A conditional traceable ring signature method, system, electronic device and storage medium

Abstract

This invention discloses a conditionally traceable ring signature method, system, electronic device, and storage medium. The method includes: setting system parameters; generating keys for the user and the anonymous revocation authority based on the digital signature algorithm and system parameters; generating a ring signature based on the keys; verifying the ring signature, outputting a first predetermined result if the verification passes, and outputting a second predetermined result if the verification fails; linking the ring signatures, and determining whether to add the ring signature to a signature list based on the ring signature link; if the ring signature appears in the signature list, and the anonymous revocation authority wants to recover the signing public key using its private key, it substitutes the private key of the anonymous revocation authority into a pre-mixed set of public keys to trace the public key of the actual signer; the ring signature algorithm of this invention incorporates a signature list function, enabling the anonymous revocation authority to revoke the anonymity of ring signatures in the signature list only, thereby reducing the authority of the anonymous revocation authority and achieving partial traceability of the ring signature.

Description

Technical Field

[0001] This invention relates to the field of digital signatures, and more particularly to a conditionally traceable ring signature method, system, electronic device, and storage medium. Background Technology

[0002] In digital signatures, one identity-based ring signature scheme distributes private keys through a Private Key Generator (PKG). This scheme can simultaneously achieve chainability and traceability of the ring signature. However, if the PKG is compromised by an adversary, the user's signing private key will be leaked, posing a security risk. Furthermore, the anonymous revocation authority in traditional traceable ring signatures has excessively high authority; theoretically, it can revoke the anonymity of all traceable ring signatures. However, in practical applications, the goal is only to identify malicious signers. If the attacker colludes with the anonymous revocation authority, it poses a security risk to the honest signer.

[0003] Therefore, there is an urgent need for a solution that can achieve partial traceability of ring signatures. Summary of the Invention

[0004] The main objective of this invention is to provide a conditionally traceable ring signature method, system, electronic device, and storage medium that can achieve partial traceability of ring signatures.

[0005] To achieve the above objectives, a first aspect of the present invention provides a conditionally traceable ring signature method, comprising: setting system parameters; generating keys for a user and an anonymous revocation authority according to a preset digital signature algorithm and the system parameters; generating a ring signature according to the keys; verifying the ring signature, and if the verification passes, outputting a first predetermined result, and if the verification fails, outputting a second predetermined result; linking the verified ring signature to a ring signature list, and determining whether to add the ring signature to a signature list based on the ring signature link; if the ring signature appears in the signature list, the anonymous revocation authority attempts to recover the signature public key using its private key. The private key of the anonymous revocation authority is then substituted into the pre-mixed public key set to trace the public key of the actual signer. The ring signature linking of the verified ring signature includes: obtaining the key mirror I in the verified ring signature σ, determining whether the key mirror I has appeared in the mirror list Ω. If it has appeared, and the message M in the ring signature σ is not equal to the message M′ of the existing signature σ′ in the mirror list Ω, then output 1 and delete σ from the signature list θ. If M equals M′, then reject the ring signature σ. If it has not appeared, output 0, accept the ring signature σ, and add the ring signature σ to the signature list θ.

[0006] Furthermore, the system parameter setting includes: inputting security parameter l qChoose two cyclic groups G1 and G2 of the same prime order q. T Let g be a generator of G1, and e denote the bilinear mapping G1×G1→G T H s Represents {0, 1} * →Z q The hash function, where Z q For a finite field, H p Represents the deterministic hash function G1→G1, outputting the common parameter param=(l q ,q,g,G1,G T H s H p ).

[0007] Furthermore, the user's private key is generated by a random number d. i ∈Z q The structure is as follows, with the public key being P. i =d i g; The private key of the anonymous revocation authority is d′ u ∈Z q The public key is P′ u =d′ u g.

[0008] Furthermore, the method for generating a ring signature based on the key includes:

[0009] Randomly select the public keys of n-1 users and mix them with the signing public keys of n-1 users to obtain a set S = {P1, P2, ..., P...} n}, set the signing public key to P π The private key is d π The signer selects l anonymous revocation authorities, whose public key set is denoted by T, where T = {P′1, P′2, ..., P′}. l};

[0010] Calculate d π The key mirror I, I = d π H p (P π );

[0011] In the finite field Z q Select {q i |i=1,...,n,i≠π} and {w i Calculate L |i=1,...,n,i≠π}, i =q i g+w i P i (i≠π) and R i =q i H p (Pi )+w i I(i≠π), and in the finite field Z q Select a random number q π Calculate L π =q π g and R π =q π H p (P π );

[0012] In the finite field z q Select a random number r revoke Calculate R revoke =t revoke g;

[0013] Choose u = 1, ..., l, and calculate...

[0014] Calculate c = H s (M, L1, ..., L) n R1, ..., R n ), c i =w i (i≠π), r i =q i (i≠π), r i =q π -c π d π mod q (i = π);

[0015] In the finite field Z q Select random numbers p1, p2, s i , c′ i = Calculation s=p1-c′d π , s π =p2-c′ π d π mod q;

[0016] Generate a ring signature σ;

[0017] Where σ=(I, c1, ..., c n r1, ..., r n c′1, ..., c′ n ,s,s1,...s n R revoke E1, ..., E l ).

[0018] Furthermore, the verification of the ring signature includes:

[0019] For i = 1...n, calculate L′ i =r i g+c i P i , R′ i =r i H p (P i )+c i I;

[0020] Calculate w1 = H s (M|L′0,...,L′ n ||R′0,...,R′ n )mod q,

[0021] like and If the result is true, output the first predetermined result 1, indicating successful verification; otherwise, output the second predetermined result 0, indicating failed verification.

[0022] Furthermore, the step of substituting the private key of the anonymous revocation authority into a pre-mixed set of public keys to trace the public key of the actual signer includes: substituting the private key d′ of the anonymous revocation authority into the pre-mixed set of public keys. u Substitute the public keys from set S sequentially, and for i = 1, ..., n, calculate... Does the equation hold true? Find the public key P that makes the equation true. π Public key P π This is the public key of the actual signer.

[0023] A second aspect of the present invention provides a conditionally traceable ring signature system, comprising: a parameter setting module for setting system parameters; a key generation module for generating keys for users and anonymous revocation authorities according to a preset digital signature algorithm and the system parameters; a ring signature generation module for generating ring signatures according to the keys; a ring signature verification module for verifying the ring signatures, outputting a first predetermined result if the verification passes, and outputting a second predetermined result if the verification fails; a ring signature linking module for linking the verified ring signatures, and determining whether to add the ring signatures to a signature list based on the ring signature linking; and a tracking module for, if the ring signature linking module determines that the ring signature appears in the signature list, if the ring signature linking module determines that the ring signature appears in the signature list, then... If an anonymous revocation authority wants to recover the signing public key using its private key, it substitutes the private key of the anonymous revocation authority into a pre-mixed set of public keys to trace the public key of the actual signer. The ring signature linking module includes a judgment unit and an execution unit. The judgment unit is used to obtain the key image I in the verified ring signature σ and determine whether the key image I has appeared in the image list Ω. The execution unit is used to output 1 and delete σ from the signature list θ if the judgment unit determines that it has appeared and the message M in the ring signature σ is not equal to the message M′ of the existing signature σ′ in the image list Ω. If M equals M′, the ring signature σ is rejected. If it has not appeared, the execution unit outputs 0, accepts the ring signature σ, and adds the ring signature σ to the signature list θ.

[0024] A third aspect of the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory stores a computer program executable on the processor, and when the processor executes the computer program, it implements any one of the aforementioned conditionally traceable ring signature methods.

[0025] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements any one of the conditionally traceable ring signature methods described above.

[0026] This invention provides a conditionally traceable ring signature method, system, electronic device, and storage medium. The beneficial effects are as follows: A signature list function is added to the linkable ring signature algorithm. If both parties to the transaction are honest, the signature list is empty. If there is a dishonest party, their signature will be retained in the signature list. This forces anonymous revocation authorities to only revoke the anonymity of ring signatures in the signature list, thereby reducing the authority of anonymous revocation authorities and achieving partial traceability of the ring signature. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a flowchart of the conditionally traceable ring signature method according to an embodiment of the present invention;

[0029] Figure 2 This is a framework diagram of the conditionally traceable ring signature system according to an embodiment of the present invention;

[0030] Figure 3 This is a schematic block diagram of the electronic device according to an embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, features, and advantages of this invention more apparent and understandable, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0032] Please see Figure 1 This is a conditionally traceable ring signature method, including:

[0033] S101. Set system parameters;

[0034] S102. Generate keys for users and anonymous revocation authorities according to preset digital signature algorithms and system parameters;

[0035] S103. Generate a ring signature based on the key;

[0036] S104. Verify the ring signature. If the verification passes, output the first predetermined result; if the verification fails, output the second predetermined result.

[0037] S105. Perform ring signature linking on the verified ring signature, and determine whether to add the ring signature to the signature list based on the ring signature link;

[0038] S106. If a ring signature appears in the signature list, and the anonymous revocation authority wants to recover the signature public key using its private key, then substitute the private key of the anonymous revocation authority into the pre-mixed set of public keys to trace the public key of the actual signer.

[0039] In this embodiment, three roles are included: an anonymous revocation authority, a signer, and a verifier, each with different responsibilities. The anonymous revocation authority acts as the regulator in the transaction, the signer is the transaction sender, and the verifier is the verification node of the blockchain. This application embodiment proposes a conditionally traceable ring signature, including six algorithms: system parameter setting, key generation, ring signature generation, ring signature verification, ring signature linking, and anonymous revocation.

[0040] In step S101, setting system parameters includes: inputting security parameter l q Choose two cyclic groups G1 and G2 of the same prime order q. T Let g be a generator of G1, representing the bilinear mapping G1×1→G T H s Represents {0, 1} * →Z q The hash function, where Z q For a finite field, H p Represents the deterministic hash function G1→G1, outputting the common parameter param=(l q ,q,g,G1,G T H s H p ).

[0041] In step S102, the user's private key is generated by a random number d. i ∈Z q The structure is as follows, with the public key being P. i =d i g;

[0042] The private key for the anonymous revocation agency is d′ u ∈Z q The public key is P′ u =d′ u g.

[0043] In step S103, the method for generating a ring signature based on the key includes:

[0044] Randomly select the public keys of n-1 users and mix them with the signing public keys of n-1 users to obtain a set S = {P1, P2, ..., P...} n}, set the signing public key to P π The private key is d π The signer selects l anonymous revocation authorities, whose public key set is denoted by T, where T = {P′1, P′2, ..., P′}. l};

[0045] Calculate d π The key mirror I, I = d π H p (Pπ );

[0046] In the finite field Z q Select {q i |i=1,...,n,i≠π} and {w i Calculate L |i=1,...,n,i≠π}, i =q i g+w i P i (i≠π) and R i =q i H p (P i )+w i I(i≠π), and in the finite field Z q Select a random number q π Calculate L π =q π g and R π =q π H p (P π );

[0047] In the finite field Z q Select a random number r revoke Calculate R revoke =r revoke g;

[0048] Choose u = 1, ..., l, and calculate...

[0049] Calculate c = H s (M, L1, ..., L) n R1, ..., R n ), c i =w i (i≠π), r i =q i (i≠π), r i =q π -c π d π mod q (i = π);

[0050] In the finite field Z q Select random numbers p1, p2, s i , c′ i = Calculation s=p1-c′d π , s π =p2-c′ π d π mod q;

[0051] Generate a ring signature σ;

[0052] Where σ=(I, c1, ..., c n r1, ..., r n c′1, ..., c′ n ,s,s1,...s n R revoke E1, ..., E l ).

[0053] In step S104, verifying the ring signature includes:

[0054] For i = 1...n, calculate L′ i =r i g+c i P i , R′ i =r i H p (P i )+c i I;

[0055] Calculate w1 = H s (M|L′0,...,L′ n ||R′0,...,R′ n )mod q,

[0056] like and If the result is true, output the first predetermined result 1, indicating successful verification; otherwise, output the second predetermined result 0, indicating failed verification.

[0057] In step S105, linking the verified ring signature includes: obtaining the key mirror I in the verified ring signature σ, determining whether the key mirror I has appeared in the mirror list Ω, if it has appeared, and the message M in the ring signature σ is not equal to the message M′ of the existing signature σ′ in the mirror list Ω, then output 1 and delete σ from the signature list θ, if M equals M′, then reject the ring signature σ; if it has not appeared, output 0, then accept the ring signature σ and add the ring signature σ to the signature list θ.

[0058] If the ring signature appears in the signature list, an anonymous revocation occurs; if the ring signature does not appear in the signature list, it indicates that both parties to the transaction are honest.

[0059] In step S105, the verifier obtains the key image I from the verified ring signature σ.

[0060] In step S106, the private key of the anonymous revocation authority is substituted into the pre-mixed public key set, and the public key of the actual signer is traced to include: the private key d′ of the anonymous revocation authority. u Substitute the public keys from set S sequentially, and for i = 1, ..., n, calculate... Does the equation hold true? Find the public key P that makes the equation true. π Public key P π This is the public key of the actual signer.

[0061] Therefore, the conditionally traceable ring signature method provided in this application, in order to achieve partial traceability of ring signatures, incorporates a signature list function into the linkable ring signature algorithm. If both parties to the transaction are honest, the signature list is empty. If there is a dishonest party, their signature will be retained in the signature list. This ensures that the anonymous revocation authority can only revoke the anonymity of the ring signatures in the signature list, thereby reducing the authority of the anonymous revocation authority and achieving partial traceability of the ring signature.

[0062] Please see Figure 2 This application also provides a conditionally traceable ring signature system, including: a parameter setting module 1, a key generation module 2, a ring signature generation module 3, a ring signature verification module 4, a ring signature linking module 5, and a tracking module 6.

[0063] Parameter setting module 1 is used to set system parameters;

[0064] Key generation module 2 is used to generate keys for users and anonymous revocation authorities according to preset digital signature algorithms and system parameters;

[0065] Ring signature generation module 3 is used to generate ring signatures based on the key;

[0066] The ring signature verification module 4 is used to verify the ring signature. If the verification passes, it outputs the first predetermined result; if the verification fails, it outputs the second predetermined result.

[0067] The ring signature linking module 5 is used to link verified ring signatures and determine whether to add the ring signature to the signature list based on the ring signature linking.

[0068] The tracking module 6 is used to track the public key of the actual signer if the ring signature linking module determines that the ring signature appears in the signature list and if the anonymous revocation agency wants to recover the signature public key through the private key.

[0069] Parameter setting module 1 is specifically used to input safety parameters. q Choose two cyclic groups G1 and G2 of the same prime order q. TLet g be a generator of G1, and e denote the bilinear mapping G1×G1→G T H s Represents {0, 1} * →Z q The hash function, where Z q For a finite field, H p Represents the deterministic hash function G1→G1, outputting the common parameter param=(l q ,q,g,G1,G T H s H p ).

[0070] In the key generated by key generation module 2, the user's private key is composed of a random number d. i ∈Z q The structure is as follows, with the public key being P. i =d i g; The private key for the anonymous revocation authority is d′ u ∈Z q The public key is P′ u =d′ u g.

[0071] The ring signature generation module 3 includes: a public key selection unit, a mirror calculation unit, a first calculation unit, a second calculation unit, a first selection unit, a third calculation unit, a fourth calculation unit, and a ring signature generation unit.

[0072] The public key selection unit is used to randomly select the public keys of n-1 users and mix them with the signature public keys of n-1 users to obtain a set S = {P1, P2, ..., P...} n}, set the signing public key to P π The private key is d π The signer selects l anonymous revocation authorities, whose public key set is denoted by T, where T = {P′1, P′2, ..., P′}. l};

[0073] The mirror computing unit is used to calculate d π The key mirror I, I = d π H p (P π );

[0074] The first computational unit is used in the finite field Z. q Select {q i |i=1,...,n,i≠π} and {w i Calculate L |i=1,...,n,i≠π}, i =q i g+w i P i (i≠π) and Ri =q i H p (P i )+w i I(i≠π), and in the finite field Z q Select a random number q π Calculate L π =q π g and R π =q π H p (P π );

[0075] The second computational unit is used in the finite field Z. q Select a random number r revoke Calculate R revoke =r revoke g;

[0076] The first selection unit is used to select u = 1, ..., l, and to calculate...

[0077] The third calculation unit is used to calculate c = H. s (M, L1, ..., L) n R1, ..., R n ), c i =w i (i≠π), r i =q i (i≠π), r i =q π -c π d π mod q (i = π);

[0078] The fourth computational unit is used in the finite field Z q Select random numbers p1, p2, s i , c′ i = Calculation s=p1-c′d π , s π =p2-c′ π d π mod q;

[0079] The ring signature generation unit is used to generate the ring signature σ;

[0080] Where σ=(I, c1, ..., c n r1, ..., r n c′1, ..., c′ n ,s,s1,...s n Rrevoke E1, ..., E l ).

[0081] The ring signature linking module 5 includes a judgment unit and an execution unit. The judgment unit is used to obtain the key image I in the verified ring signature σ and determine whether the key image I has appeared in the image list Ω. The execution unit is used to determine whether the key image I has appeared in the image list Ω. If the judgment unit determines that the key image I has appeared in the image list Ω and the message M in the ring signature σ is not equal to the message M′ of the existing signature σ′, then the execution unit outputs 1 and deletes σ from the signature list θ. If M is equal to M′, then the ring signature σ is rejected. If the key image I has not appeared in the image list Ω, then the execution unit outputs 0, accepts the ring signature σ, and adds the ring signature σ to the signature list θ.

[0082] The ring signature verification module 4 includes: a fifth calculation unit, a sixth calculation unit, and an output unit;

[0083] The fifth calculation unit is used to calculate L′ for i = 1...n. i =r i g+c i P i , R′ i =r i H p (P i )+c i I;

[0084] The sixth calculation unit is used to calculate w1 = H s (M|L′0,...,L′ n ||R′0,...,R′ n )mod q,

[0085]

[0086] The output unit is used for if and If the result is true, output the first predetermined result 1, indicating successful verification; otherwise, output the second predetermined result 0, indicating failed verification.

[0087] Module 6 is specifically used to track the private key d′ of the anonymous revocation authority. u Substitute the public keys from set S sequentially, and for i = 1, ..., n, calculate... Does the equation hold true? Find the public key P that makes the equation true. π Public key P π This is the public key of the actual signer.

[0088] Therefore, the conditionally traceable ring signature system provided in this application, in order to achieve partial traceability of ring signatures, incorporates a signature list function into the linkable ring signature algorithm. If both parties to the transaction are honest, the signature list is empty. If there is a dishonest party, their signature will be retained in the signature list. This forces the anonymous revocation authority to revoke the anonymity of the ring signatures in the signature list, thereby reducing the authority of the anonymous revocation authority and achieving partial traceability of the ring signature.

[0089] This application provides an electronic device; please refer to [link / reference]. Figure 3 The electronic device includes a memory 601, a processor 602, and a computer program stored in the memory 601 and executable on the processor 602. When the processor 602 executes the computer program, it implements the conditionally traceable ring signature method described above.

[0090] Furthermore, the electronic device also includes at least one input device 603 and at least one output device 604.

[0091] The aforementioned memory 601, processor 602, input device 603, and output device 604 are connected via bus 605.

[0092] The input device 603 can specifically be a camera, touch panel, physical buttons, or mouse, etc. The output device 604 can specifically be a display screen.

[0093] The memory 601 can be a high-speed random access memory (RAM) or a non-volatile memory, such as a disk storage device. The memory 601 is used to store a set of executable program code, and the processor 602 is coupled to the memory 601.

[0094] Furthermore, this application embodiment also provides a computer-readable storage medium, which may be disposed in the electronic device of the above embodiments, and the computer-readable storage medium may be the aforementioned memory 601. The computer-readable storage medium stores a computer program, which, when executed by the processor 602, implements the conditionally traceable ring signature method described in the foregoing embodiments.

[0095] Furthermore, the storage medium of the computer can also be a USB flash drive, a portable hard drive, a read-only memory (ROM), RAM, a magnetic disk, or an optical disk, or any other medium that can store program code.

[0096] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0097] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0098] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0099] If the integrated module is implemented as a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0100] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0101] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0102] The above is a description of a conditionally traceable ring signature method, system, electronic device, and storage medium provided by the present invention. For those skilled in the art, based on the ideas of the embodiments of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A conditionally traceable ring signature method, characterized in that, include: Set system parameters; Generate keys for users and anonymous revocation authorities based on a preset digital signature algorithm and the system parameters; Generate a ring signature based on the key; The ring signature is verified. If the verification passes, a first predetermined result is output; if the verification fails, a second predetermined result is output. The verified ring signature is linked with a ring signature chain, and the ring signature chain is used to determine whether to add the ring signature to the signature list; If the ring signature appears in the signature list, and the anonymous revocation authority wants to recover the signing public key using its private key, it substitutes the private key of the anonymous revocation authority into a pre-mixed set of public keys to trace the public key of the actual signer. The step of linking the verified ring signature includes: obtaining the verified ring signature. Key mirror in Determine the key image Is it in the mirror list? If it has appeared in the above, and the ring signature is present... News in With the aforementioned mirror list Signature already exists in China News If they are not equal, output 1 and remove the signature list. In ,like equal If so, then the signature of that ring is rejected. ; If it has not appeared before, output 0, and accept the signature of this ring. and ring signature Add to signature list middle.

2. The conditionally traceable ring signature method according to claim 1, characterized in that, The system parameters settings include: inputting security parameters. Choose two prime numbers of the same order. Cyclic group and , for generator, Represents a bilinear mapping , express The hash function, where For a finite field, express A deterministic hash function that outputs common parameters. .

3. The conditionally traceable ring signature method according to claim 2, characterized in that, The user's private key is generated by a random number. The structure is as follows: public key is ; The private key of the anonymous revocation authority is The public key is .

4. A conditionally traceable ring signature system, characterized in that, include: The parameter setting module is used to set system parameters; The key generation module is used to generate keys for users and anonymous revocation authorities according to a preset digital signature algorithm and the system parameters. A ring signature generation module is used to generate a ring signature based on the key; The ring signature verification module is used to verify the ring signature. If the verification passes, a first predetermined result is output; if the verification fails, a second predetermined result is output. The ring signature linking module is used to link the verified ring signatures and determine whether to add the ring signature to the signature list based on the ring signature linking. The tracking module is used to track the public key of the actual signer if the ring signature linking module determines that the ring signature appears in the signature list and if the anonymous revocation authority wants to recover the signature public key through its private key. The ring signature linking module includes: a judgment unit and an execution unit; The judgment unit is used to obtain the verified ring signature. Key mirror in Determine the key image Is it in the mirror list? It has appeared in the process; the execution unit is used to determine, in the judgment unit, if it has appeared, and the ring signature News in With the aforementioned mirror list Signature already exists in China News If they are not equal, output 1 and remove the signature list. In ,like equal If so, then the signature of that ring is rejected. If it has not appeared before, output 0, and accept the signature of this ring. and ring signature Add to signature list middle.

5. An electronic device comprising: A memory and a processor, wherein the memory stores a computer program executable on the processor, characterized in that, when the processor executes the computer program, it implements the method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 3.

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