message The hash function value is Randomize the index The parameter is from Group of integers of order Random elements selected from, Values .

[0035] (4) Single signature verification

[0036] Perform single signature verification B using the following formula:

[0037] ;

[0038] ;

[0039] ;

[0040] Where e represents the bilinear mapping function, and the input is... Group and The elements of the group are output as the group. One of the elements, This represents the system's public key.

[0041] If the verification result B is 1, the signature passes verification; if the verification result B is 0, the signature fails verification.

[0042] (5) Aggregate signature

[0043] Given Each tuple contains a message. An identity and the corresponding signature .

[0044] 1) Calculate the aggregated identity value

[0045] Calculate the aggregated identity value using the following formula :

[0046] ;

[0047] in, Indicates the first A number of identity vectors express The coefficient is from In the group of integers of order 1 Selected random elements; Indicates the number of signatures. The value can be a finite number of positive integers.

[0048] 2) Calculate the aggregated signature

[0049] Calculate the aggregated signature value using the following formula :

[0050] ;

[0051] in, Indicates to the general As the first The linear combination coefficients of the signatures are used to perform an exponential operation on the first part of the signature. Indicates the first The second part of the signature is subjected to an exponentiation operation, with the exponent being... .

[0052] (6) Aggregate signature verification

[0053] The verifier receives a list of message vectors. Aggregated signature and the identity after aggregation Calculate and verify the results using the following formula. :

[0054] ;

[0055] ;

[0056] ;

[0057] in, Indicates the first A message vector, Indicates the first The first identity vector Bits.

[0058] If the verification result is 1, aggregate signature The verification was successful, but the result was 0, indicating that the verification failed.

[0059] In step (1) of the present invention, system initialization and key generation, 1) constructing a bilinear group system, the...

[0060] Is the order as cyclic group , For parameters, The value ranges from 60 to 100.

[0061] In step (1) of the present invention, system initialization and key generation, 1) constructing a bilinear group system, the... Is the order as cyclic group , For parameters, The optimal value is 80.

[0062] In step (1) system initialization and key generation of the present invention, and step (2) constructing group elements and determining the hash function, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 10 to 50.

[0063] In step (1) system initialization and key generation of the present invention, and step (2) constructing group elements and determining the hash function, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The optimal value range for is 30.

[0064] In step (5) of the present invention, the step 1) calculating the aggregated identity value of the aggregated signature, the following... Indicates the number of signatures, ranging from 10 to 50.

[0065] In step (5) of the present invention, the step 1) calculating the aggregated identity value of the aggregated signature, the following... This indicates the number of signatures; the optimal value is 30.

[0066] This invention employs linear homomorphic signature technology and proposes an identity-based aggregation signature method. It solves technical problems in existing aggregation signature technologies, such as the size of the aggregated signature and the key size, demonstrating significant improvements in computational efficiency and reduced communication overhead, further optimizing the overall performance of the identity-based aggregation signature mechanism. In this invention, the length of the aggregated signature is linearly related to the number of signatures involved in the aggregation, resulting in lower storage and transmission costs compared to existing methods. This method supports unified aggregation and authentication of signatures from different users for different messages, significantly improving verification efficiency, and is particularly suitable for scenarios with limited computing resources, such as mobile terminals or IoT devices. This invention can achieve efficient data source authentication while ensuring data integrity, combining high practicality with low communication costs. It can be widely applied in key technology areas such as large-scale data authentication, distributed system security, and lightweight cryptographic protocols. Attached Figure Description

[0067] Figure 1 This is a flowchart of Embodiment 1 of the present invention. Detailed Implementation

[0068] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0069] Example 1

[0070] The identity-based signature method supporting multi-message aggregation in this embodiment consists of the following steps (see...). Figure 1 ):

[0071] (1) System initialization and key generation

[0072] 1) Construct a bilinear group system

[0073] Construct a bilinear group system F using the following formula:

[0074] F=

[0075] in, Is the order as cyclic group , For parameters, The value ranges from 60 to 100 in this embodiment. The value is 80. for Group elements, It is a bilinear mapping.

[0076] 2) Construct the group elements and determine the hash function

[0077] Random selection indivual The elements of the group { }, indivual Group elements and define the hash function. .

[0078] in, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 10 to 50, in this embodiment and The value range is 30.

[0079] 3) Generate the master private key and public key

[0080] from Group of integers of order Randomly select the master private key According to the master private key Calculate the public key .

[0081] Calculate the public key u using the following formula:

[0082] ;

[0083] Where h is An element in the group.

[0084] (2) Generate user signature key

[0085] Generate user signature key using the following formula ;

[0086] ;

[0087] in, Indicates the first indivual Group elements, Represents identity vector The bit , Represents identity vector The Bits; for An element in the group, Represents identity vector The last bit as The index.

[0088] (3) Construct message signature

[0089] The user's signature key is generated by the Key Generation Center (KGC). Sign the message M.

[0090] 1) Calculate the hash function value

[0091] Calculate the hash function value using the following formula :

[0092] ;

[0093] in, express Group elements, Represents the message vector M's first... bit ; From the group One of the elements, Represents the message vector Each bit is exponentially multiplied, then multiplied by the sum of the results. As the value of the hash function.

[0094] 2) Calculate the signature value

[0095] Calculate the signature value using the following formula :

[0096]

[0097]

[0098]

[0099] in, It is a signature The first part, It is a signature Part Two; yes Group elements, Indicates the message The hash function value is Randomize the index The parameter is from Group of integers of order Random elements selected from, Values In this embodiment Values / 2 .

[0100] (4) Single signature verification

[0101] Perform single signature verification B using the following formula:

[0102] ;

[0103] ;

[0104] ;

[0105] Where e represents the bilinear mapping function, and the input is... Group and The elements of the group are output as the group. One of the elements, This represents the system's public key.

[0106] If the verification result B is 1, the signature passes verification; if the verification result B is 0, the signature fails verification.

[0107] (5) Aggregate signature

[0108] Given Each tuple contains a message. An identity and the corresponding signature .

[0109] 1) Calculate the aggregated identity value

[0110] Calculate the aggregated identity value using the following formula :

[0111] ;

[0112] in, Indicates the first A number of identity vectors express The coefficient is from In the group of integers of order 1 Selected random elements; Indicates the number of signatures. The value ranges from 10 to 50 in this embodiment. The value is 30.

[0113] 2) Calculate the aggregated signature

[0114] Calculate the aggregated signature value using the following formula :

[0115] ;

[0116] in, Indicates to the general As the first The linear combination coefficients of the signatures are used to perform an exponential operation on the first part of the signature. Indicates the first The second part of the signature is subjected to an exponentiation operation, with the exponent being... .

[0117] (6) Aggregate signature verification

[0118] The verifier receives a list of message vectors. Aggregated signature and the identity after aggregation Calculate and verify the results using the following formula. :

[0119] ;

[0120] ;

[0121] ;

[0122] in, Indicates the first A message vector, Indicates the first The first identity vector Bits.

[0123] If the verification result is 1, aggregate signature The verification was successful, but the result was 0, indicating that the verification failed.

[0124] Complete the identity-based signature method that supports multi-message aggregation.

[0125] Example 2

[0126] The identity-based signature method supporting multi-message aggregation in this embodiment consists of the following steps:

[0127] (1) System initialization and key generation

[0128] 1) Construct a bilinear group system

[0129] Construct a bilinear group system F using the following formula:

[0130] F=

[0131] in, Is the order as cyclic group , For parameters, The value ranges from 60 to 100 in this embodiment. The value is 60. Other parameters, variables, and value ranges are the same as in Example 1.

[0132] 2) Construct the group elements and determine the hash function

[0133] Random selection indivual The elements of the group { }, indivual Group elements and define the hash function. .

[0134] in, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 10 to 50, in this embodiment and The value range is 10.

[0135] The other steps in this procedure are the same as in Example 1.

[0136] (3) Construct message signature

[0137] The user's signature key is generated by the Key Generation Center (KGC). Sign the message M.

[0138] 1) Calculate the hash function value

[0139] The steps are the same as in Example 1.

[0140] 2) Calculate the signature value

[0141] Calculate the signature value using the following formula :

[0142] Signature value The expression is the same as in Example 1. In this expression, Indicates the message The hash function value is Randomize the index The parameter is from Group of integers of order Random elements selected from, Values In this embodiment Values .

[0143] (4) Single signature verification

[0144] The steps are the same as in Example 1.

[0145] (5) Aggregate signature

[0146] Given Each tuple contains a message. An identity and the corresponding signature .

[0147] 1) Calculate the aggregated identity value

[0148] Calculate the aggregated identity value using the following formula :

[0149] Identity value The expression is the same as in Example 1. In this expression, Indicates the number of signatures. The value ranges from 10 to 50 in this embodiment. The value is 10. Other parameters, variables, and their ranges are the same as in Example 1.

[0150] The other steps in this procedure are the same as in Example 1.

[0151] The other steps are the same as in Example 1, thus completing the identity-based signature method that supports multi-message aggregation.

[0152] Example 3

[0153] The identity-based signature method supporting multi-message aggregation in this embodiment consists of the following steps:

[0154] (1) System initialization and key generation

[0155] 1) Construct a bilinear group system

[0156] Construct a bilinear group system F using the following formula:

[0157] F=

[0158] in, Is the order as cyclic group , For parameters, The value ranges from 60 to 100 in this embodiment. The value is 100. Other parameters, variables, and value ranges are the same as in Example 1.

[0159] 2) Construct the group elements and determine the hash function

[0160] Random selection indivual The elements of the group { }, indivual Group elements and define the hash function. .

[0161] in, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 10 to 50, in this embodiment and The value range is 50.

[0162] The other steps in this procedure are the same as in Example 1.

[0163] (3) Construct message signature

[0164] The user's signature key is generated by the Key Generation Center (KGC). Sign the message M.

[0165] 1) Calculate the hash function value

[0166] The steps are the same as in Example 1.

[0167] 2) Calculate the signature value

[0168] Calculate the signature value using the following formula :

[0169] Signature value The expression is the same as in Example 1. In this expression, Indicates the message The hash function value is Randomize the index The parameter is from Group of integers of order Random elements selected from, Values In this embodiment The value is P.

[0170] (4) Single signature verification

[0171] The steps are the same as in Example 1.

[0172] (5) Aggregate signature

[0173] Given Each tuple contains a message. An identity and the corresponding signature .

[0174] 1) Calculate the aggregated identity value

[0175] Calculate the aggregated identity value using the following formula :

[0176] Identity value The expression is the same as in Example 1. In this expression, Indicates the number of signatures. The value ranges from 10 to 50 in this embodiment. The value is 50. Other parameters, variables, and value ranges are the same as in Example 1.

[0177] The other steps in this procedure are the same as in Example 1.

[0178] The other steps are the same as in Example 1, thus completing the identity-based signature method that supports multi-message aggregation.

Claims

1. An identity-based signature method supporting multi-message aggregation, characterized in that... It consists of the following steps: (1) System initialization and key generation 1) Construct a bilinear group system Construct a bilinear group system F using the following formula: F= in, Is the order as cyclic group , The parameter q takes the value of a finite number of positive integers. for Group elements, It is a bilinear mapping; 2) Construct the group elements and determine the hash function Random selection indivual The elements of the group { }, indivual Group elements and define the hash function. ; in, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector is represented by n and m, where n and m are finite positive integers. 3) Generate the master private key and public key from Group of integers of order Randomly select the master private key According to the master private key Calculate the public key ; Calculate the public key u using the following formula: ； Where h is An element in the group; (2) Generate user signature key Generate user signature key using the following formula ; ； in, Indicates the first indivual Group elements, Represents identity vector The Bits , Represents identity vector The Bits; for An element in the group, Represents identity vector The last bit as The index; (3) Construct message signature The user's signature key is generated by the Key Generation Center (KGC). Sign the message M; 1) Calculate the hash function value Calculate the hash function value using the following formula : ； in, express Group elements, Represents the message vector M's first... Bits ; From the group One of the elements, Represents the message vector Each bit is exponentially multiplied, then multiplied by the sum of the results. As the value of the hash function; 2) Calculate the signature value Calculate the signature value using the following formula : ； in, It is a signature Part 1 It is a signature Part Two; yes Group elements, Indicates the message The hash function value is Randomize the index The parameter is from Group of integers of order Random elements selected from, Values ; (4) Single signature verification Perform single signature verification B using the following formula: ； ； ； Where e represents the bilinear mapping function, and the input is... Group and The elements of the group are output as the group. One of the elements, This represents the system's public key; If the verification result B is 1, the signature passes verification; if the verification result B is 0, the signature fails verification. (5) Aggregate signature Given Each tuple contains a message. An identity and the corresponding signature ; 1) Calculate the aggregated identity value Calculate the aggregated identity value using the following formula : ; in, Indicates the first A number of identity vectors express The coefficient is from In the group of integers of order 1 Selected random elements; Indicates the number of signatures. The value can be a finite number of positive integers; 2) Calculate the aggregated signature Calculate the aggregated signature value using the following formula : ； in, Indicates to the general As the first The linear combination coefficients of the signatures are used to perform an exponential operation on the first part of the signature. Indicates the first The second part of the signature is subjected to an exponentiation operation, with the exponent being... ; (6) Aggregate signature verification The verifier receives a list of message vectors. Aggregated signature and the identity after aggregation Calculate and verify the results using the following formula. : ； ； ； in, Indicates the first A message vector, Indicates the first The first identity vector Bits; If the verification result is 1, aggregate signature. The verification was successful, but the result was 0, indicating that the verification failed.

2. The identity-based signature method supporting multi-message aggregation according to claim 1, characterized in that: In step (1) system initialization and key generation, 1) constructing a bilinear group system, the... Is the order as cyclic group , For parameters, The value ranges from 60 to 100.

3. The identity-based signature method supporting multi-message aggregation according to claim 1 or 2, characterized in that: In step (1) system initialization and key generation, 1) constructing a bilinear group system, the... Is the order as cyclic group , For parameters, The value is 80.

4. The identity-based signature method supporting multi-message aggregation according to claim 1, characterized in that: In step (1) system initialization and key generation, and step (2) constructing group elements and determining the hash function, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 10 to 50.

5. The identity-based signature method supporting multi-message aggregation according to claim 1 or 4, characterized in that: In step (1) system initialization and key generation, and step (2) constructing group elements and determining the hash function, The dimension of the identity vector. This represents a string of length m. The dimension of the message vector. and The value range is 30.

6. The identity-based signature method supporting multi-message aggregation according to claim 1, characterized in that: In step (5), the step of calculating the aggregated identity value in the aggregated signature 1), the aforementioned Indicates the number of signatures, ranging from 10 to 50.

7. The identity-based signature method supporting multi-message aggregation according to claim 1 or 6, characterized in that: In step (5), the step of calculating the aggregated identity value in the aggregated signature 1), the aforementioned This indicates the number of signatures, with a value of 30.

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