Proof verification device and proof verification method

Abstract

This proof verification device includes: a forward propagation unit that guarantees, by zero-knowledge proof, the correctness of computation in forward propagation processing of a batch normalization system of a neural network or a deep neural network; and an inverse propagation unit that guarantees, by zero-knowledge proof, the correctness of computation in the inverse propagation processing of the neural network or deep neural network.

Description

Proof verification device and proof verification method

[0001] The present disclosure relates to a proof verification device that ensures the transparency of an AI model.

[0002] In recent years, various systems using AI have been widely deployed. System providers use AI models (hereafter referred to as models) operated within the system to make inferences on data received from system users. Only the inference results are sent to the system users.

[0003] There is a problem in that the accuracy of the learning of the models used in our company's systems cannot be proven, as it is not known what model or what dataset was used to create them.

[0004] On the other hand, disclosing and verifying machine learning models and datasets in order to verify the correctness of such learning is undesirable from the perspective of the high asset value of machine learning models and the need to protect the privacy of datasets.

[0005] In recent years, there has been a growing interest in guaranteeing learning for machine learning models using zero-knowledge proofs, which can prove the correctness of calculations while keeping information secret.

[0006] For example, Non-Patent Document 1 guarantees update calculations only for parameter updates of logistic regression, while Non-Patent Document 2 guarantees update calculations only for simple architectures such as AlexNet and LeNet.

[0007] Sanjam Garg, Aarushi Goel, Somesh Jha, Saeed Mahloujifar, Mohammad Mahmoody, Guru-Vamsi Policharla, Mingyuan Wang, “Experimenting with Zero-Knowledge Proofs of Training,” [online], September 11, 2020 (approved), [retrieved June 12, 2020], Internet <URL: https: / / eprint.iacr.org / 2023 / 1345> Kasra Abbaszadeh, Christodoulos Pappas, Dimitrios Papadopoulos, Jonathan Katz, “Zero-Knowledge Proofs of Training for Deep Neural Networks,” [online], February 5, 2020 (last of 2 revisions), [searched on June 12, 2020], Internet <URL: https: / / eprint.iacr.org / 2024 / 162>

[0008] Meanwhile, with the recent trend toward multi-layered AI architectures, stability and speed of learning have become increasingly important, and batch normalization, which normalizes and scales / shifts the values ​​calculated at each layer, is one technique that has become widespread.

[0009] The techniques described in the above two documents have a problem in that they cannot guarantee update operations for a model incorporating a batch normalization system.

[0010] Therefore, an object of the present disclosure is to provide a proof verification device that guarantees update operations for a model in which a batch normalization system is incorporated.

[0011] The proof verification device disclosed herein includes a forward propagation unit and a back propagation unit. The forward propagation unit uses zero-knowledge proof to guarantee the correctness of operations in the forward propagation process of a batch normalization system of a neural network or a deep neural network. The back propagation unit uses zero-knowledge proof to guarantee the correctness of operations in the back propagation process of the neural network or the deep neural network.

[0012] According to the proof verification device of the present disclosure, it is possible to guarantee update operations for a model incorporating a batch normalization system.

[0013] 1 is a block diagram showing the functional configuration of a proof verification device of the prior art that does not include a batch normalization system. FIG. 2 is a flowchart showing the operation of a proof verification device of the prior art that does not include a batch normalization system. FIG. 3 is a block diagram showing the functional configuration of a proof verification device of Example 1. FIG. 4 is a flowchart explaining the main operations of a forward propagation unit and a back propagation unit. FIG. 5 is a flowchart explaining the main operations of a back propagation unit and an update process proof unit. FIG. 6 is a flowchart explaining the main operations of a back propagation unit and an update process proof unit.

[0014] Hereinafter, embodiments of the present disclosure will be described in detail. Note that components having the same functions are assigned the same numbers, and redundant explanations will be omitted.

[0015] Hereinafter, a proof verification device according to a first embodiment will be described, which guarantees update operations for a model incorporating a batch normalization system. In this explanation, the functional configuration and operation of a conventional proof verification device that does not include a batch normalization system will be described with reference to FIGS. 1 and 2.

[0016] 1, a conventional proof verification device 9 that does not include a batch normalization system includes a forward propagation unit 91, a backpropagation unit 92, an update processing proof unit 93, and a DNN storage unit 94. A DNN (deep neural network) is stored in the DNN storage unit 94, but this DNN may also be a single-layer neural network.

[0017] The forward propagation unit 91 includes a linear operation unit 911 , a linear operation zero-knowledge proof unit 912 , an activation function unit 913 , and an activation function zero-knowledge proof unit 914 .

[0018] The back propagation unit 92 includes an activation function differentiation unit 921 , a linear operation differentiation unit 922 , a gradient G zero-knowledge proving unit 923 , and a back propagation R zero-knowledge proving unit 924 .

[0019] The update process proving unit 931 includes a weight w update process proving unit 931 .

[0020] 2, the linear operation unit 911 of the forward propagation unit 91 of the conventional proof verification device 9 executes linear operation processing of a deep neural network (or neural network) (S911). The linear operation zero-knowledge proof unit 912 proves the correctness of the linear operation processing by zero-knowledge proof (S912). The activation function unit 913 executes activation function processing (S913). The activation function zero-knowledge proof unit 914 proves the correctness of the activation function processing by zero-knowledge proof (S914).

[0021] The activation function differentiation unit 921 of the backpropagation unit 92 of the conventional proof verification device 9 performs activation function differentiation processing (S921). The linear operation differentiation unit 922 performs linear operation differentiation processing (S922). The gradient G zero-knowledge proving unit 923 proves that the calculation of gradient G is correct by zero-knowledge proof (S923). The backpropagation R zero-knowledge proving unit 924 proves that the calculation of backpropagation R is correct by zero-knowledge proof (S924).

[0022] The weight w update process proving unit 931 of the update process proving unit 93 of the conventional proof verification device 9 proves that the update process of the weight w of the deep neural network (or neural network) is correct (S931).

[0023] In contrast to the prior art, the proof verification device 1 of this embodiment performs the following proof and verification (1) to (3).

[0024] (1) Proof and verification that the calculation of the gradient G and backpropagation parameter R is correct for normalization, scale-shift processing of the batch normalization system.

[0025] (2) Proof and verification of update operations for parameters required for scale-shift processing.

[0026] (3) Mean μ and variance σ in the batch normalization device ２ Proof and verification regarding.

[0027] 3, the proof verification device 1 of this embodiment includes a forward propagation unit 11, a back propagation unit 12, an update processing proof unit 13, and a DNN storage unit 94. A DNN (deep neural network) is stored in the DNN storage unit 94, but this DNN may be a single-layer neural network.

[0028] The main operations of the forward propagation unit 11, the back propagation unit 12, and the update processing proof unit 13 will be described with reference to FIGS.

[0029] As shown in FIG. 4, the forward propagation unit 11 of the proof verification device 1 of this embodiment is configured to guarantee the correctness of the operations in the forward propagation process of the batch normalization system of a neural network or a deep neural network by zero-knowledge proof (S11), and the back propagation unit 12 is configured to guarantee the correctness of the operations in the back propagation process of the neural network or the deep neural network by zero-knowledge proof (S12A).

[0030] As shown in FIG. 5, the backpropagation unit 12 of the proof verification device 1 of this embodiment is configured to guarantee the correctness of the gradient calculation of parameters required for the scale-shift calculation process in the batch normalization system of a neural network or a deep neural network by zero-knowledge proof (S12B), and the update process proving unit 13 is configured to guarantee the correctness of the update process of each parameter by zero-knowledge proof (S13A).

[0031] As shown in FIG. 6, the backpropagation unit 12 of the proof verification device 1 of this embodiment may be configured to guarantee the correctness of the parameter gradient calculation without using a zero-knowledge proof technique by disclosing one of the two parameters γ and β required for the scale-shift calculation process in the batch normalization system of a neural network or a deep neural network (S12C), and the update process proving unit 13 may be configured to guarantee the correctness of the update process of each parameter without using a zero-knowledge proof technique (S13B).

[0032] As shown in FIG. 7, the backpropagation unit 12 of the proof verification device 1 of this embodiment uses zero-knowledge proof to guarantee the correctness of the commitment of parameters required for normalization processing in a batch normalization system for a neural network or a deep neural network (S12D), and the update processing proof unit 13 is configured to guarantee the correctness of the update processing of each parameter (S13C).

[0033] As shown in FIG. 8, the backpropagation unit 12 of the proof verification device 1 of this embodiment may guarantee the correctness of the parameter commitment without using a zero-knowledge proof technique by disclosing one of the two parameters μ and σ required for the normalization process in the batch normalization system of a neural network or a deep neural network (S12E), and the update process proving unit 13 may be configured to guarantee the correctness of the update process of each parameter without using a zero-knowledge proof technique (S13D).

[0034] The configuration and operation of the proof verification device 1 of this embodiment will be described in more detail below with reference to Figures 3 and 9. Note that the following describes an example using a zero-knowledge proof technique.

[0035] As shown in FIG. 3, the forward propagation unit 11 of the proof verification device 1 of this embodiment includes a batch normalization unit 111, a batch normalization zero-knowledge proof unit 112, a mean / standard deviation commitment unit 113, a linear operation unit 911, a linear operation zero-knowledge proof unit 912, an activation function unit 913, and an activation function zero-knowledge proof unit 914, and components 911 to 914 are the same as the components of the conventional proof verification device 9 with the same numbers.

[0036] As shown in the figure, the backpropagation unit 12 of the proof verification device 1 of this embodiment includes a batch normalization differentiation unit 121, a gradient γ'β' zero-knowledge proof unit 122, an activation function differentiation unit 921, a linear operation differentiation unit 922, a gradient G zero-knowledge proof unit 123, and a backpropagation R zero-knowledge proof unit 124, and 921 and 922 are the same as the constituent elements of the same number in the conventional proof verification device 9.

[0037] As shown in the figure, the update process proving unit 13 of the proof verification device 1 of this embodiment includes a γ, β update process proving unit 131, a mean / standard deviation update process proving unit 132, and a weight w update process proving unit 931, and the weight w update process proving unit 931 has the same constituent element as the same name in the conventional proof verification device 9.

[0038] Below, we will explain the detailed operation of each component, which is a difference from the conventional proof verification device 9. Note that there are multiple proof and verification methods that can be used in the processing (each step) of each component below, but in this embodiment, we will use the GKR protocol (Reference Non-Patent Document 1), which is a representative method, and describe the proof and verification method for the specific learning process during the i-th loop of AI learning. Other proof protocols are disclosed in Reference Non-Patent Documents 2 and 3, for example.

[0039] (Reference non-patent document 1: Shafi Goldwasser, Yael Tauman Kalai, and Guy N. Rothblum, “Delegating Computation: Interactive Proofs for Muggles,” [online], September 11, 2015, ACM Journals, Journal of the ACM [searched on June 12, 2020], Internet < URL: https: / / www.microsoft.com / en-us / research / wp-content / uploads / 2016 / 12 / 2008-DelegatingComputation.pdf>) (Reference non-patent document 2: Tiacheng Xie, Jiaheng Zhang, Yupeng Zhang, Charalampos Papamanthou, and Dawn Song. “Libra: Succinct Zero-Knowledge Proofs with Optimal Prover Computation,” [online], August 1, 2019, Advances in Cryptology-Crypto 2019, [Retrieved June 12, 2024], Internet <URL: https: / / eprint.iacr.org / 2019 / 317>) (Reference non-patent document 3: Jiaheng Zhang, Tianyi Liu, Weijie Wang, Yinuo Zhang, Dawn Song, Xiang Xie, and Yupeng Zhang, “Doubly Efficient Interactive Proofs for General Arithmetic Circuits with Linear Prover Time,” [online], May 19, 2021 (revised), In Conf. on Computer and Communications Security, [Retrieved June 12, 2024], Internet <URL: https: / / eprint.iacr.org / 2020 / 1247>) <Initialization processing phase> The proof verification device 1 of this embodiment initializes each parameter as shown below in the initialization processing phase of the GKR protocol.

[0040] Weight parameter before update: W i-1 ={W i-1,l} L l=1 , Batch data: B i-1 , propagation parameter: U i ={U i,l} L l=1 , gradient: G i ={G i,l} L l=1 , backpropagation parameter: R i ={R i,l} L l=1 , updated weight parameter: W i ={W i,l} L l=1 , Auxiliary information AUX i ={AUX i,l} L l=1 , scale parameter: γ i ={γ i,l} L l=1 , shift parameter: β i ={β i,l} L l=1 , average parameter: μ i ={μ i,l} L l=1 , standard deviation parameter: σ={σ i,l} L l=1 Note that L is the number of layers in a neural network or deep neural network, l refers to any layer from 1 to L, and i represents the loop number.

[0041] <<Commitment Processing Phase>> The proof verification device 1 of this embodiment executes the following commitments as the commitment processing phase of the GKR protocol.

[0042] C Wi ←PCS.Commit(w i ~,r Wi )),C Wi-1 ←PCS.Commit((w i-1 ~),rWi-1 )),C Bi-1 ←PCS.Commit(B i-1 ~,r Bi-1 ), C AUXi ←PCS.Commit(AUX i ~,r AUXi ), C μi ←PCS.com(μ i ~,r μi ), C σi ←PCS.com(σ i ~,r σi ), C γi ←PCS.com(γ i ~,r γi ), C βi ←PCS.com(β i ~,r βi ) PCS.Commit is the algorithm that executes the commitment process.

[0043] <Batch normalization unit 111> The batch normalization unit 111 executes batch normalization processing (S111). A specific calculation of the batch normalization processing is expressed by the following equation.

[0044] x'=γ(x−μ) / σ+β (1) <Batch normalization zero-knowledge proving unit 112> The batch normalization zero-knowledge proving unit 112 proves that the arithmetic expression (1) of the batch normalization unit 111 is correct (S112).

[0045] In the GKR protocol, step S112 is executed as the proof phase (1) of the forward propagation process.

[0046] <Proof Phase (1) of Forward Propagation Processing> The batch normalized zero-knowledge proof unit 112 calculates the evaluation point N i,l ~(r 3,Ni,l ), N i,l =T i,l -μ i,l / σ i,l The correctness of the operation is T i,l ~(r (3) 3,Tl ), μ i,l ~(r 3,μi,l ), σ i,l ~(r 3,σi,l ) is proven by the evaluation points.

[0047] <Mean and Standard Deviation Commitment Unit 113> The mean and standard deviation commitment unit 113 is a unit that generates a commitment c μ ←com(μ),c σ ← com(σ) and the committed value c μ ,c σ It is verified whether the mean and variance of each layer are correctly calculated (S113).

[0048] In the GKR protocol, step S113 is executed as the proof phase (2) of the forward propagation process.

[0049] <Proof Phase (2) of Forward Propagation Processing> The mean and standard deviation commitment unit 113 μi,l =PCS.commit(μ i,l ), C σi,l =PCS.commit(σ i,l ) is correct and 1 / NΣ N i=1 T i,l ,√(Σ N i=1 (T i,l -μ) 2 / N).

[0050] <Batch normalization differentiation unit 121> The batch normalization differentiation unit 121 executes batch normalization differentiation processing (S121).

[0051] <Gradient γ'β' Zero-Knowledge Proving Unit 122> The gradient γ'β' zero-knowledge proving unit 122 proves the correctness of the gradients γ'=dL / dγ, β'=dL / dβ of γ and β required for the scale-shift processing calculation of batch normalization (S122).

[0052] In the GKR protocol, step S122 is executed as the proof phase (1) of the backpropagation process.

[0053] <<Proof Phase (1) of Backpropagation Processing>> The gradient γ′β′ zero-knowledge proving unit 122 proves the gradient value γ′ of the scale-shift parameter i,l , β' i,l Regarding γ' i,l =Σ N i=1 (N'i,l 。 R i,l*1 ) 。 T i,l -μ i,l / σ i,l β' i,l =Σ N i=1 (N' i,l 。 R i,l+1 ) γ' i,l , β' i,l For evaluation point N' i,l ~(r 1,T'i,l ), R i,l+1 ~(r (3) 2,Rl+1 ), μ i,l ~(r 1,μi,l ), σ i,l ~(r 1,σi,l ) proves the correctness of the above operations.

[0054] <Gradient G zero-knowledge proving unit 123> The gradient G zero-knowledge proving unit 123 proves that G=dL / dW has been correctly calculated (S123).

[0055] In the GKR protocol, step S123 is executed as the proof phase (2) of the backpropagation process.

[0056] <<Proof phase of backpropagation processing (2)>> The gradient G is G i,l =(R i,l+1 。 N' i,l 。 T' i,l )・U T i,l-1 In the case of convolution (calculation for each channel), G i,l =(R i,l+1 。 N' i,l 。 T' i,l )*U T i,l-1 It is expressed as:

[0057] The gradient G zero-knowledge proving unit 123 proves the G i,l Evaluation point G i,l (r1,G i,l) for each evaluation point R i,l+1 ~(r 2,Rl+1 ), U i,l-1 ~(r 2,U'l-1 ), T' i,l ~(r 2,T'l ), γ i,l ~(r (1) 2,γi,l ), σ i,l ~(r (1) 2,σi,l ), μ i,l ~(r (1) 2,μi,l ) proves that the above operation holds.

[0058] <Backpropagation R zero-knowledge proving unit 124> The backpropagation R zero-knowledge proving unit 124 proves the backpropagation parameter R=dL / dx to be transmitted to the previous layer (S124).

[0059] In the GKR protocol, step S124 is executed as the proof phase (3) of the backpropagation process.

[0060] <<Proof phase of backpropagation processing (3)>> Backpropagation R is R in the case of matrix operations. i,l =pad(W T i-1,l )*(R i,l+1 。 N' i,l 。 T' i,l ) and in the case of convolution operation (calculation for each channel) R i,l =W T i-1,l ・(R i,l+1 。 N' i,l 。 T' i,l )

[0061] The backpropagation R zero-knowledge proof unit 124 i,l For each evaluation point R i,l+1 ~(r (2) 2,Rl+1 ), W i,l-1 ~(r (2) 2,U'l-1 ), T' i,l ~(r (2) 2,T'l ), γ i,l ~(r (2)2,γi,l ), σ i,l ~(r (2) 2,σi,l ), μ i,l ~(r (2) 2,μi,l ) proves the correctness of the above operation.

[0062] <γ, β Update Process Proving Unit 131> The γ, β update process proving unit 131 proves that the calculation process of γ←γ-ηγ' β←β-ηβ' is correct in addition to the conventional weight update process during update processing (S131).

[0063] In the GKR protocol, step S131 is executed as the proof phase (1) of the update process. The proof phase (1) of the update process is performed by the γ, β update process proof unit 131. i,l ←W i-1,l -ηG i,l gamma i,l ←γ i-1,l -ηγ' i,l β i,l ←β i-1,l -ηβ' i,l The GKR protocol does not track all the calculations, but narrows down the evaluation points of each value on the finite field. W i,l =W i-1,l -η・G i,l - The calculation itself is evaluated as r 1,Wi-1,l , r 1,Gi,l Using W i-1,l ~(r1,w i-1,l ), G i,l ~(r 1,Gi,l ) and prove that the above calculation is correct. The same applies to β and γ, and γ i-1,l ~(r 1,γi-1,l ), β i-1,l ~(r 1,βi-1,l ), γ' i,l ~(r 1,γi,l ), β' i,l ~(r 1,βi,l ) Prove that the operation is correct for each.

[0064] <Mean and standard deviation update process proving unit 132> The mean and standard deviation update process proving unit 132 is a unit for proving the value c μ,c σ In contrast, E(c μ ),E(c σ ) and prove the correctness of the calculation (S132).

[0065] In the GKR protocol, step S132 is executed as the proof phase (2) of the update process. The proof phase (2) of the update process is executed by the mean and standard deviation update process proving unit 132. μi-1,l , C' σi-1,l For μ calculated in the current i-th loop, i,l , σ i,l Prove that the value is calculated using

[0066] C' μi,l , C' σi,l ←Update(μ i,l , σ i,l , C' μi-1,l , C' σi-1,l ) <Verification Phase> The proof verification device 1 of this embodiment executes the <verification phase> in the GKR protocol as follows.

[0067] When the proof of the backpropagation process and the forward propagation process is performed from l=L to l=1, the correctness of the calculation of the backpropagation and the forward propagation process is evaluated by each evaluation point, W i-1,l ~(r 2,Wi-1,l ), U i,l ~(r 2，Ui,l ), B i-1 ~(r 2,Bi-1 ), AUX i,l ~(r 2,AUXi,l ), γ i-1,l ~(r 2,γi-1,l ), σ i-1,l ~(r 2,σi,l ), μ i-1,l ~(r 2,μi-1,l ), β i-1,l ~(r 2,βi,l ) can be proved.

[0068] The proof verification device 1 checks whether each evaluation point matches the committed value, and verifies whether the learning process was performed using the correctly committed value.

[0069] <Effects Obtained by the Invention> According to the proof verification device 1 of this embodiment, by guaranteeing the correctness of the calculation of each parameter μ, σ, γ, and β required for a batch normalization system and the correctness of the gradient calculation, it is possible to guarantee how model parameters have been updated for architectures that have batch normalization processing systems that are widespread in the world.

[0070] During inference, it is possible to ensure that the parameters of the batch normalization system used are the parameters actually calculated during training.

[0071] It is known that when a batch normalization system is introduced, the parameters required for the calculations of the batch normalization system change between inference and learning. Therefore, in the proof verification device 1 of this embodiment, when guaranteeing updates, the parameters used for inference are also calculated at the same time, and the correctness of the parameters required for inference is also guaranteed.

[0072] <Additional Notes> The functions performed by the components described herein may be implemented in circuitry or processing circuitry, including general-purpose processors, application-specific processors, integrated circuits, ASICs (Application Specific Integrated Circuits), a CPU (a Central Processing Unit), conventional circuits, and / or combinations thereof, programmed to perform the described functions. A processor includes transistors and other circuits and is considered to be circuitry or processing circuitry. A processor may also be a programmed processor that executes a program stored in a memory.

[0073] In this specification, a circuitry, unit, or means is hardware that is programmed to realize or performs the described functions, which may be any hardware disclosed herein or any hardware known to be programmed to realize or perform the described functions.

[0074] If the hardware is a processor considered to be a type of circuitry, the circuitry, means, or unit is a combination of the hardware and software used to configure the hardware and / or processor.

[0075] The various processes described above can be implemented by loading a program that executes each step of the above method into the recording unit 10020 of the computer shown in Figure 10 and operating the control unit 10010, input unit 10030, output unit 10040, etc.

[0076] The program describing the processing contents can be recorded on a computer-readable recording medium, which may be, for example, a magnetic recording device, an optical disk, a magneto-optical recording medium, a semiconductor memory, or any other suitable recording medium.

[0077] The program may be distributed, for example, by selling, transferring, or lending portable recording media such as DVDs or CD-ROMs on which the program is recorded. Furthermore, the program may be stored in a storage device of a server computer and then transferred from the server computer to other computers via a network, thereby distributing the program.

[0078] A computer that executes such a program may first temporarily store the program recorded on a portable recording medium or transferred from a server computer in its own storage device. Then, when executing a process, the computer reads the program stored on its own recording medium and executes the process in accordance with the read program. Alternatively, the computer may read the program directly from a portable recording medium and execute the process in accordance with the program. Furthermore, the computer may execute the process in accordance with the program each time a program is transferred from a server computer to the computer. Alternatively, the server computer may not transfer the program to the computer, but may instead execute the process through a so-called ASP (Application Service Provider) service, which realizes the processing function by issuing an execution instruction and obtaining the results. Furthermore, the server computer may execute the process at the terminal using a so-called SaaS (Software as a Service) service, which allows users to use part of a server computer along with the program. In this embodiment, the program includes information used for processing by an electronic computer that is equivalent to a program (such as data that is not a direct instruction to a computer but has properties that dictate computer processing).

[0079] Furthermore, in this embodiment, the device is configured by executing a predetermined program on a computer, but at least a part of the processing contents may be realized by hardware.

Claims

1. A proof verification device including: a forward propagation unit that uses zero-knowledge proof to guarantee the correctness of operations in the forward propagation process of a batch normalization system of a neural network or a deep neural network; and a back propagation unit that uses zero-knowledge proof to guarantee the correctness of operations in the back propagation process of the neural network or the deep neural network.

2. A proof verification device including a backpropagation unit that uses zero-knowledge proof to guarantee the correctness of the gradient calculation of parameters required for scale-shift calculation processing in a batch normalization system of a neural network or deep neural network, and an update processing proof unit that uses zero-knowledge proof to guarantee the correctness of the update processing of each parameter.

3. A proof verification device including: a backpropagation unit that publishes one of two parameters required for scale-shift calculation processing in a batch normalization system of a neural network or a deep neural network, and guarantees the correctness of the gradient calculation of said parameter; and an update processing proof unit that guarantees the correctness of the update processing of each parameter.

4. A proof verification device including a backpropagation unit that uses zero-knowledge proof to guarantee the correctness of parameter commitments required for normalization processing in a batch normalization system for a neural network or deep neural network, and an update processing proof unit that uses zero-knowledge proof to guarantee the correctness of the update processing of each parameter.

5. A proof verification device including: a backpropagation unit that publishes one of two parameters required for normalization processing in a batch normalization system for a neural network or a deep neural network and guarantees the correctness of the commitment of the parameter; and an update processing proof unit that guarantees the correctness of the update processing of each parameter.

6. A proof verification method executed by a proof verification device, comprising: a step of guaranteeing the correctness of operations in a forward propagation process of a batch normalization system of a neural network or a deep neural network using zero-knowledge proof; and a step of guaranteeing the correctness of operations in a back propagation process of the neural network or the deep neural network using zero-knowledge proof.

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