PCD-based digital signature batch verification method and system

Abstract

The invention belongs to the technical field of network space security, and provides a PCD-based digital signature batch verification method and system, and the method comprises the steps: verifying the validity of an obtained digital signature, and calculating a commitment; a PCD and SNARK certification system is initialized, and a public parameter and key pair is generated; carrying out arithmetic expression on the proved calculation; and operating a PCD protocol based on arithmetic expression, operating an SNARK protocol after the PCD protocol generates a PCD proof, summarizing to generate a final proof, and performing legality verification on the final proof. According to the method, the memory friendly characteristic of the protocol carrying the proving data (PCD) is utilized for optimization, so that the expandability of the proving system can be enhanced, the proving time is greatly shortened, and meanwhile, the large-scale signature verification is supported.

Description

Technical Field

[0001] The present invention belongs to the field of cyberspace security technology, and in particular relates to a PCD-based digital signature batch verification method and system. Background Art

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

[0003] The security of the blockchain system is highly dependent on digital signature technology to ensure the authenticity of transactions and data integrity. Digital signature technology requires that all transactions must pass the node's digital signature validity check before being included in the blockchain.

[0004] However, as the scale of transactions continues to expand, the computational burden generated by the signature verification process has increased dramatically, which has directly affected the blockchain system and its expansion potential. The traditional one-by-one verification method can no longer meet the needs of large-scale transactions. Batch verification technology can effectively improve overall verification efficiency by processing multiple signatures simultaneously.

[0005] However, existing batch verification schemes have significant shortcomings: some algorithms can achieve fast signature aggregation, but their additive homomorphic nature makes them incompatible with widely adopted signature standards in blockchains, significantly limiting the number of signatures that can be processed in batches. Other algorithms, while versatile, suffer from drawbacks such as inefficient proof generation and excessive memory usage, limiting the application prospects of blockchain technology in resource-constrained environments. Summary of the Invention

[0006] In order to solve the above problems, the present invention proposes a digital signature batch verification method and system based on PCD. The present invention optimizes the memory-friendly characteristics of the Proof Data (PCD) protocol, which can enhance the scalability of the proof system, significantly reduce the proof time, and support large-scale signature verification.

[0007] According to some embodiments, the present invention adopts the following technical solutions:

[0008] A digital signature batch verification method based on PCD, comprising the following steps:

[0009] For the obtained digital signature, verify the legitimacy of the signature and calculate the commitment;

[0010] Initialize PCD and SNARK proof systems, generate public parameters and key pairs;

[0011] Arithmetically represent the computation being proved;

[0012] Based on the arithmetic representation, the PCD protocol is run. After the PCD protocol generates the PCD proof, the SNARK protocol is run to aggregate and generate the final proof, and the legitimacy of the final proof is verified.

[0013] As an optional implementation, the obtained digital signature includes a verification key, a message, and a signature.

[0014] As an optional implementation, the process of verifying the legitimacy of the signature includes the prover running a verification algorithm for each collected digital signature using its public verification key, message, and signature to determine its legitimacy, and sending all verified digital signatures to the verifier.

[0015] As an optional implementation, the process of calculating the commitment includes: the prover divides all verified digital signatures into multiple groups, constructs a tree structure, the prover applies the tree structure of the hash function to the signature information in each group, calculates the output tree root commitment value root, and uses the root as the commitment.

[0016] As an optional implementation, the process of initializing the PCD and SNARK proof systems includes: the prover and the verifier generate the public parameters required for the operation of the PCD protocol and the SNARK protocol, disclose the public parameters of the adopted hash function and commitment scheme, and the key pair generation includes the prover generating a proof key and the verifier generating a verification key.

[0017] As an optional implementation, the process of arithmetically representing the proved computation includes: representing the signature verification algorithm and the tree folding scheme verification algorithm and hash function included in the PCD as an R1CS constraint system.

[0018] As an optional embodiment, the process of running the PCD protocol includes running the PCD protocol on a tree-type PCD computation assertion to generate a PCD proof.

[0019] As an optional implementation, the process of running the SNARK protocol includes running the tree folding scheme in the PCD to obtain the SNARK assertion to be proved, and running the SNARK protocol to generate the SNARK proof.

[0020] As an optional implementation, the process of verifying the legitimacy of the final proof includes the verifier grouping all digital signatures sent by the prover according to the grouping method in the public parameters, running the same algorithm as the prover to calculate the hash value, and running the verification process. If all verification steps are passed, the verifier accepts the proof and believes that all received digital signatures are legal. Otherwise, the verifier rejects the proof.

[0021] A digital signature batch verification system based on PCD, comprising:

[0022] A preliminary verification module is configured to verify the legitimacy of the obtained digital signature and calculate the commitment;

[0023] An initialization module is configured to initialize the PCD and SNARK proof system and generate public parameters and key pairs;

[0024] an arithmetic module, configured to perform an arithmetic representation of the proved computation;

[0025] The proof module is configured to run the PCD protocol based on the arithmetic representation. After the PCD protocol generates the PCD proof, it runs the SNARK protocol to aggregate and generate the final proof.

[0026] The verification module is configured to verify the legitimacy of the final certificate.

[0027] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the steps in the above method are completed.

[0028] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps in the above method are completed.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] (1) The digital signature batch verification scheme of the present invention can enhance system scalability, reduce memory consumption, be compatible with resource-constrained computing devices, and support large-scale signature batch verification tasks. Based on an advanced tree folding scheme, the construction method of the present invention reduces the computational scale of SNARK protocol proof during the proof process. Compared with the scheme of directly applying the SNARK protocol to prove the legitimacy of all signatures, it can improve the proof efficiency, verification efficiency and scalability. The present invention provides an efficient transaction verification solution for large-scale blockchain applications.

[0031] (2) In blockchain applications, the digital signature batch verification scheme of the present invention enables the prover to gradually generate PCD proofs while receiving signatures from other nodes in the blockchain system. Traditional batch verification schemes usually need to wait until a sufficient number of legitimate signatures are collected before starting to generate proofs. The present invention utilizes the recursive nature of PCD to convert the idle waiting time into effective computing resources. This optimization strategy not only optimizes system resource allocation but also significantly reduces the time consumption of the block verification process; this advantage makes the scheme of great value in high-performance blockchain networks.

[0032] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0034] Figure 1 Flowchart of the PCD-based digital signature batch verification method according to an embodiment of the present invention;

[0035] Figure 2 Schematic diagram of PCD calculation assertion in an embodiment of the present invention;

[0036] Figure 3 Schematic diagram of the PCD protocol certification method described in an embodiment of the present invention;

[0037] Figure 4 Schematic diagram of generating proof and verifying proof according to an embodiment of the present invention;

[0038] Figure 5 Schematic diagram of a PCD-based digital signature batch verification system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0040] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0041] 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 invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0042] In the absence of conflict, the embodiments and features in the embodiments of this application can be combined with each other.

[0043] Example 1:

[0044] The purpose of this embodiment is to provide a digital signature batch verification method based on PCD, such as Figure 1 and Figure 4 As shown, the specific process includes the following:

[0045] S101: The prover collects digital signatures and verifies the validity of the signatures.

[0046] Each collected digital signature contains the verification key pk, the message m, and the signature σ. Specifically, the prover runs the verification algorithm Verify(pk,m,σ) for each collected digital signature to determine its legitimacy. Finally, all the N digital signatures that have passed verification (sig=(pk,m,σ)) are sent to the verifier. The prover groups all the digital signatures that have passed verification into groups of The parameter b represents the number of signatures contained in each group. The PCD protocol processes one group at each step. The function V represents the signature verification algorithm Verify(pk,m,σ), so n is the number of nodes in the tree structure of the PCD assertion. For each i∈[n], V(sig i )=1 indicates signature sig i legitimate.

[0047] Further, combined with Figure 2 The prover applies a Merkle-Tree (variant) structure of a hash function to the signature information in each group and calculates the output tree root commitment value root. Let H represent the hash function. The prover uses the output of the root node as the signature commitment.

[0048] S102: Initialize the PCD and SNARK proof system and generate public parameters and key pairs. This includes:

[0049] S1021: Run the PCD common parameter generation algorithm.

[0050] S1022: Run the SNARK protocol public parameter generation algorithm.

[0051] S1023: Run the PCD key generation algorithm.

[0052] S1024: Run the SNARK protocol key generation algorithm.

[0053] S1025: Output the certification key and verification key of the digital signature batch verification scheme.

[0054] The proof key includes the proof key of the PCD and SNARK protocols, as well as the signature function V and the hash function H. The verification key includes the verification key of the PCD and SNARK protocols, as well as the signature function V and the hash function H.

[0055] The public parameter generation algorithm and the key generation algorithm determine the elliptic curve group and its generators, finite fields Public parameters such as the signature verification function V and the hash function H.

[0056] Furthermore, the hash function H used by Merkle-Tree (variant) to calculate the commitment is implemented using a SNARK-friendly hash function.

[0057] S103: Perform arithmetical representation on digital signature verification algorithm, hash and other calculations.

[0058] Specifically, the arithmetic representation adopts the (commitment-relaxed) R1CS constraint system.

[0059] Furthermore, the (commitment-relaxed) R1CS requires an instance-evidence pair Satisfies the correspondence used to describe the proven computation.

[0060] Specifically, the matrix (k, l are part of the public parameters described in S102, and k>l, used to represent the number of R1CS constraints and the number of variables) describes the structure of the proved computation, in, Let vector Z = (W, x, s), the (commitment-relaxed) R1CS “instance-evidence” pair Satisfying the corresponding relationship is equivalent to satisfying the following conditions: and

[0061] Commit is a vector commitment algorithm, and the present invention uses Pedersen vector commitment to implement it.

[0062] Furthermore, the digital signature verification algorithm is a partial signature verification algorithm in the signature verification process except for the calculation of the message digest, and the calculation of the message digest does not participate in the proof process.

[0063] S104: Based on the arithmetic representation, run the PCD protocol. After the PCD protocol ends and generates the PCD proof, run the SNARK protocol to summarize and generate the final proof.

[0064] include:

[0065] S1041: For tree-type computation assertions, combined Figure 2 , that is, the hash value of the Merkle-Tree (variant) root node can be calculated from the signatures of all nodes in the tree, combined with Figure 3 , the prover runs the prover algorithm of the PCD protocol and generates a PCD proof Here, the proof Π consists of two sets of "instance-evidence" pairs of (commitment-relaxed) R1CS constraint systems.

[0066] S1042: The prover runs the Tree-FS prover algorithm of the PCD protocol, folding the "instance-evidence" in every two adjacent nodes in a layer to obtain a new "instance-evidence" And fold proof π FS , output

[0067] S1043: The prover runs the SNARK protocol prover algorithm to verify the instance-evidence pair. Generate SNARK proof π ′ .

[0068] S1044: The prover summarizes the proof of the digital signature batch verification scheme and outputs

[0069] S105: Verify the legitimacy of the generated certificate. This includes:

[0070] S1051: The verifier parses the received proof π into

[0071] S1052: The verifier groups the received signatures and combines Figure 2 , apply the Merkle-Tree (variant) structure of the hash function to the signature information in each group, and calculate the output tree root commitment value root.

[0072] Check whether the final output commitment is equal to the root in the proof π. If they are equal, execute S1053. Otherwise, reject the proof and terminate the protocol.

[0073] S1053: The verifier runs the Tree-FS verifier algorithm to calculate the folding of the two sets of instances to obtain a new instance.

[0074] S1054: The verifier runs the SNARK protocol verifier algorithm to check π ′ The legitimacy of ′ If the verification is successful, output 1 to accept the proof; otherwise, output 0 to reject the proof.

[0075] Example 2:

[0076] The purpose of this embodiment is to provide a PCD-based digital signature batch verification system, including:

[0077] A preliminary verification module is configured to verify the legitimacy of the obtained digital signature and calculate the commitment;

[0078] The initialization module is configured to initialize the PCD and SNARK proof system and generate public parameters and key pairs.

[0079] an arithmetic module configured to: perform arithmetic representation of a proven calculation such as a digital signature verification algorithm and a hash function;

[0080] The PCD proof module is configured to: run the PCD protocol based on the arithmetic representation to generate a PCD proof;

[0081] The SNARK proof module is configured to: after the PCD protocol is completed and the PCD proof is generated, run the SNARK protocol to generate the SNARK proof, and aggregate and generate proofs for batch verification of digital signatures;

[0082] The verification module is configured to verify the legitimacy of the generated certificate.

[0083] Furthermore, the system described in this embodiment corresponds to the method described in Example 1, and its technical details are described in detail in Example 1, so they will not be repeated here.

[0084] Example 3:

[0085] The purpose of this embodiment is to provide an electronic device.

[0086] An electronic device includes a memory, a processor, and a computer program stored and running on the memory. When the processor executes the program, it implements the PCD-based digital signature batch verification method described in Example 1.

[0087] Example 4:

[0088] The purpose of this embodiment is to provide a non-transitory computer-readable storage medium.

[0089] A non-transitory computer-readable storage medium stores a computer program, which, when executed by a processor, implements a digital signature batch verification method based on PCD described in Example 1.

[0090] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0091] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce 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 flowcharts and / or block diagrams. 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.

[0092] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0093] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0094] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made by those skilled in the art that fall within the spirit and principles of the present invention and do not require creative effort are intended to be within the scope of protection of the present invention.

Claims

1. A digital signature batch verification method based on PCD, characterized in that: The following steps are involved: For the obtained digital signature, verify the legitimacy of the signature and calculate the commitment; Initialize PCD and SNARK proof systems, generate public parameters and key pairs; Arithmetically represent the computation being proved; Based on the arithmetic representation, the PCD protocol is run. After the PCD protocol generates the PCD proof, the SNARK protocol is run to aggregate and generate the final proof, and the legitimacy of the final proof is verified.

2. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The obtained digital signature includes a signature verification key, a message, and a signature.

3. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of verifying the legitimacy of a signature includes the prover running a verification algorithm on each collected digital signature using its public verification key, message, and signature to determine its legitimacy, and sending all verified digital signatures to the verifier.

4. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of calculating the commitment includes: the prover divides all verified digital signatures into multiple groups, constructs a tree structure, applies the tree structure of the hash function to the signature information in each group, calculates the output tree root commitment value root, and uses the root as the commitment.

5. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of initializing the PCD and SNARK proof system includes: the prover and the verifier generate the public parameters required for the operation of the PCD protocol and the SNARK protocol, disclose the public parameters of the hash function and commitment scheme used, and the key pair generation includes the prover generating the proof key and the verifier generating the verification key.

6. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of arithmetically representing the computation to be proved includes: representing the signature verification algorithm and the tree folding scheme verification algorithm and hash function contained in the PCD as an R1CS constraint system.

7. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of running the PCD protocol includes running the PCD protocol on the tree-type PCD computation assertion to generate a PCD proof.

8. The PCD-based digital signature batch verification method according to claim 1, wherein: The process of running the SNARK protocol includes running the tree folding scheme in PCD to obtain the SNARK assertion to be proved, and running the SNARK protocol to generate the SNARK proof.

9. A PCD-based digital signature batch verification method as claimed in claim 1, characterized in that: The process of verifying the legitimacy of the final proof includes the verifier grouping all digital signatures sent by the prover according to the grouping method in the public parameters, running the same algorithm as the prover to calculate the hash value, and running the verification process. If all verification steps are passed, the verifier accepts the proof and believes that all received digital signatures are legal. Otherwise, the verifier rejects the proof.

10. A digital signature batch verification system based on PCD, characterized in that: include: A preliminary verification module is configured to verify the legitimacy of the obtained digital signature and calculate the commitment; An initialization module is configured to initialize the PCD and SNARK proof system and generate public parameters and key pairs; an arithmetic module, configured to perform an arithmetic representation of the proved computation; The proof module is configured to run the PCD protocol based on the arithmetic representation. After the PCD protocol generates the PCD proof, it runs the SNARK protocol to aggregate and generate the final proof. The verification module is configured to verify the legitimacy of the final certificate.

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