Adapter signature method and device based on finite field

Abstract

The present invention discloses a finite field-based adapter signature method and device, which includes: a second user obtains the public information of a first user, where the first user is the user who signs based on the object to be signed; the second user generates a pre-signature based on its own private key and the public information; the first user verifies the pre-signature, and after the verification is passed, adapts the pre-signature to a formal signature; the second user obtains the formal signature and extracts the candidate difficult relationship evidence of the first user from the formal signature; the extracted candidate difficult relationship evidence of the first user is verified, and if the verification is passed, it is determined that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the formal signature confirms that the first user has signed the object to be signed. The present invention is efficient, secure, and highly adaptable, and can ensure the secure generation, verification, and traceability of signatures in scenarios with multiple users and multiple parties.

Description

Technical Field

[0001] The present invention relates to the field of information security and cryptography technology, and in particular to a finite field-based adapter signature method and device. Background Art

[0002] With the rapid development of information technology and the internet, electronic signatures and digital authentication have become essential foundations of network security. Digital signatures are widely used in fields such as electronic contracts, financial transactions, and data encryption to ensure the authenticity, integrity, and non-repudiation of information. However, traditional digital signature schemes are vulnerable to replay attacks or signature forgery in response to increasingly complex network attacks. Most signature schemes lack flexible matching mechanisms and cannot effectively support signature conversion or interaction in multi-user scenarios. In environments requiring multi-party signatures, ensuring flexibility and security is a critical issue. To address these issues, adapter signature schemes have become a research hotspot in cryptography in recent years. Adapter signatures not only ensure the security, adaptability, and non-repudiation of signatures, but also support complex multi-party signature scenarios, making them particularly suitable for emerging applications such as blockchain. Summary of the Invention

[0003] In view of this, the present invention provides an adapter signature method and device based on a finite field, which can solve the above technical problems.

[0004] In order to solve the above technical problems, the present invention is implemented as follows.

[0005] An adapter signature method based on a finite field, comprising:

[0006] Step S1: A second user obtains the public information of a first user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information;

[0007] Step S2: The first user verifies the pre-signature. If the verification is successful, the pre-signature is adapted to a formal signature.

[0008] Step S3: The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature; the extracted candidate difficult relationship evidence of the first user is verified. If the verification passes, it is determined that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the official signature confirms that the first user has signed the object to be signed.

[0009] Preferably, in step S1, the second user obtains the public information of the first user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information, including:

[0010] Step S11: The second user obtains the object to be signed and generates a private key x B and public key Where g is a finite field The generator on , p is a prime number of length 2048 bits, x for g B Power, for Modulo p; obtain the message M to be signed sent by the first user; select a random number k and calculate the temporary public key K = g k (mod p), g k is the kth power of g, g k (mod p) is g k Modulo p; calculate the hash value e=h(M) of the message to be signed M, where h(·) is a hash function using the SM3 algorithm, and calculate r=f(K||Y||M) through the key derivation function f(·), where K, Y, and M are the temporary public key, the public difficulty relationship of the first user, and the message to be signed, respectively, || is a connection symbol indicating string concatenation, and r is the calculation result; the object to be signed is an electronic contract or data to be encrypted, and Y=g y (modp), y is the difficult relationship evidence of the first user, g y is g to the power of y, g y (mod p) is g y module p;

[0011] Step S12: The second user generates a pre-signature And the pre-signed value Sent to the first user; wherein, ex B The hash value e and the second user's private key x B The product of kr is the product of random number k and r, ex B -kr(mod p-1) is (ex B -kr) modulo p-1.

[0012] Preferably, the step S2: the first user verifies the pre-signature, and after the verification is passed, adapts the pre-signature to a formal signature, including:

[0013] The first user obtains the pre-signature Calculate separately and Xe (mod p); where is the value calculated in the pre-signature, indicating g Power, K r is the rth power of the temporary public key K, X e is the second user's public key X to the power of e, X e (mod p) is X e module p;

[0014] if Equal to X e (mod p), the verification is successful, and the first user uses the difficult relationship evidence y, which is calculated by the following formula:

[0015]

[0016] Adapt the pre-signature to the formal signature (S, K), y -1 is the inverse element of y, for Modulo p-1.

[0017] Preferably, step S3: the second user obtains the official signature, extracts the candidate difficult relationship evidence of the first user from the official signature; verifies the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determines that the candidate difficult relationship evidence is the same as the difficult relationship evidence, including:

[0018] The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature. The extraction formula is as follows:

[0019]

[0020] Among them, y′ is the candidate difficult relation evidence, S -1 is the inverse element of the formal signature S, for modulo p-1;

[0021] Verify the extracted candidate difficult relationship evidence of the first user and calculate g y′ and Y(modp), where g y′ is g raised to the power of y′, and Y(mod p) is Y modulo p;

[0022] If g y′ If it is equal to Y(mod p), the verification is successful;

[0023] If the verification is successful, it is determined that y′ is the same as the difficult relationship evidence.

[0024] Preferably, the difficult relationship evidence y is associated with the identity information of the first user, and is one of the private key, cryptographic certificate, and biometric feature of the first user.

[0025] An adapter signature device based on a finite field, comprising:

[0026] The device comprises:

[0027] Pre-signature module: configured to obtain the public information of the first user for the second user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information;

[0028] Adaptation module: configured to verify the pre-signature for the first user, and adapt the pre-signature to a formal signature after the verification is successful;

[0029] Verification module: configured to obtain the formal signature for the second user, extract the candidate difficult relationship evidence of the first user from the formal signature; verify the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determine that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the formal signature confirms that the first user has signed the object to be signed.

[0030] The present invention provides a computer-readable storage medium, wherein a plurality of instructions are stored in the storage medium; the plurality of instructions are used for a processor to load and execute the method described above.

[0031] The present invention provides an electronic device, characterized in that the electronic device includes:

[0032] A processor, which is used to execute multiple instructions;

[0033] A memory for storing a plurality of instructions;

[0034] The plurality of instructions are used to be stored by the memory and loaded and executed by the processor to implement the method as described above.

[0035] Beneficial effects:

[0036] (1) This invention combines hash functions, key derivation functions, and random number generation to provide higher security and efficiency for digital signatures. It is widely used in digital authentication, electronic signatures, blockchain, and other scenarios requiring high-security signatures.

[0037] (2) The present invention is efficient, secure, and highly adaptable, and can ensure the secure generation, verification, and traceability of signatures in multi-user, multi-party scenarios, ensuring that only users with evidence of difficult relationships can complete signature conversion;

[0038] (3) The present invention introduces a random number k during the signature generation process. Combined with the discrete logarithm problem, attackers cannot infer the private key or forge a valid signature from a known signature sample. The signature adaptation process relies on the user's difficult relationship evidence y. Only users who possess this evidence can complete the signature conversion, which enhances the security of the signature process. Through the extraction algorithm, any legitimate formal signature can extract the difficult relationship evidence y, ensuring the traceability of the signature and preventing the signer from denying their participation in the signing behavior. At the same time, the signer cannot deny their participation in the signing behavior afterwards, which enhances the legal validity and credibility of the signature. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the flow of the adapter signature method based on finite fields of the present invention;

[0040] Figure 2 Schematic diagram of the interaction of the adapter signature method based on finite fields of the present invention;

[0041] Figure 3 This is a schematic diagram of the pre-signature generation and verification process of the present invention;

[0042] Figure 4 Schematic diagram of the signature adaptation and difficulty relationship evidence extraction process of the present invention;

[0043] Figure 5 Schematic diagram of the structure of the adapter signature device based on finite fields of the present invention. DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0045] like Figure 1-Figure 2 As shown, the present invention proposes an adapter signature method based on a finite field, the method comprising:

[0046] Step S1: A second user obtains the public information of a first user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information;

[0047] Step S2: The first user verifies the pre-signature. If the verification is successful, the pre-signature is adapted to a formal signature.

[0048] Step S3: The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature; the extracted candidate difficult relationship evidence of the first user is verified. If the verification passes, it is determined that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the official signature confirms that the first user has signed the object to be signed.

[0049] In the present invention, if the verification is successful, it is determined that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the official signature confirms that the first user has signed the object to be signed, thereby ensuring the authenticity and non-repudiation of the official signature.

[0050] In step S1, the second user obtains the public information of the first user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information, including:

[0051] Step S11: The second user obtains the object to be signed and generates a private key x B and public key Where g is a finite field The generator on , p is a prime number of length 2048 bits, x for g B Power, for Modulo p; obtain the message M to be signed sent by the first user; select a random number k and calculate the temporary public key K = g k (mod p), g k is the kth power of g, g k (mod p) is g k Modulo p; calculate the hash value e=h(M) of the message to be signed M, where h(·) is a hash function using the SM3 algorithm, and calculate r=f(K||Y||M) through the key derivation function f(·), where K, Y, and M are the temporary public key, the public hard relation of the first user, and the message to be signed, respectively, and || is a connection symbol indicating string concatenation; the object to be signed is an electronic contract or data to be encrypted, and Y=g y (mod p), y is the difficult relationship evidence of the first user, g y is g to the power of y, g y (mod p) is g y module p;

[0052] Step S12: The second user generates a pre-signature And the pre-signed value Sent to the first user; wherein, ex B The hash value e and the second user's private key x B The product of kr is the product of random number k and r, ex B -kr(mod p-1) is (ex B -kr) modulo p-1.

[0053] The step S2: the first user verifies the pre-signature, and after the verification is passed, adapts the pre-signature to a formal signature, including:

[0054] The first user obtains the pre-signature Calculate separately in, is the value calculated in the pre-signature, indicating g Power, K r is the rth power of the temporary public key K, X e is the second user's public key X to the power of e, X e (mod p) is X e module p;

[0055] if Equal to X e (mod p), the verification is successful, and the first user uses the difficult relationship evidence y, which is calculated by the following formula:

[0056]

[0057] Adapt the pre-signature to the formal signature (S, K), y -1 is the inverse element of the difficult relation evidence y, for Modulo p-1.

[0058] In the present invention, K r Used to ensure the randomness and uniqueness of the signature generation process, Used to confirm the validity of the signature during the verification process, X e Used to verify the validity of the signature.

[0059] The step S3: the second user obtains the official signature, extracts the candidate difficult relationship evidence of the first user from the official signature; verifies the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determines that the candidate difficult relationship evidence is the same as the difficult relationship evidence, including:

[0060] The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature. The extraction formula is as follows:

[0061]

[0062] Among them, y′ is the candidate difficult relation evidence, S -1 is the inverse element of the formal signature S, for modulo p-1;

[0063] Verify the extracted candidate difficult relationship evidence of the first user and calculate g y′ and Y(modp), where g y′ is g raised to the power of y′, and Y(mod p) is Y modulo p;

[0064] If g y′ If it is equal to Y(mod p), the verification is successful;

[0065] If the verification is successful, it is determined that y′ is the same as the difficult relationship evidence.

[0066] Furthermore, the difficult relationship evidence y is associated with the identity information of the first user, such as the private key, cryptographic certificate, biometric data, etc. of the first user.

[0067] The present invention introduces a random number k when generating a pre-signature and ensures that k≠0, avoiding the generation of an invalid temporary public key K=1, effectively improving the uniqueness and anti-attack properties of the signature and avoiding replay attacks; using the national cryptographic algorithm SM3 as a hash function, combined with the key derivation function f(K||Y||M), improves the randomness and anti-collision properties of the pre-signature, ensuring the high security of the signature generation process. The extraction algorithm can safely extract the first user's difficult relationship evidence y from the formal signature (S, K), and confirm the legitimacy of the signature through verification, thereby enhancing the traceability and verification validity of the signature; the formal signature contains the first user's difficult relationship evidence y to ensure that the signature is non-repudiable, making it impossible for the signer to deny participating in the signing, thereby enhancing the legal effect of the signature; the adaptive signature is implemented based on the first user's difficult relationship evidence y, so even if an attacker obtains the pre-signature It is also impossible to generate a legal formal signature without y, ensuring the security of the adaptation process, and guaranteeing the unforgeability and non-repudiation of the signature by binding the difficult relationship evidence with the user identity.

[0068] The present invention is based on finite fields The public key cryptosystem based on the discrete logarithm problem is used to ensure the security of the signature scheme. A 2048-bit prime number p and a generator g are used to construct a public-private key pair, and signature generation and verification are performed based on this.

[0069] The present invention designs four main algorithms, namely pre-signature generation algorithm, pre-signature verification algorithm, adaptation algorithm and extraction algorithm.

[0070] The present invention uses the SM3 hash function and the key derivation function f(·) to ensure the anti-collision and randomness of the signature.

[0071] The present invention provides an embodiment of an adapter signature method based on a finite field.

[0072] System initialization

[0073] In the adapter signature scheme of the present invention, the system initialization phase is used to generate the user's public-private key pair and difficulty relationship evidence, providing a basis for subsequent signature generation and verification.

[0074] The second user's private key and public key are generated: the second user randomly selects a private key x B , by calculating Get the public key X of the second user, where g is a finite field The generator of X is public and is used by the first user and other verification parties, while x B It is private and used only for signature generation.

[0075] User 1's difficult relationship evidence generation: The first user randomly selects a difficult relationship evidence y for the signature adaptation process and calculates the public difficult relationship Y = g y (mod p), the first user discloses Y to the second user, but retains y as private information for subsequent signature adaptation and verification processes.

[0076] Pre-signature generation

[0077] The second user generates a pre-signature: The second user receives the first user's public difficulty relationship Y and the message to be signed M∈{0,1} * , randomly select a temporary key k to enhance the randomness and uniqueness of the pre-signature, and calculate the corresponding temporary public key K = g k (mod p). Calculate the hash value e = h(M) of the message M, where h(·) is the SM3 hash function, ensuring the message's collision resistance. Calculate the derived value r using the key derivation function f(K||Y||M), which combines the temporary public key K, the difficulty relation Y, and the message M to ensure the randomness and unpredictability of the generated derived value. Use the private key x of the second user. B And the calculated e and r, generate a pre-signature

[0078]

[0079] The second user will generate a pre-signed Sent to the first user as the pre-signed value Value_PreSign for subsequent verification and adaptation operations by the first user.

[0080] Pre-signature verification

[0081] The first user verifies the second user's pre-signature: the first user receives the pre-signature value sent by the second user To ensure that the message sent by the second user has not been tampered with, the first user verifies the message using the verification algorithm Verify and calculates the hash value e′=h(M) of the message M, where h(·) is the hash function selected by the second user. Calculate r′=f(K||Y||M) to ensure that the derived value during verification is consistent with that of the second user, preventing the pre-signature from being tampered with during transmission. The first user uses the public key of the second user Verify that the pre-signature satisfies the following equation:

[0082]

[0083] If the verification passes (i.e. the equation holds true), the first user receives the signature and outputs true; otherwise, the first user outputs false and rejects the pre-signature.

[0084] Signature Adaptation

[0085] After the first user verifies the second user's pre-signature, the first user can convert the pre-signature into a formal signature through an adaptation algorithm. The adaptation process relies on the difficult relationship evidence y held by the first user.

[0086] The first user converts the pre-signature into a formal signature: After verifying the legitimacy of the pre-signature, the first user uses his own difficult relationship evidence y and the pre-signature The pre-signed Adapt to S:

[0087]

[0088] where y -1 This is the inverse of the first user's difficult relationship evidence y modulo p-1, ensuring that only the first user can convert the pre-signature into a valid official signature. After outputting the official signature (S, K), namely Value_Sign, it is sent to the second user. At this point, the second user can verify the signature and extract the first user's difficult relationship evidence y using the extraction algorithm.

[0089] Difficult Relationship Evidence Extraction

[0090] The second user extracts the difficult relationship evidence from the formal signature: the second user receives the first user's formal signature (S, K), pre-signature and the open difficult relationship Y=g y After (modp), the validity of the signature is verified by the extraction algorithm, and the first user's difficult relationship evidence y is tried to be extracted from the signature. The second user uses the pre-signed And the official signature S is calculated as follows:

[0091]

[0092] In order to verify the legitimacy of the extracted y′, the second user verifies whether y′ satisfies:

[0093] g y′ =Y(modp)

[0094] If the verification succeeds, the second user confirms that y′ is a valid difficult relationship evidence y, confirms that the signature is legal, and outputs the extraction result y′; if the verification fails, the second user extracts the failure symbol ⊥.

[0095] Security Analysis

[0096] The adapter signature scheme of the present invention ensures the signature's unforgeability, adaptability, extractability, and non-repudiation through a multi-layered security design:

[0097] Unforgeability: Since signature generation depends on the private key x of the second user B , random number k and the first user's difficult relationship evidence y. Without knowing these parameters, the adversary cannot forge a valid signature.

[0098] Adaptability: The signature adaptation process completely relies on the first user’s difficult relationship evidence y, ensuring that only users who possess this difficult relationship evidence can convert the pre-signature into a formal signature.

[0099] Extractability: The formal signature contains the first user’s hard relationship evidence y. The second user can securely extract the hard relationship evidence through an extraction algorithm and verify the legitimacy of the signature.

[0100] Non-repudiation: Since the generation of the formal signature depends on the first user’s difficult relationship evidence y, and the extraction algorithm can extract this evidence from the signature, it ensures that the first user cannot deny his participation in the signing process.

[0101] Through this multi-level design of signature generation, verification, adaptation, and extraction, the present invention provides a highly secure and adaptable signature scheme, which is particularly suitable for application scenarios with high security requirements such as blockchain, electronic contracts, and digital currencies.

[0102] The present invention also provides an adapter signature device based on a finite field, the device comprising:

[0103] The device comprises:

[0104] Pre-signature module: configured to obtain the public information of the first user for the second user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information;

[0105] Adaptation module: configured to verify the pre-signature for the first user, and adapt the pre-signature to a formal signature after the verification is successful;

[0106] Verification module: configured to obtain the formal signature for the second user, extract the candidate difficult relationship evidence of the first user from the formal signature; verify the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determine that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the formal signature confirms that the first user has signed the object to be signed.

[0107] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A finite field-based adapter signature method, characterized in that: The method comprises: Step S1: A second user obtains the public information of a first user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information, including: Step S11: The second user obtains the object to be signed and generates a private key x B and public key Where g is a finite field The generator on , p is a prime number of length 2048 bits, x for g B Power, for Modulo p; obtain the message M to be signed sent by the first user; select a random number k and calculate the temporary public key K = g k (modp), g k is the kth power of g, g k (mod p) is g k Modulo p; calculate the hash value e=h(M) of the message to be signed M, where h(·) is a hash function using the SM3 algorithm, and calculate r=f(K‖Y‖M) through the key derivation function f(·), where K, Y, and M are the temporary public key, the public difficulty relationship of the first user, and the message to be signed, respectively, || is a connection symbol indicating string concatenation, and r is the calculation result; the object to be signed is an electronic contract or data to be encrypted, and Y=g y (mod p), y is the difficult relationship evidence of the first user, g y is g to the power of y, g y (mod p) is gy modulo p; Step S12: The second user generates a pre-signature And the pre-signed value Sent to the first user; wherein, ex B The hash value e and the second user's private key x B The product of kr is the product of random number k and r, ex B -kr(mod p-1) is (ex B -kr) modulo p-1; Step S2: The first user verifies the pre-signature. If the verification is successful, the pre-signature is adapted to a formal signature. Step S3: The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature; the extracted candidate difficult relationship evidence of the first user is verified. If the verification passes, it is determined that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the official signature confirms that the first user has signed the object to be signed.

2. The method according to claim 1, wherein The step S2: the first user verifies the pre-signature, and after the verification is passed, adapts the pre-signature to a formal signature, including: The first user obtains the pre-signature Calculate separately and X e (mod p); where is the value calculated in the pre-signature, indicating g Power, K r is the rth power of the temporary public key K, X e is the second user's public key X to the power of e, X e (mod p) is X e module p; if Equal to X e (mod p), the verification is successful, and the first user uses the difficult relationship evidence y, which is calculated by the following formula: Adapt the pre-signature to the formal signature (S, K), y -1 is the inverse element of y, for Modulo p-1.

3. The method according to claim 1, wherein The step S3: the second user obtains the official signature, extracts the candidate difficult relationship evidence of the first user from the official signature; verifies the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determines that the candidate difficult relationship evidence is the same as the difficult relationship evidence, including: The second user obtains the official signature and extracts the candidate difficult relationship evidence of the first user from the official signature. The extraction formula is as follows: Among them, y′ is the candidate difficult relation evidence, S -1 is the inverse element of the formal signature S, for modulo p-1; Verify the extracted candidate difficult relationship evidence of the first user and calculate g y′ and Y(mod p), where g y′ is g raised to the power of y′, and Y(mod p) is Y modulo p; If g y′ If it is equal to Y(mod p), the verification is successful; If the verification is successful, it is determined that y′ is the same as the difficult relationship evidence.

4. The method according to any one of claims 1 to 3, wherein The difficult relationship evidence y is associated with the identity information of the first user and is one of the private key, cryptographic certificate, and biometric feature of the first user.

5. An adapter signature device based on a finite field, characterized in that: The device comprises: Pre-signature module: configured to obtain the public information of the first user for the second user, where the first user is the user who signs the object to be signed; the second user generates a pre-signature based on its own private key and the public information, including: Step S11: The second user obtains the object to be signed and generates a private key x B and public key Where g is a finite field The generator on , p is a prime number of length 2048 bits, x for g B Power, for Modulo p; obtain the message M to be signed sent by the first user; select a random number k and calculate the temporary public key K = g k (modp), g k is the kth power of g, g k (mod p) is g k Modulo p; calculate the hash value e=h(M) of the message to be signed M, where h(·) is a hash function using the SM3 algorithm, and calculate r=f(K‖Y‖M) through the key derivation function f(·), where K, Y, and M are the temporary public key, the public difficulty relationship of the first user, and the message to be signed, respectively, || is a connection symbol indicating string concatenation, and r is the calculation result; the object to be signed is an electronic contract or data to be encrypted, and Y=g y (mod p), y is the difficult relationship evidence of the first user, g y is g to the power of y, g y (mod p) is g y module p; Step S12: The second user generates a pre-signature And the pre-signed value Sent to the first user; wherein, ex B The hash value e and the second user's private key x B The product of kr is the product of random number k and r, ex B -kr(mod p-1) is (ex B -kr) modulo p-1; Adaptation module: configured to verify the pre-signature for the first user, and adapt the pre-signature to a formal signature after the verification is successful; Verification module: configured to obtain the formal signature for the second user, extract the candidate difficult relationship evidence of the first user from the formal signature; verify the extracted candidate difficult relationship evidence of the first user, and if the verification passes, determine that the candidate difficult relationship evidence is the same as the difficult relationship evidence, that is, the formal signature confirms that the first user has signed the object to be signed.

6. A computer-readable storage medium, characterized in that The storage medium stores a plurality of instructions; the plurality of instructions are used by a processor to load and execute the method according to any one of claims 1 to 4.

7. An electronic device, characterized in that: The electronic device comprises: A processor, which is used to execute multiple instructions; A memory for storing a plurality of instructions; The plurality of instructions are used to be stored in the memory and loaded and executed by the processor according to any one of claims 1 to 4.

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