WO2021012574A1

WO2021012574A1 - Multisignature method, signature center, medium and electronic device

Info

Publication number: WO2021012574A1
Application number: PCT/CN2019/123094
Authority: WO
Inventors: 蒋福强; 贾牧; 张鹏程
Original assignee: 深圳壹账通智能科技有限公司
Priority date: 2019-07-24
Filing date: 2019-12-04
Publication date: 2021-01-28
Also published as: CN110351096B; CN110351096A

Abstract

The present disclosure relates to the field of information encryption, and disclosed are a multisignature method, a signature center, a medium and an electronic device. The method is executed by the signature center, the signature center comprising a signature unit and a plurality of signing participants. The method comprises: each signing participant acquires a cyclic group of prime order under an elliptic curve equation; the signing participants receive private keys which are generated by a secret key generation center according to the identities of the signing participants; the signing participants acquire public keys thereof by using a formula on the basis of the private keys of the signing participants; each signing participant generates a random number, and a signature unit acquires a target random point by using a formula on the basis of the random number; according to the formula, on the basis of the target random point, each signing participant signs a message to be signed respectively and sends same to the signature unit, and the signatures of said message are composited by the signature unit. The described method improves the security of signing and the maintainability of a signature system, reduces resource consumption when there are multiple signatures and improves the efficiency of signing.

Description

Multi-signature method, signature center, medium and electronic equipment

This application claims the priority of a Chinese patent application filed with the Chinese Patent Office on July 24, 2019, the application number is 201910671776.9, and the application name is "Multi-signature method, signature center, medium and electronic equipment", the entire content of which is incorporated by reference In this application.

Technical field

The present disclosure relates to the field of information encryption technology, in particular to a multi-signature method, signature center, medium and electronic equipment.

Background technique

When the blockchain is running, in order to verify the security of encrypted transaction information, such as verifying the integrity of the information and the certainty of the identity of the information generator, it is often necessary to use a signature algorithm. In order to further improve the security of signatures, multi-signature schemes have also begun to appear. Under the existing technology, the multi-signature scheme proposed by the blockstream team is mainly as follows: each signature participant arbitrarily takes an integer as a private Key, and then use the generator in the cyclic group to obtain the corresponding public key from the private key to obtain the public key set of the signing participants, and then calculate the public key commitment based on the public key set and each public key; each participant obtains A random number, for each random number to obtain a random point after generating a random number of operations; for each signing participant, the binary operation result between each random point, the message to be signed, and the public key of the signing participant Perform a hash operation, then perform a binary operation on the operation result, public key commitment, and public key, and add the random number of the signature participant to the calculated result to obtain the signature of the signature participant, and finally The binary operation result between each random point and the signature of each signature participant are connected to obtain a signature.

The disadvantage of the prior art is that since the private key of the signing participant is randomly generated, its security is uncontrollable and difficult to maintain systematically. At the same time, the prior art needs to calculate the public key commitment, so this link requires a lot of calculations. The amount will lead to inefficient signatures.

Summary of the invention

In the field of information encryption technology, in order to solve or at least partially solve the above technical problems, the purpose of the present disclosure is to provide a multi-signature method, a signature center, a medium, and an electronic device.

According to an aspect of the present application, a multi-signature method is provided, the method is executed by a signature center, the signature center includes a signature unit and a plurality of signature participants, and the method includes:

Each signature participant in the signature center obtains a cyclic group of prime order established based on a preset elliptic curve equation, the cyclic group includes generators, and the signature participant has an identifier;

Each signature participant in the signature center receives the private key generated by the key generation center according to the signature of the signature participant;

Each signature participant in the signature center uses the following formula to obtain the signature participant's public key based on the signature participant's private key:

X _i ＝g^x _i ,

Wherein, X _i is the i-th signature obtained participating party public key, g is a generator of the cyclic group, x _i is the i-th signature participant private key;

When a signature request for a message to be signed is received, each signature participant in the signature center generates a random number, and the signature unit in the signature center uses the following formula to set the preset elliptic curve based on the random number of each signature participant Get random points on the target:

R _i =g^r _i ,

R=R ₁ *R ₂ *...*R _n ,

Among them, R _i is a random point obtained for the i-th signature participant on the preset elliptic curve, r _i is a random number generated by the i-th signature participant, and R is a random number based on each signature participant Random points of the target obtained;

Each signature participant in the signature center uses the following formula to sign the message to be signed based on the target random point, and sends it to the signature unit in the signature center, and the signature unit synthesizes the signature of each signature participant Obtain the signature of the message to be signed:

s _i = r _i +c*ID _i *x _i ,

Among them, ID _i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is the public signature of all signing participants in the signature center. A set of keys, s _i is the signature of the i-th signature participant to the message to be signed, and the signature of the message to be signed synthesized by the signature unit is (R, S), S=s ₁ +s ₂ +…+s _n .

According to another aspect of the present application, a signature center is provided, which includes a signature unit and a plurality of signature participants, the signature unit includes a target random point acquisition module and a synthesis module, and the signature participant includes an acquisition module and a receiving module , Public key acquisition module, generation module and signature module, these modules can perform the method as described above.

According to another aspect of the present application, a computer-readable program medium is provided, which stores computer program instructions, and when the computer program instructions are executed by a computer, the computer executes the aforementioned method. Optionally, the computer-readable program medium may also be called a computer-readable storage medium, for example, it may be a non-volatile computer-readable storage medium.

According to another aspect of the present application, there is provided an electronic device, the electronic device including:

processor;

A memory, where computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, the method as described above is implemented.

The technical solutions provided by the embodiments of the present application may include the following beneficial effects:

Since the private key of each signature participant is generated by the key generation center according to the signature of the signature participant, it is possible to avoid the occurrence of the phenomenon of reducing the reliability of the signature by generating the private key in a random manner, and improve the security and safety of the signature. The maintainability of the system saves the steps that require a large amount of computing resources on the basis of the existing technology, and improves the efficiency of the signature.

Description of the drawings

The drawings here are incorporated into the specification and constitute a part of the specification, show embodiments that conform to the application, and are used together with the specification to explain the principle of the application.

Fig. 1 is a schematic diagram showing a system architecture of a multi-signature method according to an exemplary embodiment;

Fig. 2 is a flowchart showing a multi-signature method according to an exemplary embodiment;

Fig. 3 is a flowchart of steps after step 230 and steps after step 260 according to an embodiment corresponding to Fig. 2;

Fig. 4 is a block diagram showing a signature center according to an exemplary embodiment;

Fig. 5 is a block diagram showing an example of an electronic device implementing the above multi-signature method according to an exemplary embodiment;

Fig. 6 shows a computer-readable storage medium for implementing the above-mentioned multi-signature method according to an exemplary embodiment.

Detailed ways

Here, exemplary embodiments will be described in detail, and examples thereof are shown in the accompanying drawings.

The present disclosure first provides a multi-signature method. Signing is the process of generating digital signatures. A digital signature is a digital string that can only be generated by the sender of the information and that others cannot forge. This digital string is also an effective proof of the authenticity of the information sent by the sender. Multi-signature refers to a signature that requires multiple signing parties to complete together, and each signing party plays a role in the signing process.

The signature participant can be any device with computing and processing functions. The device can be connected to an external device to receive or send information. It can be a portable mobile device, such as a smart phone, a tablet, a laptop, or a PDA (Personal Digital). Assistant), etc., can also be fixed devices, such as computer equipment, field terminals, desktop computers, servers, workstations, etc., or a collection of multiple devices, such as the physical infrastructure of cloud computing.

Preferably, the signature participant may be a server or a computer device.

Fig. 1 is a schematic diagram showing a system architecture of a multi-signature method according to an exemplary embodiment.

As shown in FIG. 1, the signature center 100 includes a signature unit 110 and a plurality of signature participants 120, all of which can communicate with the signature unit 110; besides the signature center 100, there is also a key generation center 130. The key generation center 130 can communicate with the signature participant 120 in the signature center 100. The signature participant 120 has an identity, and multiple signature participants 120 in the signature center 100 can respectively receive the private key generated by the key generation center according to the identity of each signature participant 120, and then the signature participant 120 can use the private key to generate The corresponding public key; then, if the signature center 100 receives a signature request for the message to be signed, each signature participant 120 in the signature center 100 will generate a random number, and the signature unit 110 will generate a random number for each signature participant 120 The random number obtains a random point on the preset elliptic curve, and then performs a binary operation on each random point in a predetermined order to obtain the target random point existing on the preset elliptic curve. Finally, the signature unit 110 will perform a signature for each signature Participant 120 first performs a hash operation on the set of public keys of all signing participants 120, the target random point, and the message to be identified, and then performs an ellipse based on the result of the hash operation and the identity and private key of the signing participant 120 The two-dimensional calculation of the curve, and the random number generated by the signing participant 120 is added to the result of the two-dimensional calculation to obtain the signature of the signing participant; finally, the target random point and the signature of each signing participant 120 are combined As the signature of the message to be signed finally.

It is worth mentioning that FIG. 1 is only one embodiment of the present disclosure, although in the embodiment of FIG. 1,

Each signature participant 120 is a desktop computer, and the key generation center 130 is also located outside the signature center 100. However, in actual applications, the signature participant 120 may be the aforementioned various types of terminals. The key generation center 130 and the signature The inclusion relationship of the center 100 can be arbitrary, that is, the key generation center 130 can be located outside the signature center 100 or inside the signature center 100, so the present disclosure does not limit this, and the protection scope of the present disclosure should not be therefore And subject to any restrictions.

Fig. 2 is a flowchart showing a multi-signature method according to an exemplary embodiment. Among them, the method shown in the embodiment of Fig. 2 is executed by a signature center, which includes a signature unit and multiple signature participants, as shown in Fig. 2, including the following steps:

Step 210: Each signature participant in the signature center obtains a prime order cyclic group established based on a preset elliptic curve equation.

The cyclic group includes generators, and the signature participants have identifiers.

The signature center is a system that includes multiple units or modules. The included signature units and multiple signature participants are organically integrated in the signature center, and the signature unit and the signature participants can interact or interact with each other. The signature center can be an organic combination of software, hardware, and firmware.

In practical applications, the signature participant can be a module, a terminal, or even a separate system or subsystem.

A group is a concept in group theory. A group is a non-empty set that satisfies the conditions of closure, associative law, existence of identity elements, and existence of inverse elements. A unit in a group is called an element in the group. Is the number of elements in the group. A cyclic group is a group that satisfies the condition: each element in the group is a power of a fixed element in the group, so the generator of the cyclic group is the fixed element, and the prime order cyclic group A group is a cyclic group in which the number of elements contained is prime.

In an embodiment, the general formula of the preset elliptic curve equation is:

y^2=x^3+a*x+b(mod p),

Wherein, a and b are the coefficients of the preset elliptic curve equation, and p is the modulus.

The general elliptic curve equation can adopt the above form, for example:

y ² =x ³ -5x+4 (mod 25).

All points in the elliptic curve form an additive group, so each element in the prime order cyclic group established based on the preset elliptic curve equation is a point.

In one embodiment, the set of all points satisfying the preset elliptic curve equation is used as the established prime order cyclic group.

The process of establishing the cyclic group of prime order based on the preset elliptic curve equation is established by using the addition algorithm of the elliptic curve.

The identity of the signing participant is a string used to uniquely determine the identity of the signing participant, which can include letters, numbers, underscores and other characters, such as MAC address (Media Access Control Address), mobile phone number, bank Card number, account number or ID (Identification, serial number) assigned in advance for each signing participant.

In one embodiment, the type of the identity of each signature participant in the signature center is the same, and the type of the identity of the signature participant is one of an ID number, a mobile phone number, and an email address.

Step 220: Each signature participant in the signature center receives the private key generated by the key generation center according to the signature of the signature participant.

The private key is the key used for encryption in the field of asymmetric encryption. The information encrypted by the private key can only be decrypted with the corresponding public key.

In one embodiment, the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses a hash algorithm specific to the key generation center to hash the identity of each signature participant to obtain the private key of each signature participant.

The key generation center uses its own private key to encrypt the identity of each signing participant to obtain the private key of each signing participant.

For each signature participant, the key generation center generates a random character sequence corresponding to the signature of the signature participant as the private key of the signature participant, and combines the private key generated for each signature participant with the corresponding The identity of the signing participant is stored correspondingly.

In one embodiment, the identities of all signature participants are generated by the key generation center and maintained by the key generation center.

In an embodiment, before each signature participant in the signature center receives the private key generated by the key generation center according to the signature of the signature participant, the method further includes:

Each signature participant in the signature center sends the signature of the signature participant to the key generation center, so that the key generation center generates a private key according to the signature of the signature participant.

In one embodiment, the key generation center has a script embedded at the local end (namely, the signature center), and before each signature participant in the signature center receives the private key generated by the key generation center according to the signature of the signature participant, The key generation center uses a script to crawl the identity of the signing participants in the signature center, and generates a corresponding private key according to the identity of each signing participant.

In step 230, each signature participant in the signature center obtains the public key of the signature participant by using the following formula based on the private key of the signature participant:

X _i ＝g^x _i ,

Wherein, X _i is the i-th signature obtained participant public key, g is a generator of the cyclic group, x _i is the i-th signature participant private key.

It can be seen that the public key of each signature participant is obtained by performing binary operations on the elliptic curve a specific number of times on the generator, where the generator is the initial point of the elliptic curve, and the generator The specified number is equal to the private key of the corresponding signing participant.

Step 250: When a signature request for the message to be signed is received, each signature participant in the signature center generates a random number, and the signature unit in the signature center uses the following formula based on the random number of each signature participant in the preset Get the target random point on the elliptic curve:

R _i =g^r _i ,

R=R ₁ *R ₂ *...*R _n ,

Among them, R _i is a random point obtained for the i-th signature participant on the preset elliptic curve, r _i is a random number generated by the i-th signature participant, and R is a random number based on each signature participant Random points of the target obtained.

In one embodiment, the random number generated by each signature participant is greater than 0 and less than the order of the cyclic group.

The signature request for the message to be signed may be a network request based on various protocols, for example, it may be a request under the HTTP protocol.

In one embodiment, the signature request includes the message to be signed.

In one embodiment, before receiving the signature request for the message to be signed, the signature unit in the signature center obtains a plurality of messages to be signed, wherein each message to be signed has an identifier, and the signature request for the message to be signed Contains the identity of the message to be signed, and then when a signature request for the message to be signed is received, the signature unit in the signature center obtains the identity and the identity of the message to be signed included in the signature request from the plurality of messages to be signed. Identifies the same message to be signed.

Step 260, each signature participant in the signature center uses the following formula to sign the message to be signed based on the target random point, and sends it to the signature unit in the signature center, and the signature unit synthesizes each signature participant The signature of the party obtains the signature of the message to be signed:

s _i = r _i +c*ID _i *x _i ,

It can be seen that the finally synthesized signature of the message to be signed is related to the private key, the identity of each signing participant, the public key of each signing participant, the target random point, and the message to be signed. This improves The complexity of the signature is improved, and the reliability and security of the signature are improved.

In summary, according to the multi-signature method shown in the embodiment of FIG. 2, since the private key of each signature participant is generated by the key generation center according to the signature of the signature participant, it is possible to avoid random generation of the private key leading to signature The appearance of the phenomenon of reduced reliability. Both the private key of the signing participant and the signature of the message to be signed are related to the identity of each signing participant, which improves the security of the signature and the maintainability of the system. At the same time, on the basis of the existing technology, the steps that require a large amount of computing resources are eliminated, resources are saved, and the efficiency of signatures is improved.

FIG. 3 is a flowchart of steps after step 230 and steps after step 260 according to an embodiment shown in the embodiment corresponding to FIG. 2. As shown in Figure 3, it includes the following steps:

In step 240, each signature participant in the signature center publishes the public key of the signature participant, so that the signature verification party can obtain a public key set composed of the public keys of all the signature participants in the signature center.

In one embodiment, the signing participant publishes its public key through the network. For example, the signing participant adds the public key to the preset webpage code template, generates a webpage file that records the public key and stores it locally; when the signature verifier needs to obtain the public key of the signing participant, the public key is sent to the signing participant Obtain the request, the signing party will return a web page file containing the public key to the signature verifier according to the request, so that the signature verifier can obtain the public key from the web page file, and the signature verifier sends the public key to each signing party Obtain the request to obtain the public key set.

In one embodiment, after all signature participants in the signature center generate public keys, the signature center will package the public key set and send it to each signature verifier with which it has established a communication connection, so that the signature verifier can obtain Public key.

The signature verifier is an entity with computing processing and communication capabilities, and can be the same type of terminal or system as the signature participant.

Step 270: The signature unit in the signature center sends the signature of the message to be signed to the target signature verifier, so that the target signature verifier uses the public key set to verify the signature of the message to be signed.

The target signature verifier is a party qualified to verify the signature of the message to be signed.

In one embodiment, the target signature verifier has an identifier and is stored locally in the signature unit. When the signature unit in the signature center receives a request to obtain the signature of the message to be signed, if the identifier in the request is stored locally in the signature unit If the identifiers in are consistent, the signature for the message to be signed is sent to the sender of the request according to the request.

In one embodiment, the target signature verifier uses the public key set to verify the signature of the message to be signed based on the following formula:

g^S=R*(X ₁ ^ID ₁ +...+X _n ^ID _n )*c.

Wherein, g is a generator of the cyclic group, R is a random number based on the target random points each acquired signature _{_{participants, S = s 1 + s 2}} + ... + s n, X it is the i-th signature obtained The public key of the participant, ID _i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is all signatures in the signature center The collection of public keys of the participants.

The present disclosure also provides a signature center. Fig. 4 is a block diagram showing a signature center according to an exemplary embodiment. As shown in FIG. 4, the signature center 400 includes a signature unit 420 and a plurality of signature participants 410. The signature unit 420 includes a target random point acquisition module 421 and a synthesis module 422. The signature participant 410 includes an acquisition module 411, Module 412, public key acquisition module 413, generation module 414 and signature module 415, where:

The obtaining module 411 is configured to obtain a prime order cyclic group established based on a preset elliptic curve equation, the cyclic group including generators, and the signature participant has an identifier;

The receiving module 412 is configured to receive the private key generated by the key generation center according to the identity of the signature participant;

The public key obtaining module 413 is configured to obtain the public key of the signature participant by using the following formula based on the private key of the signature participant:

X _i ＝g^x _i ,

The generating module 414 is configured to generate a random number when a signature request for a message to be signed is received;

The target random point obtaining module 421 is configured to obtain a target random point on the preset elliptic curve based on the random number of each signature participant using the following formula:

R _i =g^r _i ,

R=R ₁ *R ₂ *...*R _n ,

The signature module 415 is configured to respectively sign the message to be signed based on the target random point using the following formula, and send it to the signature unit in the signature center:

s _i = r _i +c*ID _i *x _i ,

Among them, ID _i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is the public signature of all signing participants in the signature center. A set of keys, s _i is the signature of the message to be signed by the i-th signing participant;

The synthesis module 422 is used to synthesize the signatures of each signing participant to obtain the signature (R, S) of the message to be signed, where S=s ₁ +s ₂ +...+s _n .

According to the third aspect of the present disclosure, there is also provided an electronic device capable of implementing the above method.

Those skilled in the art can understand that various aspects of the present application can be implemented as a system, method, or program product. Therefore, each aspect of the present application can be specifically implemented in the following forms, namely: complete hardware implementation, complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which can be collectively referred to herein as "Circuit", "Module" or "System".

The electronic device 500 according to this embodiment of the present application will be described below with reference to FIG. 5. The electronic device 500 shown in FIG. 5 is only an example, and should not bring any limitation to the function and use scope of the embodiments of the present application.

As shown in FIG. 5, the electronic device 500 is represented in the form of a general-purpose computing device. The components of the electronic device 500 may include, but are not limited to: the aforementioned at least one processing unit 510, the aforementioned at least one storage unit 520, and a bus 530 connecting different system components (including the storage unit 520 and the processing unit 510).

Wherein, the storage unit stores program code, and the program code can be executed by the processing unit 510, so that the processing unit 510 executes the various exemplary methods described in the above-mentioned "Embodiment Method" section of this specification. Implementation steps.

The storage unit 520 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 521 and/or a cache storage unit 522, and may further include a read-only storage unit (ROM) 523.

The storage unit 520 may also include a program/utility tool 524 having a set of (at least one) program module 525. Such program module 525 includes but is not limited to: an operating system, one or more application programs, other program modules, and program data, Each of these examples or some combination may include the implementation of a network environment.

The bus 530 may represent one or more of several types of bus structures, including a storage unit bus or a storage unit controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local area using any bus structure among multiple bus structures. bus.

The electronic device 500 may also communicate with one or more external devices 700 (such as keyboards, pointing devices, Bluetooth devices, etc.), and may also communicate with one or more devices that enable a user to interact with the electronic device 500, and/or communicate with Any device (such as a router, modem, etc.) that enables the electronic device 500 to communicate with one or more other computing devices. This communication can be performed through an input/output (I/O) interface 550. In addition, the electronic device 500 may also communicate with one or more networks (for example, a local area network (LAN), a wide area network (WAN), and/or a public network, such as the Internet) through the network adapter 560. As shown in the figure, the network adapter 560 communicates with other modules of the electronic device 500 through the bus 530. It should be understood that although not shown in the figure, other hardware and/or software modules can be used in conjunction with the electronic device 500, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives And data backup storage system, etc.

Through the description of the foregoing embodiments, those skilled in the art can easily understand that the exemplary embodiments described herein can be implemented by software, or can be implemented by combining software with necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (can be a CD-ROM, U disk, mobile hard disk, etc.) or on the network , Including several instructions to make a computing device (which may be a personal computer, a server, a terminal device, or a network device, etc.) execute the method according to the embodiments of the present disclosure.

According to the fourth aspect of the present disclosure, there is also provided a computer-readable storage medium on which is stored a program product capable of implementing the above method of this specification. In some possible implementation manners, various aspects of the present application can also be implemented in the form of a program product, which includes program code. When the program product runs on a terminal device, the program code is used to enable the The terminal device executes the steps according to various exemplary embodiments of the present application described in the above-mentioned "Exemplary Method" section of this specification.

Referring to FIG. 6, a program product 600 for implementing the above method according to an embodiment of the present application is described. It can adopt a portable compact disk read-only memory (CD-ROM) and include program code, and can be installed in a terminal device, For example, running on a personal computer. However, the program product of this application is not limited to this. In this document, the readable storage medium can be any tangible medium that contains or stores a program, and the program can be used by or combined with an instruction execution system, device, or device.

The program product can use any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or device, or a combination of any of the above. More specific examples (non-exhaustive list) of readable storage media include: electrical connections with one or more wires, portable disks, hard disks, random access memory (RAM), read only memory (ROM), erasable Type programmable read only memory (EPROM or flash memory), optical fiber, portable compact disk read only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination of the above.

The computer-readable signal medium may include a data signal propagated in baseband or as a part of a carrier wave, and readable program code is carried therein. This propagated data signal can take many forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the foregoing. The readable signal medium may also be any readable medium other than a readable storage medium, and the readable medium may send, propagate, or transmit a program for use by or in combination with the instruction execution system, apparatus, or device.

The program code contained on the readable medium can be transmitted by any suitable medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the foregoing.

The program code used to perform the operations of this application can be written in any combination of one or more programming languages. The programming languages include object-oriented programming languages—such as Java, C++, etc., as well as conventional procedural Programming language-such as "C" language or similar programming language. The program code can be executed entirely on the user's computing device, partly on the user's device, executed as an independent software package, partly on the user's computing device and partly executed on the remote computing device, or entirely on the remote computing device or server Executed on. In the case of a remote computing device, the remote computing device can be connected to a user computing device through any kind of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (for example, using Internet service providers) Business to connect via the Internet).

The processing shown in the above drawings does not indicate or limit the time sequence of these processings. In addition, it is easy to understand that these processes can be executed synchronously or asynchronously in multiple modules, for example. It should be understood that the present application is not limited to the precise structure that has been described above and shown in the drawings, and various modifications and changes can be performed without departing from its scope.

Claims

A multi-signature method, characterized in that the method is executed by a signature center, the signature center includes a signature unit and a plurality of signature participants, and the method includes:

Each signature participant in the signature center obtains a cyclic group of prime order established based on a preset elliptic curve equation, the cyclic group includes generators, and the signature participant has an identifier;

Each signature participant in the signature center receives the private key generated by the key generation center according to the signature of the signature participant;

Each signature participant in the signature center uses the following formula to obtain the signature participant's public key based on the signature participant's private key:

X i ＝g^x i ,

Wherein, X i is the i-th signature obtained participating party public key, g is a generator of the cyclic group, x i is the i-th signature participant private key;

When a signature request for a message to be signed is received, each signature participant in the signature center generates a random number, and the signature unit in the signature center uses the following formula to set the preset elliptic curve based on the random number of each signature participant Get random points on the target:

R i =g^r i ,

R=R 1 *R 2 *...*R n ,

Among them, R i is a random point obtained for the i-th signature participant on the preset elliptic curve, r i is a random number generated by the i-th signature participant, and R is a random number based on each signature participant Random points of the target obtained;

Each signature participant in the signature center uses the following formula to sign the message to be signed based on the target random point, and sends it to the signature unit in the signature center, and the signature unit synthesizes the signature of each signature participant Obtain the signature of the message to be signed:

s i = r i +c*ID i *x i ,

Among them, ID i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is the public signature of all signing participants in the signature center. A set of keys, s i is the signature of the i-th signature participant to the message to be signed, and the signature of the message to be signed synthesized by the signature unit is (R, S), S=s 1 +s 2 +…+s n .
The method according to claim 1, wherein after each signature participant in the signature center uses the following formula to obtain the public key of the signature participant based on the private key of the signature participant, the method further include:

Each signature participant in the signature center publishes the public key of the signature participant, so that the signature verification party can obtain a public key set composed of the public keys of all signature participants in the signature center;

In the signature center, each signature participant uses the following formula to sign the message to be signed based on the target random point, and sends it to the signature unit in the signature center, and the signature unit synthesizes the signature of each signature participant After the step of obtaining the signature of the message to be signed, the method further includes:

The signature unit in the signature center sends the signature of the message to be signed to the target signature verifier, so that the target signature verifier uses the public key set to verify the signature of the message to be signed.
The method according to claim 2, wherein the target signature verifier uses the public key set to verify the message to be signed based on the following formula:

g^S=R*(X 1 ^ID 1 +...+X n ^ID n )*c.
The method according to claim 1, wherein the general formula of the preset elliptic curve equation is:

y^2=x^3+a*x+b(mod p),

Wherein, a and b are the coefficients of the preset elliptic curve equation, and p is the modulus.
The method according to claim 1, wherein the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses a hash algorithm specific to the key generation center to hash the identity of each signature participant to obtain the private key of each signature participant.
The method according to claim 1, wherein the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses its own private key to encrypt the identity of each signing participant to obtain the private key of each signing participant.
The method according to any one of claims 1 to 6, wherein the types of the identities of the signature participants in the signature center are the same, and the types of the identities of the signature participants are ID number, mobile phone One of the number and email address.
A signature center, comprising: a signature unit and a plurality of signature participants, the signature unit includes a target random point acquisition module and a synthesis module, and the signature participants include an acquisition module, a receiving module, and a public key acquisition module , Generation module and signature module, where:

An obtaining module, configured to obtain a prime order cyclic group established based on a preset elliptic curve equation, the cyclic group including generators, and the signature participant has an identifier;

The receiving module is used to receive the private key generated by the key generation center according to the identity of the signature participant;

The public key acquisition module is used to obtain the public key of the signature participant using the following formula based on the private key of the signature participant:

X i ＝g^x i ,

Wherein, X i is the i-th signature obtained participating party public key, g is a generator of the cyclic group, x i is the i-th signature participant private key;

The generation module is used to generate a random number when a signature request for a message to be signed is received;

The target random point obtaining module is used to obtain the target random point on the preset elliptic curve based on the random number of each signature participant using the following formula:

R i =g^r i ,

R=R 1 *R 2 *...*R n ,

Among them, R i is a random point obtained for the i-th signature participant on the preset elliptic curve, r i is a random number generated by the i-th signature participant, and R is a random number based on each signature participant Random points of the target obtained;

The signature module is configured to respectively sign the message to be signed based on the target random point using the following formula, and send it to the signature unit in the signature center:

s i = r i +c*ID i *x i ,

Among them, ID i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is the public signature of all signing participants in the signature center. A set of keys, s i is the signature of the message to be signed by the i-th signing participant;

The synthesis module is used to synthesize the signatures of each signing participant to obtain the signature (R, S) of the message to be signed, where S=s 1 +s 2 +...+s n .
The signature center according to claim 8, wherein:

The public key acquisition module is also used to publish the public key of the signature participant after acquiring the public key of the signature participant based on the private key of the signature participant, so that the signature verification party can obtain the signature from the signature center. A set of public keys composed of the public keys of all signing parties;

The signature module is further configured to use the following formula to sign the message to be signed based on the target random point, and send it to the signature unit in the signature center, and the signature unit synthesizes each signature participant After obtaining the signature of the message to be signed, send the signature of the message to be signed to the target signature verifier, so that the target signature verifier uses the public key set to perform the signature on the message to be signed Sign verification.
The signature center according to claim 9, wherein the target signature verifier uses the public key set to verify the message to be signed based on the following formula:

g^S=R*(X 1 ^ID 1 +...+X n ^ID n )*c.
The signature center according to claim 8, wherein the general formula of the preset elliptic curve equation is:

y^2=x^3+a*x+b(mod p),

Wherein, a and b are the coefficients of the preset elliptic curve equation, and p is the modulus.
The signature center according to claim 8, wherein the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses a hash algorithm specific to the key generation center to hash the identity of each signature participant to obtain the private key of each signature participant.
The signature center according to claim 8, wherein the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses its own private key to encrypt the identity of each signing participant to obtain the private key of each signing participant.
The signature center according to any one of claims 8 to 13, wherein the type of the identity of each signature participant in the signature center is the same, and the type of the identity of the signature participant is an ID number, One of mobile phone number and email address.
A computer-readable program medium, characterized in that it stores computer program instructions, and when the computer program instructions are executed by a computer, the computer executes the method according to any one of claims 1 to 7.
An electronic device, characterized in that the electronic device is deployed in a signature center, the signature center includes a signature unit and a plurality of signature participants, and the electronic device includes:

processor;

A memory, where computer-readable instructions are stored, and when the computer-readable instructions are executed by the processor, the following steps are implemented:

Acquiring a cyclic group of prime order established based on a preset elliptic curve equation, the cyclic group including generators, and the signature participants have identifiers;

Receive the private key generated by the key generation center according to the identity of the signature participant;

Use the following formula to obtain the public key of the signature participant based on the private key of the signature participant:

X i ＝g^x i ,

Wherein, X i is the i-th signature obtained participating party public key, g is a generator of the cyclic group, x i is the i-th signature participant private key;

When receiving a signature request for the message to be signed, a random number is generated, and the signature unit in the signature center uses the following formula to obtain the target random point on the preset elliptic curve based on the random number of each signature participant:

R i =g^r i ,

R=R 1 *R 2 *...*R n ,

Among them, R i is a random point obtained for the i-th signature participant on the preset elliptic curve, r i is a random number generated by the i-th signature participant, and R is a random number based on each signature participant Random points of the target obtained;

Based on the target random points, the following formulas are used to sign the message to be signed and sent to the signature unit in the signature center. The signature unit synthesizes the signature of each signing participant to obtain the message to be signed signature:

s i = r i +c*ID i *x i ,

Among them, ID i is the identity of the i-th signing participant, c=H(X,R,m), H is the hash function, m is the message to be signed, and X is the public signature of all signing participants in the signature center. A set of keys, s i is the signature of the i-th signature participant to the message to be signed, and the signature of the message to be signed synthesized by the signature unit is (R, S), S=s 1 +s 2 +…+s n .
The electronic device according to claim 16, wherein after the step of obtaining the public key of the signing participant using the following formula based on the private key of the signing participant, the processor further performs the following steps:

Publish the public key of the signature participant so that the signature verifier can obtain a public key set composed of the public keys of all signature participants in the signature center;

Based on the target random points, the following formulas are used to sign the message to be signed and sent to the signature unit in the signature center. The signature unit synthesizes the signature of each signing participant to obtain the signature of the message to be signed After signing, the processor further executes the following steps:

The signature of the message to be signed is sent to the target signature verifier through the signature unit in the signature center, so that the target signature verifier uses the public key set to verify the signature of the message to be signed.
The electronic device according to claim 17, wherein the target signature verifier uses the public key set to verify the message to be signed based on the following formula:

g^S=R*(X 1 ^ID 1 +...+X n ^ID n )*c.
The electronic device according to claim 16, wherein the general formula of the preset elliptic curve equation is:

y^2=x^3+a*x+b(mod p),

Wherein, a and b are the coefficients of the preset elliptic curve equation, and p is the modulus.
The electronic device according to claim 16, wherein the key generation center generates a private key according to the identity of each signing participant in the following manner:

The key generation center uses a hash algorithm specific to the key generation center to hash the identity of each signature participant to obtain the private key of each signature participant.