Data verification method and system based on non-interactive zero-knowledge proof construction

Abstract

The invention provides a data verification method and system based on non-interactive zero-knowledge proof construction, and relates to the technical field of information security, and the method comprises the steps: carrying out the initialization of a zk-SNARKs protocol for verification data, carrying out the coding of an evaluation value of a polynomial at a certain point through employing an on-ring security coding algorithm, generating a public reference character string and a verification key, and carrying out the verification of the public reference character string and the verification key. Constructing a QRP problem about the calculation task; based on the common reference character string, generating a proof for the satisfiability of the on-ring arithmetic circuit corresponding to the executed calculation; coding content in the generated proof is decoded by using a secret key in the verification key in combination with a decoding algorithm, and the validity of data in the received proof and the exact division relationship of a polynomial in a QRP problem corresponding to a calculation task are verified on a plaintext, so that the correctness of data calculation is verified; and meanwhile, the time required for executing the verification algorithm is shorter than the time required for re-executing the calculation task.

Description

Technical Field

[0001] The present disclosure relates to the field of information security technology, and in particular to a data verification method and system based on a non-interactive zero-knowledge proof structure. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] In recent years, with the development of emerging technologies such as blockchain and cryptocurrency and the rise of privacy computing needs, zero-knowledge proof technology has once again become the focus of attention in related industries such as financial technology and big data. For example, in cross-border transactions, users want to hide transaction details while still being able to prove the legitimacy of the transaction; in smart contracts, it is necessary to verify the correctness of contract execution while not exposing private data during the execution process.

[0004] Zero-knowledge proof technology provides a secure way to verify the authenticity of information, allowing users to verify their identities without revealing sensitive information and preventing fraud. Some zero-knowledge proof schemes, such as zk-SNARKs and zk-STARKs, can prove the correctness of the calculations without revealing sensitive data, and the proof length is short, and the verification time is much less than the time required to re-execute the original calculation. Therefore, zero-knowledge proof technology allows users to delegate calculations to untrusted servers, such as cloud servers, thereby solving problems such as outsourcing of computing tasks and scalability of centralized ledgers when computing resources and storage space are limited. This provides an innovative solution for protecting privacy and improving security, and is currently showing great potential and value in practical applications.

[0005] The main contents and existing problems of the current scheme are as follows: 1) Existing SNARK structures usually assume that the computation to be proved can be effectively expressed as an arithmetic circuit over a finite field, which is further expressed as a field arithmetic circuit satisfiability problem. The computation is performed over a prime field. This is not universal enough in proving computations on encrypted data such as BGV ciphertext or proving arithmetic operations under a standard CPU architecture in reality, because simulating arithmetic on a ring in a finite field operating environment will significantly increase the overhead; 2) Data in many practical problems naturally exist in ring structures, such as polynomial operations, integer operations, etc. At the same time, the widely used zk-SNARKs schemes, such as Pinocchio, Groth16 and other publicly verifiable schemes, usually use bilinear pairing for verification in the verification algorithm, and bilinear pairing usually involves complex mathematical calculations, including large integer multiplication and modular operations, and the pairing calculation is relatively slow, especially when multiple pairings are required.

[0006] 3) The NTRU-GSW homomorphic encryption scheme is a NTRU-based GSW-like homomorphic scheme constructed based on the NTRU problem and the GSW (Gentry-Sahai-Waters) scheme, which combines the advantages of both. NTRU encryption is based on the NTRU lattice problem, which involves solving the short vector problem on a polynomial ring. To generalize the domain-restricted non-interactive zero-knowledge proof scheme to the ring, it is necessary to find a secure encoding scheme on the ring that is compatible with the ciphertext space of the underlying homomorphic encryption scheme. The NTRU-GSW homomorphic encryption scheme provides an idea for this. Summary of the invention

[0007] In order to solve the above problems, the present disclosure proposes a data verification method and system based on non-interactive zero-knowledge proof construction, generalizes the domain-restricted zk-SNARK scheme to the ring, executes the zero-knowledge proof protocol on encrypted data, and proposes a concise non-interactive zero-knowledge proof construction method for designated verifiers based on NTRU-GSW homomorphic encryption, which does not require data to be converted to a finite field and can verify complex computational relationships and mathematical propositions without leaking the original data.

[0008] According to some embodiments, the present disclosure adopts the following technical solutions: The data verification method based on non-interactive zero-knowledge proof construction includes: For the verification data, the zk-SNARKs protocol is initialized, the evaluation of the polynomial at a certain point is encoded using the ring-based secure coding algorithm, a public reference string and a verification key are generated, and a QRP problem about the computing task is constructed; Generate a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed, based on the public reference string; The secret key in the verification key is used in combination with the decoding algorithm to decode the encoded content in the generated proof, and the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task are verified in plain text, thereby verifying the correctness of the data calculation and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

[0009] According to some embodiments, the present disclosure adopts the following technical solutions: The data verification system based on non-interactive zero-knowledge proof construction includes: The initialization setting module is used to initialize the zk-SNARKs protocol for verification data, encode the evaluation of the polynomial at a certain point using the ring-based secure coding algorithm, generate a public reference string and verification key, and construct a QRP problem about the computing task; a proof generation module for generating a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed based on the public reference string; The verification module is used to use the secret key in the verification key in combination with the decoding algorithm to decode the encoded content in the generated proof, verify the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task in plain text, thereby verifying the correctness of the data calculation, and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

[0010] According to some embodiments, the present disclosure adopts the following technical solutions: A computer program product includes a computer program, and when the computer program is executed by a processor, the data verification method based on non-interactive zero-knowledge proof construction is implemented.

[0011] According to some embodiments, the present disclosure adopts the following technical solutions: A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the data verification method based on non-interactive zero-knowledge proof construction is implemented.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions: An electronic device comprises: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the data verification method based on the non-interactive zero-knowledge proof construction.

[0013] Compared with the prior art, the present invention has the following beneficial effects: The data verification method based on non-interactive zero-knowledge proof construction disclosed in the present invention can provide verifiable calculations on encrypted data. Users with weak computing power can share their data with staff in the form of plain text or ciphertext and outsource the computing tasks to the staff. The staff can be a powerful server or cloud platform. The staff uses this solution to provide proof. The user as a verifier can quickly verify the correctness of the calculation. At the same time, the workload required for verification is significantly less than the workload of directly running the computing task. If the data provided by the user is FHE ciphertext data, such as BGV ciphertext, the original data can be better hidden.

[0014] The disclosed data verification method based on non-interactive zero-knowledge proof construction is statistically zero-knowledge. No one except the prover and verifier can obtain valid information from the proof, which can effectively protect the user's data privacy. It can resist the attack of quantum computers. The disclosed encoding method is based on NTRU-GSW homomorphic encryption, and its security is based on the NTRU lattice problem. Compared with encryption or encoding schemes based on traditional mathematical problems, the encoding scheme based on difficult problems on the lattice still maintains high security when quantum computers appear.

[0015] The data verification method based on non-interactive zero-knowledge proof construction disclosed in the present invention provides a new type of concise non-interactive zero-knowledge proof scheme for designated verifiers. Based on this design, the verification time of zk-SNARK is effectively reduced. The polynomial encoding scheme is designed using NTRU-GSW homomorphic encryption. Compared with the use of bilinear pairing or JL encryption scheme, the encoding scheme of this scheme is based on the lattice difficulty problem and has stronger security, especially in the face of quantum computing attacks.

[0016] The data verification method based on non-interactive zero-knowledge proof construction disclosed in the present invention combines FHE and zk-SNARKs technologies, and uses the zk-SNARKs protocol on a ring to perform efficient zero-knowledge proof on encrypted data without converting the data to a finite field. At the same time, complex computational relationships and mathematical propositions can be verified without leaking the original data. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0018] Figure 1 A schematic diagram of an initialization setting algorithm of an embodiment of the present disclosure; Figure 2 A schematic diagram of a proof generation algorithm for an embodiment of the present disclosure; Figure 3 A schematic diagram of a verification algorithm according to an embodiment of the present disclosure; Figure 4 The figure is an overall framework diagram of the method of the embodiment of the present disclosure. DETAILED DESCRIPTION

[0019] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0020] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0021] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0022] Example 1 In one embodiment of the present disclosure, a data verification method based on a non-interactive zero-knowledge proof construction is provided, comprising: Step 1: Initialize the zk-SNARKs protocol for the verification data, use the ring-based secure coding algorithm to encode the evaluation of the polynomial at a certain point, generate a public reference string and a verification key, and construct a QRP problem about the computing task; Step 2: Generate a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed, based on the public reference string; Step 3: Use the secret key in the verification key in combination with the decoding algorithm to decode the encoded content in the generated proof, verify the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task in plain text, thereby verifying the correctness of the data calculation, while ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

[0023] As an embodiment, the present invention discloses a data verification method based on non-interactive zero-knowledge proof construction, including a linear homomorphic ring secure encoding algorithm, an initialization setting algorithm, a proof generation algorithm, and a verification algorithm; the secure encoding algorithm is used to encode data on the ring for use in the subsequent zk-SNARKs protocol; the initialization setting algorithm is used by the verifier to initialize the protocol, construct a QRP problem about the computing task and call the encoding algorithm to generate a public reference string and a verification key; the proof generation algorithm is used by the prover to generate a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the performed calculation, and the proof is used by the verifier to verify that the prover has correctly performed the calculation, and the given proof is short; the verification algorithm is used to verify the proof of the correctness of the calculation provided by the prover, and the time required to execute the verification algorithm is much less than the time required to re-execute the computing task, wherein the linear homomorphic ring secure encoding method is implemented by the NTRU-GSW homomorphic encryption scheme, and the key generation, encoding, and decoding algorithms of the linear homomorphic ring secure encoding algorithm are respectively The specific implementation process of the disclosed method is as follows: Step 1: Initialize the zk-SNARKs protocol for the verification data, use the ring-based secure coding algorithm to encode the evaluation of the polynomial at a certain point, generate a public reference string and a verification key, and construct a QRP problem about the computing task; Specifically, the verifier executes the initialization setup algorithm and generates a secret key according to the key generation algorithm in the secure encoding algorithm. , and generate challenge points and the desired random parameters; Using a linear homomorphic ring polynomial secure encoding algorithm based on NTRU-GSW homomorphic encryption design, The power of the QRP polynomial obtained by the calculation task conversion at the challenge point s, the evaluation of the polynomial at the challenge point s after multiplying the polynomial with the random parameter as the offset, and the evaluation of the linear combination of the polynomial at the challenge point s are encoded as a public reference string ; Furthermore, we construct the QRP problem about the computational task. The method of reducing the computational task on the ring to the QRP polynomial is similar to the method of reducing the task on the field to the QAP polynomial. Both are expressed as arithmetic circuits first, and then the R1CS circuit constraints are obtained, that is, the assignment vectors of all variables and the multidimensional vectors about the circuit structure are obtained, and then the polynomial is obtained by interpolation. The QRP polynomial is the form of the combination of the assignment vector and the polynomial; the secret key , Public Reference String , challenge point s and random parameters together form the verification password. The verification key is private to the verifier and is used in the verification phase. Figure 1 As shown, the above process is specifically implemented as follows: Step A1.1: The verifier calls the key generation algorithm in the linear homomorphic encoding algorithm to generate a secret key ,exist Randomly select challenge points ,exist Randomly select parameters ,set up ,exist Randomly select parameters ; ring is a commutative ring with one. All reversible elements on , exception set satisfy ; Step A1.2: Ring Computational tasks on Can be expressed as Inputs, Output ring Arithmetic circuits on , for arithmetic circuits The processing method is similar to the classic zk-SNARKs scheme. The verifier can convert the circuit constraints into loops based on the R1CS circuit constraint system and Lagrange interpolation. The QRP polynomial constraint on and a target polynomial , these polynomials are rings For the elements in the circuit, the verifier can only obtain the input and output values ​​of the circuit in the variable assignment vector, but cannot know the values ​​of the intermediate variables in the circuit; The validator uses an encoding algorithm right The power of , the evaluation of the polynomial at s, the evaluation of the polynomial at s after multiplying it with a random parameter as an offset, and the evaluation of the linear combination of the polynomials at s are encoded to obtain:

[0024]

[0025]

[0026]

[0027]

[0028] These coded values ​​form the common reference string ; in, It represents the subscript set of the variables controlled by the prover, that is, the subscript set of the intermediate variables. The linear homomorphic encoding algorithm for polynomials on the ring designed based on the NTRU-based GSW-like homomorphic encryption scheme uses parameters To describe, yes The dimension of and are the modulus of plaintext and ciphertext respectively, is the standard deviation of the key: : Select ,set up until Exists in ,Right now To be in Reversible, output ; : Given and polynomial , select ,set up ,calculate ,return The encrypted value c is used as the encoded value; :calculate , and are very short polynomials, the noise in the ciphertext is small enough, and the plaintext By scaling and rounding Extract and calculate , output As the decrypted plaintext ; Step A1.3: Validator Public , and the challenge point ,parameter{ }、 , Private Key Together they form the validator's private verification key ; Step 2: Based on the public reference string, generate a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the performed computation, including: in the proof generation phase, the prover uses the valid assignments of the circuit inputs, outputs, and intermediate variables, and linearly homomorphically calculates the encoding of the linear combination of polynomials, and repeatedly calculates the encoding when random parameters are used as offsets, thereby providing reliability for the proof; The prover will calculate the code (the code in step A2.5 below) ), with the offset encoding (step A2.6 below) and in step A2.7 ), the encoding of the quotient polynomial at the challenge point s and its encoding with offset As evidence, it constitutes a proof, and sends the result of correctly executing the calculation task to the verifier. The verifier can confirm the correctness of the calculation performed by the prover based on the verification algorithm, and thus believe the calculation result; Figure 2 The specific implementation process is as follows: Step A2.1: The prover performs a computation based on the input specified by the verifier (i.e., the client). Perform calculations to obtain the output results of the calculation tasks; Step A2.2: The expression is Inputs, Output loop arithmetic circuit , the prover can obtain the value of the intermediate variable in addition to the input and output values ​​according to the calculation performed, that is, the prover has a set of input / output values , and the prover knows a set of intermediate variable values satisfy Divisible , that is, the corresponding arithmetic circuit satisfiability holds; in, , which can be regarded as ; Step A2.3: The prover uses all known variable values ,calculate , and then calculate the quotient polynomial , the existence of the quotient polynomial indicates the existence of the polynomial divisibility relation; Step A2.4: The prover uses a re-randomization technique to provide zero-knowledge for the scheme, i.e. the prover randomly selects parameters Used for blinding of polynomials; Step A2.5: The prover The encoding of the polynomial evaluated at point s in the code is used to calculate the blinded polynomial encoding value using the linear homomorphism property of the coding scheme , and calculate the quotient polynomial Blind The code at point s ; in, ; Step A2.6: The prover In the case where a random parameter is used as an offset, the prover crs For random parameters As the case of the offset, calculate the same as step A2.5 In a similar way, the code with offset is obtained by repeating the calculation : , because through The use of offsets can force the prover to use the The code value at the point, using different Ensure that the operands of multivariate polynomials are not interchangeable; Step A2.7: The prover uses Ensure consistency across operand variables, according to Computes linear combinations of polynomials Blinded code ,in, ; Step A2.8: The prover generates a short proof ; Step 3: Use the secret key in the verification key combined with the decoding algorithm to decode the encoded content in the generated proof, verify the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task on the plain text, thereby verifying the correctness of the data calculation, and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task, including: During the verification phase, the verifier uses the secret key Proof Decode and combine the calculation input part controlled by itself and the calculation output result received to assemble the complete QRP polynomial, verify that the polynomial divisibility relation holds, and thus prove that the arithmetic circuit on the ring can be satisfied, that is, the calculation task is correctly executed; In addition, the verifier needs to verify the offset relationship of the decoded polynomial to ensure that the proof The polynomial encoded in is correctly generated by the prover at the challenge point s, not forged, that is, the proof The data in is valid, such as Figure 3 The specific implementation process is as follows: Step A3.1: Verifier’s proof to the prover , calling the decoding algorithm of the encoding algorithm ,right Decrypted ; Step A3.2: The verifier calculates the polynomial combination corresponding to the part of the variables it knows or can control, that is, the subscript It means to verify the polynomial linear combination of the known input variables and output variables: , and use The decrypted value is used to calculate and ; Step A3.3: Verification Whether the offset is valid, thereby checking the Correctness: ; Here Take the example to explain the correctness of verification. The other 5 verification equations in the verification algorithm are similar. According to The coded value given in: ,in are random polynomials selected in the encoding algorithm, and the prover can calculate , the verifier based on And the decoding algorithm and Decode and get , so for a valid proof, Will verify passed; Step A3.4: The verifier verifies whether the offset of the linear combination of polynomials holds: , thus ensuring consistency across operand variables; Step A3.5: The verifier verifies whether the quotient polynomial is correct: , thereby verifying the correctness of the prover's calculation.

[0029] Example 2 In one embodiment of the present disclosure, a data verification system based on a non-interactive zero-knowledge proof structure is provided, comprising: The initialization setting module is used to initialize the zk-SNARKs protocol for verification data, encode the evaluation of the polynomial at a certain point using the ring-based secure coding algorithm, generate a public reference string and verification key, and construct a QRP problem about the computing task; a proof generation module for generating a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed based on the public reference string; The verification module is used to use the secret key in the verification key in combination with the decoding algorithm to decode the encoded content in the generated proof, verify the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task in plain text, thereby verifying the correctness of the data calculation, and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

[0030] Example 3 In one embodiment of the present disclosure, a computer program product is provided, characterized in that when the computer program is executed by a processor, the data verification method based on the non-interactive zero-knowledge proof construction is implemented.

[0031] Example 4 In one embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the data verification method based on the non-interactive zero-knowledge proof construction is implemented.

[0032] Example 5 In one embodiment of the present disclosure, an electronic device is provided, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the data verification method based on the non-interactive zero-knowledge proof construction.

[0033] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0034] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0035] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A data verification method based on non-interactive zero-knowledge proof construction, characterized in that: include: For the verification data, the zk-SNARKs protocol is initialized, the evaluation of the polynomial at a certain point is encoded using the ring-based secure coding algorithm, a public reference string and a verification key are generated, and a QRP problem about the computing task is constructed; Generate a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed, based on the public reference string; The secret key in the verification key is used in combination with the decoding algorithm to decode the encoded content in the generated proof, and the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task are verified in plain text, thereby verifying the correctness of the data calculation and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

2. The data verification method based on non-interactive zero-knowledge proof construction as claimed in claim 1, characterized in that: Initialize the zk-SNARKs protocol, including: the verifier executes the initialization setting algorithm, uses the linear homomorphic ring polynomial security encoding algorithm based on NTRU-GSW homomorphic encryption design, and encodes the power of the challenge point, the evaluation of the QRP polynomial obtained by computing the task conversion at the challenge point, the evaluation of the polynomial multiplied by the random parameter as the offset at the challenge point, and the evaluation of the linear combination of the polynomial at the challenge point as a public reference string.

3. The data verification method based on non-interactive zero-knowledge proof construction as claimed in claim 1, characterized in that: Constructing the QRP problem about the computing task, including: reducing the computing task on the ring to the QRP polynomial, expressing the computing task on the ring as an arithmetic circuit, obtaining the R1CS circuit constraint, that is, obtaining the assignment vector of all variables and the multidimensional vector about the circuit structure, and further obtaining the polynomial by interpolation. The QAP polynomial is the form of the combination of the assignment vector and the polynomial; the secret key, the public reference string, the challenge point and the random parameters together constitute the verification key, which is private to the verifier and used in the verification phase.

4. The data verification method based on non-interactive zero-knowledge proof construction as claimed in claim 1, characterized in that: Based on the public reference string and the encoding result, a proof is generated for the satisfiability of the arithmetic circuit on the ring corresponding to the performed calculation, including: in the proof generation stage, the prover uses the valid assignment of circuit input, output and intermediate variables and the public reference string to linearly homomorphically calculate the encoding of the linear combination of polynomials, and uses random parameters as offsets to repeatedly calculate the encoding with offsets. The prover uses the calculated encoding, the encoding with offsets, and the encoding of the quotient polynomial at the challenge point as evidence to form a proof.

5. The data verification method based on non-interactive zero-knowledge proof construction as claimed in claim 1, characterized in that: The verifier uses the secret key to decode the proof, and combines the computational input part controlled by itself and the computational output result received to assemble a complete QRP polynomial, verifying that the polynomial divisibility relation holds, thereby proving that the arithmetic circuit on the ring is satisfied, that is, the computational task is executed correctly.

6. The data verification method based on non-interactive zero-knowledge proof construction as claimed in claim 5, characterized in that: The verifier also needs to verify the offset relationship of the decoded polynomial to ensure that the polynomial value encoded in the proof is correctly generated by the prover at the challenge point, or that the data in the proof is valid.

7. A data verification system based on non-interactive zero-knowledge proof, characterized in that: include: The initialization setting module is used to initialize the zk-SNARKs protocol for verification data, encode the evaluation of the polynomial at a certain point using the ring-based secure coding algorithm, generate a public reference string and verification key, and construct a QRP problem about the computing task; a proof generation module for generating a proof for the satisfiability of the arithmetic circuit on the ring corresponding to the computation performed based on the public reference string; The verification module is used to use the secret key in the verification key in combination with the decoding algorithm to decode the encoded content in the generated proof, verify the validity of the data in the received proof and the divisibility relationship of the polynomial in the QRP problem corresponding to the calculation task in plain text, thereby verifying the correctness of the data calculation, and ensuring that the time required to execute the verification algorithm is less than the time required to re-execute the calculation task.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the data verification method based on non-interactive zero-knowledge proof construction described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the data verification method based on the non-interactive zero-knowledge proof construction as described in any one of claims 1-6 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the data verification method based on the non-interactive zero-knowledge proof construction as described in any one of claims 1-6.

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