A Post-Quantum Multi-Node Threshold Signature Method and System

Abstract

This invention provides a post-quantum multi-node threshold signature method and system. The method includes: a management node transforming original information *m*; the management node generating a first signature using its first private key and the transformed original information *m*, then combining the first signature and the original information *m* and sending them to user nodes within the organization; each user node generating a second signature using its second private key and the transformed original information *m*, and then sending the second signature to the management node; the management node verifying the received second signature using its first public key; if the verification passes, a counter is incremented by 1; at the end of a statistical period, it is determined whether the counter value is greater than a threshold; if so, each second signature is deemed valid for the original information *m*; otherwise, each second signature is deemed invalid for the original information *m*. This invention significantly reduces signature time.

Description

Technical Field

[0001] This invention relates to the fields of computer and internet technology, and more specifically, to a post-quantum multi-node threshold signature method and system. Background Technology

[0002] Currently, most mainstream threshold signature algorithms are based on RSA or elliptic cryptography. However, with the continuous improvement of computing power and the development of quantum computers, existing encryption algorithms face a security crisis. Therefore, post-quantum encryption algorithms have emerged and are applied within the framework of threshold signature algorithms as a new and more secure solution for multi-party computation.

[0003] However, as an experimental new encryption algorithm, post-quantum threshold signature still has many aspects of its process design that need optimization. For example, the process of collecting signatures from ordinary nodes and generating a group signature has redundant steps. Its design involves verifying signatures one by one, meaning that it will not send a request to the second node until it has obtained whether the first ordinary node has attached its signature. This design is useful in some scenarios, such as when different nodes have different permissions, and node B's signature is valid only if node A approves first. However, it is inefficient in some scenarios, such as counting the number of people who agree to a resolution. This design process will face the problem of excessively long counting time when the number of nodes is large.

[0004] It is evident that the existing technology using the post-quantum threshold signature algorithm suffers from excessively long statistical time in multi-node scenarios, and further improvements are needed. Summary of the Invention

[0005] To address the technical problems existing in the background art, the present invention provides a post-quantum multi-node threshold signature method, system, electronic device, and storage medium to optimize the efficiency of collecting member signatures in the post-quantum threshold signature algorithm.

[0006] A first aspect of the present invention provides a post-quantum multi-node threshold signature method, comprising the following steps:

[0007] S10, the management node transforms the original information m;

[0008] S20, the management node uses its first private key and the transformed original information m to generate a first signature, and then combines the first signature and the original information m and sends them to each user node in the organization;

[0009] S30, the user node uses its second private key and the transformed original information m to generate a second signature, and then sends the second signature to the management node;

[0010] S40, the management node uses the first public key to verify the received second signature. If the verification is successful, the counter is incremented by 1.

[0011] S50, when the statistical period arrives, determine whether the value of the counter is greater than the threshold. If yes, determine that each of the second signatures is effective for the original information m; otherwise, determine that each of the second signatures is not effective for the original information m.

[0012] Optionally, in step S10, the management node performs a transformation process on the original information m, including:

[0013] The original information m is converted into T(m), i.e., m' = T(m), where T is the conversion function;

[0014] Perform a hash calculation on m' to generate the hash value H(m') of m'.

[0015] Optionally, in step S20, the management node generates a first signature using its first private key and the first signature, including:

[0016] The first signature is generated using the following formula.

[0017]

[0018] In the formula, S r For the first signature of the management node, H(m') is the hash value of m', and k r is the first private key of the management node, F is the multivariate equation solving function, and L is the linear transformation function.

[0019] Optionally, in step S30, the user node generates a second signature using its second private key and the transformed original information m, including:

[0020] The second signature is generated using the following formula.

[0021]

[0022] In the formula, S i S is the second signature of the i-th user node. r For the first signature of the management node, k i This is the second private key of the i-th user node.

[0023] Optionally, in step S40, the management node uses the first public key to verify the received second signature, including:

[0024] The management node calculates If the calculation result is equal to the first signature S r If yes, the visa verification will pass; otherwise, the visa verification will fail.

[0025] In the formula, p r S is the first public key for the management node. i For the second signature of the i-th user node, F i Let be the multivariate polynomial evaluation function for the i-th user node.

[0026] Optionally, the multivariate functional equation can be solved by using the multivariate equation solver function F, including:

[0027] Randomly generate a vinegar variable and substitute it into a multivariate equation of the following form.

[0028] F=∑α ij O i V j +∑β i O i +∑χ ij V i V j +∑δ i V i +ε

[0029] In the formula, α, β, χ, δ, and ε are private keys in a finite field;

[0030] Substituting the private key into the multivariate equation above, we get F(y) = x;

[0031] The above multivariate equations are transformed into a linear function system based on oil variables;

[0032] Solving the linear function system based on the oil variable yields the oil variable;

[0033] The vinegar variable and the oil variable are output.

[0034] Optionally, the linear function system based on the oil variable can be solved using the Gaussian function elimination method.

[0035] A second aspect of the present invention provides a post-quantum multi-node threshold signature system, comprising a management node, user nodes, and a communication module. The management node includes a processing module and a storage module, wherein the processing module is connected to both the storage module and the communication module.

[0036] The storage module is used to store executable computer program code;

[0037] The communication module is used to enable communication between the processing module and the user node;

[0038] The processing module is configured to execute the method described above by calling the executable computer program code in the storage module.

[0039] A third aspect of the present invention provides an electronic device comprising:

[0040] Memory containing executable program code;

[0041] A processor coupled to the memory;

[0042] The processor invokes the executable program code stored in the memory to execute the method as described in any of the preceding methods.

[0043] A fourth aspect of the present invention provides a computer storage medium storing a computer program that, when executed by a processor, performs the method described in any of the preceding claims.

[0044] The beneficial effects of this invention are as follows: The management node transforms the original information m. The management node uses its first private key and the transformed original information m to generate a first signature, and then combines the first signature and the original information m and sends them to each user node in the organization. The user node uses its second private key and the transformed original information m to generate a second signature, and then sends the second signature to the management node. The management node uses its first public key to verify the received second signature. If the verification passes, a counter is incremented by 1. When the statistical period arrives, it is determined whether the value of the counter is greater than a threshold. If it is, it is determined that each second signature is effective for the original information m; otherwise, it is determined that each second signature is not effective for the original information m. The solution of this invention improves the existing method of verifying signatures one by one to synchronous verification. That is, the management node sends the first signature and the original information to each user node simultaneously. After the user node responds with the second signature information, it then performs signature verification one by one. This can greatly reduce the inefficiency of one-by-one verification, thereby greatly saving verification time. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating a post-quantum multi-node threshold signature method disclosed in an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of the structure of a post-quantum multi-node threshold signature system disclosed in an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0050] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0051] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0052] In the description of this invention, it should be noted that if terms such as "upper," "lower," "inner," or "outer" are used to indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed, they are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0053] Furthermore, the terms "first" and "second" are used only to distinguish descriptions and should not be interpreted as indicating or implying relative importance.

[0054] It should be noted that, where there is no conflict, the features in the embodiments of the present invention can be combined with each other.

[0055] Example 1

[0056] Please see Figure 1 , Figure 1 This is a flowchart illustrating a post-quantum multi-node threshold signature method disclosed in an embodiment of the present invention. Figure 1 As shown, an embodiment of the present invention provides a post-quantum multi-node threshold signature method, which includes the following steps:

[0057] S10, the management node transforms the original information m;

[0058] S20, the management node uses its first private key and the transformed original information m to generate a first signature, and then combines the first signature and the original information m and sends them to each user node in the organization;

[0059] S30, the user node uses its second private key and the transformed original information m to generate a second signature, and then sends the second signature to the management node;

[0060] S40, the management node uses the first public key to verify the received second signature. If the verification is successful, the counter is incremented by 1.

[0061] S50, when the statistical period arrives, determine whether the value of the counter is greater than the threshold. If yes, determine that each of the second signatures is effective for the original information m; otherwise, determine that each of the second signatures is not effective for the original information m.

[0062] In this embodiment of the invention, threshold signature is an important branch of ordinary digital signature, combining threshold secret sharing technology with digital signature. In 1991, Desmedt-Frankel first proposed the (t,n) threshold signature scheme, which refers to a signature group consisting of n members. This group has a public key and a private key pair. Only a combination of at least t legitimate and honest members can represent the group to sign using the private key. Anyone can verify the signature using the group's conventions. The threshold signature method can achieve the distribution of power and prevent abuse of authority. Existing technologies have involved post-quantum threshold signature methods, but their signature process is one-by-one verification. That is, if the current verification is not received or fails, subsequent verification is prohibited, which leads to excessively long statistical time.

[0063] To address the issue of excessively long statistical processing time, this invention presents a post-quantum multi-node threshold signature method. Referring to the above method flow, it can be seen that in this threshold signature verification method, the management node generates a first signature based on its private key, and then sends the first signature and the original information to each user node. Each user node then determines whether it accepts the original information. If accepted, each user node generates its own second signature based on its private key, and then sends the second signature and the original information back to the management node. This eliminates the need for each user node to sign individually; the management node only needs to count the number of returned signatures that pass verification to determine if the signature meets the standard. Thus, the problem of excessively long statistical processing time caused by signing one by one is reduced.

[0064] Optionally, in step S10, the management node performs a transformation process on the original information m, including:

[0065] The original information m is converted into T(m), i.e., m' = T(m), where T is the conversion function;

[0066] Perform a hash calculation on m' to generate the hash value H(m') of m'.

[0067] In this embodiment of the invention, the management node preprocesses the original information before generating the first signature, that is, it performs a T transformation on the original information to obtain a hash value, and then uses the transformed hash value H(m') to generate the first signature.

[0068] Refer to Table 1 below,

[0069] Table 1

[0070] function enter Output T m m'

[0071] T is the transformation function of the original information m. The transformation process is as follows: 1) Input the original information m, where m is a set of elements in a finite field; 2) Represent m as binary elements, and then rotate m to the right to obtain the output result m'.

[0072] Optionally, in step S20, the management node generates a first signature using its first private key and the transformed original information m, including:

[0073] The first signature is generated using the following formula.

[0074]

[0075] In the formula, S r For the first signature of the management node, H(m') is the hash value of m', and k r is the first private key of the management node, F is the multivariate equation solving function, and L is the linear transformation function.

[0076] In this embodiment of the invention, the management node can generate and maintain a first public key and a first private key belonging to it. Following the aforementioned scheme, the management node in this invention uses the first private key and the hash value obtained after transformation to generate the first signature. The private key is randomly generated, and its expression is k. r ={a r ,b r ,c r}, where a r b r These are the matrix and vector of the linear transformation function L, respectively, c r These are the coefficients of the function F used to solve a multivariate equation.

[0077] Additionally, please refer to Table 2 below.

[0078] Table 2

[0079] function enter Output Private key L x y a,b

[0080] L is a linear transformation function, and its transformation process is as follows:

[0081] 1) Input x, where x is a set of elements in a finite field, and substitute x into the linear transformation function y = ax + b; 2) Substitute the private key matrices a and b into the above linear transformation function to perform matrix-vector operations to obtain the output result y.

[0082] Optionally, in step S30, the user node generates a second signature using its second private key and the transformed first signature, including:

[0083] The second signature is generated using the following formula.

[0084]

[0085] In the formula, S i S is the second signature of the i-th user node. r For the first signature of the management node, k i This is the second private key of the i-th user node.

[0086] In this embodiment of the invention, after receiving the first signature and original information m sent by the management node, the user node can decide whether to accept it based on its own actual situation. If it accepts it, it can generate a second signature based on the second private key and the first signature.

[0087] Optionally, in step S40, the management node uses the first public key to verify the received second signature, including:

[0088] The management node calculates F i (S i ,p r If the calculation result is equal to the first signature S r If yes, the visa verification will pass; otherwise, the visa verification will fail.

[0089] In the formula, p r S is the first public key for the management node. i For the second signature of the i-th user node, F i Let be the multivariate polynomial evaluation function for the i-th user node.

[0090] In this embodiment of the invention, after the management node receives information from a user node, it performs a signature verification operation. Only after successful signature verification does it increment the counter by 1. The signature verification is performed by calculating... As shown in Table 3 below,

[0091] Table 3

[0092]

[0093] The evaluation process of the multivariate polynomial is described as follows: 1) Input x, where x is a set of elements in a finite field, and substitute x into a set of multivariate polynomials based on x; 2) Substitute the public key as a coefficient into the multivariate polynomial; 3) Evaluate the multivariate polynomial based on multiplication and addition in the finite field, and the result is a set of elements in the finite field, denoted by y. Thus, y is the output result.

[0094] Additionally, regarding the public key p... r public key p r It is generated based on the private key, specifically by using the private key k r Substitution Thus, the public key p is obtained. r That is, the coefficients of the multivariate polynomial evaluation function F.

[0095] Optionally, the multivariate functional equation can be solved by using the multivariate equation solver function F, including:

[0096] Randomly generate a vinegar variable and substitute it into a multivariate equation of the following form.

[0097] F=∑α ij O i V j +∑β i O i +∑χ ij V i V j +∑δ i V i +ε, where α, β, χ, δ, and ε are the private keys in the finite field;

[0098] Substituting the private key into the multivariate equation above, we get F(y) = x;

[0099] The above multivariate equations are transformed into a linear function system based on oil variables;

[0100] Solving the linear function system based on the oil variable yields the oil variable;

[0101] The vinegar variable and the oil variable are output.

[0102] Optionally, the linear function system based on the oil variable can be solved using the Gaussian function elimination method.

[0103] In this embodiment of the invention, the Gaussian function elimination method can be a conventional Gaussian function elimination method or an improved Gaussian function elimination method, such as the Gaussian-Jordan elimination method.

[0104] Example 2

[0105] Please see Figure 2 , Figure 2 This is a schematic diagram of the structure of a post-quantum multi-node threshold signature system disclosed in an embodiment of the present invention. Figure 2 As shown, a post-quantum multi-node threshold signature system (100) according to an embodiment of the present invention includes a management node (101), a user node (102), and a communication module (103). The management node (101) includes a processing module (104) and a storage module (105), wherein the processing module (104) is connected to the storage module (105) and the communication module (103) respectively; wherein,

[0106] The storage module (105) is used to store executable computer program code;

[0107] The communication module (103) is used to enable communication between the processing module (104) and the user node (102);

[0108] The processing module (104) is configured to execute the method described in Embodiment 1 by calling the executable computer program code in the storage module (105).

[0109] The specific functions of the post-quantum multi-node threshold signature system in this embodiment are the same as those in Embodiment 1 above. Since the system in this embodiment adopts all the technical solutions of the above embodiments, it has at least all the beneficial effects brought about by the technical solutions of the above embodiments, which will not be described in detail here.

[0110] Example 3

[0111] Please see Figure 3 , Figure 3 This invention discloses an electronic device comprising:

[0112] Memory containing executable program code;

[0113] A processor coupled to the memory;

[0114] The processor calls the executable program code stored in the memory to execute the method as described in Embodiment 1.

[0115] Example 4

[0116] This invention also discloses a computer storage medium storing a computer program, which is executed by a processor as described in Embodiment 1.

[0117] It should be noted that the storage module, memory, and computer storage medium in the embodiments of the present invention include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, etc.

[0118] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0119] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0120] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0121] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A post-quantum multi-node threshold signature method, characterized by, The method comprises the following steps: S10, the management node converts the original information ; S20, the management node uses its first private key and the original information after conversion processing generates a first signature, and then sends the first signature and the original information to each user node in the organization after combination, to each user node in the organization; the management node can generate and maintain its first public key and first private key S30, the user node uses its second private key and the original information after conversion processing generating a second signature, and then sending the second signature to the management node; S40, the management node uses the first public key to verify the received second signature, and if the verification is passed, sets the counter to 1; S50, when the statistical period arrives, judging whether the value of the counter is greater than the threshold value, if yes, determining that each of the second signatures is valid for the original information ; if not, determining that each of the second signatures is invalid for the original information ; if not, determining that each of the second signatures is invalid for the original information In step S20, the management node generates a first signature using its first private key and the first signature, comprising: The first signature is generated by the following formula, ； In the formula, The first signature for the management node, for hash value, The first private key for the management node, For solving multivariate equations, It is a linear transformation function; In step S30, the user node uses its second private key and the original information after conversion processing to generate a second signature generating a second signature, comprising: The second signature is generated by the following formula, ； wherein is a first signature of the first user node, is a second signature of the second user node, is a first signature of the management node, is a second private key of the second user node, and is a second private key of the second user node. 2.The post-quantum multi-node threshold signature method according to claim 1, characterized in that: In step S10, the management node performs conversion processing on the original information m, comprising: The original information is converted to i.e. wherein is a conversion function; To perform a hash calculation to generate a hash value of .​​ 3.The post-quantum multi-node threshold signature method of claim 1, wherein: In step S40, the management node uses the first public key to verify the received second signature, comprising: The management node calculates If the calculation result is equal to the first signature , the signature verification passes, otherwise the signature verification fails. wherein is a first public key of a managing node, is a second signature of a first user node, is a second public key of a first user node, is a third signature of a second user node, is a multivariate polynomial evaluation function of a second user node.

4. The post-quantum multi-node threshold signature method of claim 1, wherein: Solving functions using multivariate equations includes solving multivariate function equations, including: Randomly generate vinegar variables and substitute vinegar variables into the following multivariate equation, ； wherein , , , , is a private key in a finite field; Substitute the above private key into the above multivariate equation, i.e. ; Convert the above multivariate equation into a linear function system based on oil variables; Solve the linear function system based on oil variables, i.e. get oil variables; The vinegar variables and the oil variables are used as output. 5.The post-quantum multi-node threshold signature method of claim 1, wherein: The linear function system based on oil variables is solved by using the Gaussian function elimination method.

6. A post-quantum multi-node threshold signature system, comprising a management node, a user node and a communication module, the management node comprising a processing module, a storage module, wherein, The processing module is connected with the storage module and the communication module respectively; wherein, The storage module is used to store executable computer program code; The communication module is used to realize the communication between the processing module and the user node; Characterized in that: the processing module is used to execute the method of any one of claims 1-5 by calling the executable computer program code in the storage module.

7. An electronic device, comprising: A memory storing executable program code; A processor coupled with the memory; characterized in that: the processor calls the executable program code stored in the memory to execute the method of any one of claims 1-5.

8. A computer storage medium having stored thereon a computer program, characterized in that: The computer program is executed by the processor to execute the method of any one of claims 1-5.

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