Robustness neural network training and reasoning method supporting output result guarantee

Abstract

According to the robust neural network training and reasoning method supporting output result guarantee, safe multi-party calculation can be executed in the environment of the rational participant, and when the interests of the rational participant are threatened, it can be ensured that the protocol can still complete calculation on the premise of guaranteeing privacy even if malicious behaviors are detected. The efficiency is improved through separation of an offline stage and an online stage, and the offline stage preprocesses and calculates a part irrelevant to input, so that the calculation burden of the online stage is reduced; the innovative iJMP protocol can ensure that all honest participants can receive correct calculation results when facing malicious or rational deviation participants; the method supports a behavior model of a rational participant, allows a protocol to run in a more complex environment, and provides a security guarantee. According to the method, the security and the calculation accuracy of the protocol can be still maintained in the environment of malicious participants, and cooperation modes among different participants can be flexibly coped with.

Description

Technical Field

[0001] This application belongs to the field of secure computing technology, specifically relating to a robust neural network training and inference method that supports output result guarantees. Background Technology

[0002] Secure Multi-Party Computation (SMPC) allows mutually distrustful parties to jointly compute functions while maintaining security. The Goal of Delivery (GOD) guarantee ensures that all parties ultimately obtain the correct result—this is the strongest security and robustness metric in malicious SMPC scenarios. For SMPCs with a small number of participants, the mainstream approach to implementing GOD is to design a federated messaging protocol and utilize it for message transmission in SMPC computation. This protocol either successfully transmits messages (without malicious attacks) or identifies one or two honest parties (malicious behavior is detected) and delegates subsequent computations to these honest participants.

[0003] While the Joint Messaging Protocol (GMP) achieves God of Destruction (GOD), its successful execution relies on honest or semi-honest parties raising objections when inconsistencies arise. However, raising objections may lead to these parties being mistakenly perceived as adversaries and excluded from the protocol, thus missing out on contribution-based rewards. This consequence discourages parties from raising objections, ultimately undermining the achievement of GOD. This paper proposes a new practical security concept—the rational participant. Malicious participants are inherently rational. For honest and semi-honest participants, rationality manifests as follows: they will honestly follow the protocol as long as their own interests are not affected, but they may deviate from the protocol when their interests are threatened. Based on this, a security model is proposed: The model can tolerate up to One opponent, remaining The participants are honest and rational, making classic MPC suitable. We then present an SMPC scheme under these models: HoRGod, an implementation of GOD. The solution supports arithmetic secret sharing, making it suitable for tasks such as unintentional data substitution and privacy-preserving machine learning.

[0004] Against the backdrop of classic honest majority theory, researchers from institutions such as the Herzliya Interdisciplinary Research Center in Israel introduced the first secure three-party computation scheme for achieving GOD in their paper "Practical fully secure three-party computation via sublinear distributed zero-knowledge proofs," providing optimal overall communication cost through sublinear distributed zero-knowledge proofs. Their scheme relies on broadcast channels and a coin-flipping function to implement GOD. Researchers at the Indian Institute of Science proposed ASTRA in their paper "ASTRA: high throughput 3pc over rings with application to secure prediction," a secure three-party scheme employing an online-offline paradigm. The offline phase is data-agnostic and can be pre-computed, while the online phase is more efficient than in the paper "Practical fully secure three-party computation via sublinear distributed zero-knowledge proofs." This scheme also includes a commitment mechanism to ensure computational fairness. Building on this, researchers at Cornell University developed BLAZE in their paper "BLAZE: blazing fast privacy-preserving machine learning," which further improves efficiency while maintaining fairness. BLAZE also provides a set of primitives for machine learning training, including truncation and sigmoid operations. However, neither "ASTRA: high throughput 3pcover rings with application to secure prediction" nor "BLAZE: blazing fast privacy-preserving machine learning" supports GOD. To address this limitation, researchers at the Indian Institute of Science proposed a novel three-party computation scheme called SWIFT in their paper "SWIFT: super-fast and robust privacy-preserving machine learning," which introduces a Joint Message Passing (JMP) protocol. JMP ensures that each message is either successfully delivered (when no attack occurs) or that an honest party is identified (when an attack exists); once an honest party is identified, all participants send their shared data to that party to complete the remaining computation process.

[0005] In the context of four-party computing, researchers from institutions such as the Indian Institute of Science (IIS) proposed Trident in their paper "Trident: Efficient 4pc framework for privacy-preserving machine learning," a highly efficient PPML framework that ensures computational fairness. IIS researchers also introduced FLASH in their paper "FLASH: fast and robust framework for privacy-preserving machine learning," a robust four-party computing scheme that implements GOD. In FLASH, messages are transmitted using bidirectional primitives, ensuring that each message is either successfully delivered or that a pair of honest participants can recognize each other; thereafter, the remaining computational tasks are completed by the honest participants. Similarly, "SWIFT: super-fast and robust privacy-preserving machine learning" extends the protocol to four-party scenarios, implementing GOD through a specially designed JMP protocol. In their paper "Tetrad: Actively secure 4pc for secure training and inference," researchers from Aarhus University and other institutions further improved computational efficiency based on Trident and proposed Tetrad. This scheme employs the four-party JMP protocol from "SWIFT: super-fast and robust privacy-preserving machine learning" to ensure the implementation of GOD. However, most of these schemes rely on identifying honest parties and delegating subsequent computations to them to process plaintext data. But identifying honest parties depends on their honest execution of the JMP protocol, which can result in them being excluded from the secure multi-party computation process, leading to a loss of benefits in a reward-based system.

[0006] Therefore, the success of existing JMP protocols relies on the completely honest behavior of honest participants, while ignoring the rationality of the participants. Summary of the Invention

[0007] To address the aforementioned problems in the existing technology, this application provides a robust neural network training and inference method that supports output result guarantees. The technical problem to be solved by this application is achieved through the following technical solution: A robust neural network training and inference method that supports output guarantee includes: Construct (t, n) The HRP security model, where (t, n) The HRP security model involves n parties, with at most t parties being malicious attackers, and the remaining n parties being... t are honest and rational participants; the behavioral characteristics of the honest and rational participants are that they follow the agreement when their own interests are not affected, and may deviate from the agreement when their own interests are threatened. Define the iJMP protocol, in (t, n) Under the HRP security model, each participant uses a secret sharing protocol to share data and uses a basic protocol to perform corresponding processing on the data. During the processing, the iJMP protocol is used to assist at least two of the multiple honest and rational participants in transmitting the data to the other participants. Each participant uses the application protocol to train and infer neural networks based on its own data and the data it receives.

[0008] Beneficial effects: 1. This application proposes a security model for rational participants. The model assumes at most One opponent, the rest The participants are honest and rational, acting rationally based on their own interests, not merely on honesty or malice. Rational participants will faithfully adhere to the agreement as long as their own interests are not affected; however, they may deviate from the agreement when their interests are threatened. This allows the agreement to function in more real-world scenarios, especially when the parties' motivations go beyond mere honesty or malice.

[0009] 2. This application proposes a robust SMPC scheme with GOD (God-like) capability. Under the security model, the HoRGod scheme is proposed, a The SMPC scheme achieves GOD. The HoRGod scheme includes various protocols such as data sharing, reconstruction, and multiplication operations. All protocols operate in an online-offline mode, improving the efficiency of the online phase. Furthermore, a novel federated messaging protocol, iJMP, is designed as a fundamental building block of HoRGod. It allows three parties to reliably transmit messages to each other without relying on high-cost cryptographic primitives or the presence of rational participants, ensuring successful message transmission and guaranteeing the GOD of the HoRGod scheme.

[0010] 3. This application, based on HoRGod, constructs a GOD-enabled SMPC protocol adapted to specific scenarios, providing support for unintentional data permutation and PPML. Unintentional data permutation, as the foundation of collaborative filtering, can be used after privacy set intersection or database join operations; while PPML is widely used in collaborative training and inference. The unintentional data permutation protocol in this paper is the first permutation protocol capable of implementing GOD; The SMPC protocol used for PPML was tailored and optimized in the model to address the unique needs raised by rational parties.

[0011] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating a robust neural network training and inference method that supports output result guarantees, as provided in this application. Figure 2 This is a schematic diagram of the system structure of the HoRGod solution provided in this application. Detailed Implementation

[0013] The present application will be described in further detail below with reference to specific embodiments, but the implementation of the present application is not limited thereto.

[0014] As independent individuals, participating in computation is a more rational behavior for participating parties while protecting their own interests. This application incorporates the rationality characteristics of participating parties into the security model and constructs an SMPC protocol that can guarantee GOD delivery among rational participating parties. This application proposes an SMPC scheme based on the (t,n)-HRP security model, which ensures privacy protection among participating parties while guaranteeing GOD delivery and efficient computation. The scheme includes a security model, an iJMP protocol, a HoRGod scheme, and an application component.

[0015] Combination Figure 1 and Figure 2 This application provides a robust neural network training and inference method that supports output result guarantees, including: S100, construct (t, n) The HRP security model, where (t, n) The HRP security model involves n parties, with at most t parties being malicious attackers, and the remaining n parties being... t are honest and rational participants; the behavioral characteristics of the honest and rational participants are that they follow the agreement when their own interests are not affected, and may deviate from the agreement when their own interests are threatened. Malicious participants are essentially rational, while honest and semi-honest participants are considered rational. When their own interests are not affected, they will honestly abide by the agreement; however, when their own interests are threatened, they may deviate from the agreement. Based on this concept, a new security model is defined: Model, assumptions At most of the participating parties One party is a malicious attacker, while the remaining participants are honest and rational. Compared to existing SMPC models, this application's (t, n) The HRP security model explicitly considers the behavioral motivations of all parties, requiring them to act rationally based on their own interests.

[0016] S200 defines the iJMP protocol, in (t, n) Under the HRP security model, each participant uses a secret sharing protocol to share data and uses a basic protocol to perform corresponding processing on the data. During the processing, the iJMP protocol is used to assist at least two of the multiple honest and rational participants in transmitting the data to the other participants. iJMP protocol This allows the recipient to Holding data three parties , and The iJMP protocol-assisted process securely transmits shared messages. Step 1: Sending the message Towards send , Towards send , Towards send ,in , It is a hash function. If a participant... It is the malicious party. or A malicious party might tamper with the sent message, making it possible for... or Or refuse to send the message; It is a public value representing the data held by all three parties. Everyone knows that if someone possesses data, a malicious party might tamper with it or refuse to send the message. Second step: Message reception Receive from ( (news) ,if from The message was received and the message was set to If no message is received, then set ; Receive from hash value :if from The message was received and the message was set to If no message is received, then set ; Step 3: Message Settings: If ,but set up ;if :if or ,but Ensure message accuracy and set If neither of the above two conditions is met, set .

[0017] The improved federated messaging protocol ensures message delivery. It can reliably transfer information from at least two of the three honest participants to the other participants. Furthermore, the protocol ensures that data security is maintained even if malicious parties are involved.

[0018] Based on the aforementioned security model, this application proposes a SMPC scheme—HoRGod—suitable for a small number of participants. The SMPC scheme implements GOD. This scheme supports [the following] in a ring. HoRGod performs arithmetic / Boolean secret sharing and corresponding operations. It includes various protocols such as data sharing, reconstruction, and multiplication, all operating in an online-offline mode to improve efficiency during the online phase. The most significant innovation is the design of a novel federated messaging protocol, iJMP, a fundamental building block of HoRGod that allows three parties to reliably transmit messages to each other, ensuring a 100% message transmission success rate. Compared to traditional protocols, iJMP can perform offline multiplication without relying on costly cryptographic primitives such as distributed zero-knowledge proofs or accidental transmissions, and guarantees the GOD of the HoRGod scheme in the presence of rational participants.

[0019] The secret sharing protocol shares data through data sharing and replacement sharing.

[0020] First: Data sharing protocol Participants or Follow these steps to share messages securely.

[0021] Step 1: A value This can be represented in two forms of secret sharing, denoted as: and .

[0022] Step Two: Formal Secret Sharing: For a given participant ,gather Each party holds one share. , making .

[0023] Step 3: The secret of form: There exists a value This value is in China and Israel Secret sharing, and a value known to all participants. .

[0024] Step 4: Transformation of Data Sharing Methods: :Will Convert to ,set up and ,but , . :Will Convert to ,set up and ,but , .

[0025] Second: Replacement Sharing Protocol Step 1: Replacement Through sharing This was carried out for each participant. , The parties involved jointly hold a swap And all participants share a common permutation. , .

[0026] Step 2: Reconstruct the original permutation as follows .

[0027] Through secret sharing and To maintain data privacy, and to achieve secure data replacement using replacement sharing.

[0028] The basic protocols include a data sharing protocol, a reconstruction protocol, a linear computation protocol, a multiplication protocol, and a re-sharing protocol. All of the basic protocols adopt an online-offline mode. The iJMP protocol assists in processing when the participants use the data sharing protocol and the reconstruction protocol to perform corresponding processing on their own data.

[0029] HoRGod's fundamental protocols include data sharing, refactoring, linear computation, multiplication, and re-sharing. These protocols utilize iJMP to achieve lightweight and GOD execution.

[0030] First: Data sharing protocol In this application, HoRGod provides different types of data sharing methods. Different data sharing protocols were designed. The specific protocol steps and processes for each protocol are described below.

[0031] The data sharing protocol includes Formal joint sharing agreement, Formal sharing protocol and Formal sharing protocol.

[0032] (1) Formal joint sharing agreement

[0033] The agreement enables the three parties Able to set a value by Form in all five parties Shared among them.

[0034] Offline phase: Each party generates a random - Shared data And set during initialization ; and let Knowing all the random values ​​selected .

[0035] Online phase: Local computation Use Will Send to .

[0036] (2) Formal sharing protocol

[0037] The agreement enables the three parties Able to set a value by Form in all five parties Shared among them.

[0038] Offline phase: Each party generates a random - Shared data and allow Known All shares, calculated .

[0039] Online phase: Local computation Use Will Send to and .

[0040] (3) Formal sharing protocol

[0041] The agreement enables Able to replace a by In the form of Shared among them.

[0042] Offline phase: All participants generate a random - Shared replacement ,set up and allow Know all random permutations and calculate .

[0043] Online phase: calculate and will Send to .

[0044] Each protocol is customized to meet different data sharing needs, such as addition sharing, expansion sharing, and substitution sharing, and is suitable for computing tasks involving multiple parties.

[0045] Second: Reconfiguration Protocol The reconstruction protocol includes Agreement and protocol.

[0046] (1) protocol enter ,make Each party can recover .exist In the form of shared data, the participants Missing A share .

[0047] The offline phase includes the following operations: use The agreement will Send to ; use The agreement will Send to . use The agreement will Send to .Then, calculate .

[0048] Online phase: calculate and use Will Send to and .because Since GOD can be guaranteed, the refactoring protocol can naturally achieve GOD.

[0049] (2) protocol In a multiplication agreement, each party needs to... recover .enter and make Each party can recover .exist In formal data sharing, Only missing A share .

[0050] The protocol has no offline phase. During the online phase, use The agreement will Send to ; use The agreement will Send to . use The agreement will Send to . set up and use The agreement will Send to and .

[0051] In this way, the missing data share This supplementation allows all participants to recover the correct results by sharing data.

[0052] Third: Linear computation protocol

[0053] Protocol Input and output All parties involved know that... .

[0054] Offline phase: Each participant holds a shared share. , ,calculate , These values ​​constitute Offset sharing in the form.

[0055] Online phase: Parties utilize the common elements in the extended form , ,calculate .

[0056] Fourth: Multiplication Agreement

[0057] enter and output .

[0058] Offline phase: Generation and , Irrelevant random numbers are used to calculate multiplication in the online phase.

[0059] Step 1: The participants generate a random secret shared data. .

[0060] Step 2: Calculation . ,but .because It involves only linear computations, which can be performed locally by each party.

[0061] Step 3: Calculation .

[0062] (1) First, calculate

[0063] The calculation is broken down into 10 paired terms and 5 square terms.

[0064] (2) For each pair Three parties Local calculation is possible , .

[0065] (3) Calculate the square terms, divide the square terms into different cross terms, and add them by different tripartite groups. renew , renew , renew .

[0066] (4) Jointly share . use Shared with all parties and generate , Then you will get shared access. .

[0067] Online phase: Participants' local computation Then, the parties used Refactoring and calculate Then it can be calculated .

[0068] Fifth: Re-sharing protocol

[0069] Allow four parties In all five parties Re-share between .

[0070] Offline phase: Step 1: Generate random numbers. Use their public keys to generate random numbers. , making .

[0071] Step 2: Calculate the new share. Each side of the calculation .

[0072] Step 3: Send the share to . send Give , send Give , send Give , send Give .

[0073] Online phase: Calculate the new public value . send Give . yes The form of re-sharing.

[0074] S300, each participant uses application protocols to train and infer neural networks based on its own data and the data it receives. These application protocols include the PPML protocol and the unintentional data substitution protocol.

[0075] First: An unintentional data permutation protocol based on Horgod

[0076] enter and output . For shared vectors , For shared replacement . ,in This is known to all the parties involved. Depend on hold.

[0077] Offline phase: Step 1: Initialization , .

[0078] Step 2: For , Perform the following operations: Applied to get ; call The offline phase was restarted shared The re-shared data is represented as , as input for the next round.

[0079] Step 3: Retain the new shared data .

[0080] Online phase: Step 1: Applying substitution: For public values Application of permutation ,get .

[0081] Step 2: Update public values: calculate .

[0082] Step 3: In use Will Send to .

[0083] Finally, by and get All parties will then Applied to get .

[0084] The Horgod-based PPML protocol includes a truncation protocol, a dot product protocol, and... Bit random data generation protocol and data comparison protocol.

[0085] (1) Truncation Protocol

[0086] Performing multiplication in fixed-point arithmetic can lead to data overflow. Truncation protocols allow participants to truncate shared data to the minimum possible value without revealing their private data. Bit operations. The protocol input is shared data. The output is a shared stage value. ,in for The cutoff value, .

[0087] Offline phase: Generate a pair ,in It is a random number. yes The cutoff value.

[0088] Step 1: Each party first generates three locally. Shared random numbers in the form of, represented as ,in yes Known, and will The other shares are set to zero.

[0089] Step 2: Calculate the shared random number . The parties in the middle will Transform into binary data, let express The bits, then have Calculations by all parties Form sharing ,in Bitwise XOR. Each and every one of them Calculated as Using equations Convert XOR to addition and multiplication. Use protocols. and To calculate .

[0090] Step 3: Construction and Calculations by all parties and .use Will Transform into .

[0091] Online phase: Secure computation using masking techniques

[0092] Step 1: Calculation ,use let Refactoring .

[0093] Step Two: calculate ,use Share with all parties and generate .

[0094] Step 3: Local Calculation .

[0095] (2) Dot product protocol

[0096] The dot product protocol enables parties to compute the dot product of two vectors. It takes as input... and Output ,in and There are two vectors.

[0097] Offline phase: Step 1: Generation by all parties Shared random numbers in form .

[0098] Step Two: To obtain All parties need to calculate .have ,because It involves only linear computation and can be performed locally by each party. and Since they are secretly shared and cannot be directly multiplied, the key lies in the calculation. , .

[0099] 1) For each pair , Local computing , .

[0100] 2) Divide the square terms into different intersection terms and add them by different tripartite groups.

[0101] renew .

[0102] renew .

[0103] renew .

[0104] 3) use Shared with all parties and generate , Then you will get shared access.

[0105] Online phase: Participants' local computation Then, the parties used Refactoring and calculate Finally, all parties obtained...

[0106] (3) Bit Random Data Generation Protocol

[0107] Used for non-interactive generation by all parties during the offline phase. Shared random number of bits , .

[0108] Step 1: For a given , The parties involved use their shared key to generate a random value. , .

[0109] Step 2: All participants share a random number. , in the form of , Finally, through Will Turn to .

[0110] (4) Security Comparison Protocol

[0111] The agreement enables all parties to securely compare two [items / entities]. Bit shared data .

[0112] Offline phase: Invocation by all parties Generate two random number of bits ,satisfy , To ensure All parties only need to ensure that the generation Random numbers used Compared to generation The random number is large.

[0113] Online phase: Step 1: Each party first calculates . use Refactoring ,if , set up Otherwise, set .

[0114] Step Two: pass Will Send to .when ,express Otherwise, it means .

[0115] The process by which each participant in this application trains and infers neural networks using the application protocol, based on its own held data and the data it receives, includes: During the training phase, the participants first share data through a data sharing protocol, and then use linear computation and multiplication protocols to perform linear computation, addition and multiplication operations. After encrypted linear computation and weighting, the ReLU activation function is used to process the data and output the encrypted weights and gradients to update the neural network model. During the inference phase, the participants share input data and convert it into an encrypted shared form through a secret sharing protocol. Then, they perform inference calculations on the trained neural network model to obtain the inference result. The participants jointly recover the inference result and ensure that the inference result is accurately received by all participants through the iJMP protocol.

[0116] This application, based on HoRGod, constructs a GOD-enabled SMPC protocol adapted to specific scenarios, widely applicable to unintentional data permutation and PPML. Unintentional data permutation, as the foundation of collaborative filtering, can be used after privacy set intersection or database join operations; while PPML is widely used in collaborative training and inference. The unintentional data permutation protocol presented in this paper is the first permutation protocol capable of implementing GOD, representing a significant advancement in secure data permutation. Although previous work has extensively explored SMPC protocols for PPML, the main contribution of this paper is the optimization of these protocols under the (1,5)-HRP model, addressing the security and robustness issues of SMPC computation under the rational participant model.

[0117] This application makes a The SMPC scheme for a secure model addresses the limitations of traditional models in rational environments. This scheme enables secure multi-party computation in the presence of rational participants. While rational participants may deviate from the protocol when their interests are threatened, this scheme ensures that even if malicious behavior is detected, the protocol can still complete computation while maintaining privacy. Efficiency is improved through the separation of offline and online phases. The offline phase preprocesses computations unrelated to the input, reducing the computational burden of the online phase. Delivery is guaranteed: the innovative iJMP protocol ensures that all honest participants receive the correct computation results even when faced with malicious or rationally biased participants. It supports behavioral models of rational participants, allowing the protocol to operate in more complex environments and providing security guarantees. It exhibits high robustness and flexibility. Through mechanisms such as protocol reconstruction, multiplication, and permutation protocols, the scheme maintains the security and computational accuracy of the protocol even in the presence of malicious participants. It can flexibly handle different cooperation methods among participants, including rational, semi-honest, and malicious behavior. It has broad application scenarios, such as privacy-preserving machine learning and unintentional data permutation. In collaborative training and collaborative inference, this scheme can protect the data privacy of all parties while achieving multi-party computation.

[0118] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of this application and should not be construed as limiting the specific implementation of this application to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of this application, and all such modifications or substitutions should be considered within the scope of protection of this application.

Claims

1. A robust neural network training and inference method supporting output result guarantees, characterized in that, include: Construct (t, n) The HRP security model, where (t, n) The HRP security model involves n parties, with at most t parties being malicious attackers, and the remaining n parties being... t are honest and rational participants; the behavioral characteristics of the honest and rational participants are that they follow the agreement when their own interests are not affected, and may deviate from the agreement when their own interests are threatened. Define the iJMP protocol, in (t, n) Under the HRP security model, each participant uses a secret sharing protocol to share data and uses a basic protocol to perform corresponding processing on the data. During the processing, the iJMP protocol is used to assist at least two of the multiple honest and rational participants in transmitting the data to the other participants. Each participant uses the application protocol to train and infer neural networks based on its own data and the data it receives.

2. The robust neural network training and inference method supporting output result guarantee according to claim 1, characterized in that, The secret sharing protocol shares data through data sharing and replacement sharing.

3. The robust neural network training and inference method supporting output result guarantee according to claim 2, characterized in that, The basic protocols include a data sharing protocol, a reconstruction protocol, a linear computation protocol, a multiplication protocol, and a re-sharing protocol. All of the basic protocols adopt an online-offline mode. The iJMP protocol assists in processing when the participants use the data sharing protocol and the reconstruction protocol to perform corresponding processing on their own data.

4. The robust neural network training and inference method supporting output result guarantee according to claim 3, characterized in that, The data sharing protocol includes Formal joint sharing agreement, Formal sharing protocol and Formal sharing protocol.

5. The robust neural network training and inference method supporting output result guarantee according to claim 3, characterized in that, The reconstruction protocol includes Agreement and protocol.

6. The robust neural network training and inference method supporting output result guarantee according to claim 1, characterized in that, The iJMP protocol assistance process includes: Step 1: Sending the message Towards send , Towards send , Towards send ,in , It is a hash function. If a participant... It is the malicious party. or A malicious party might tamper with the sent message, making it possible for... or Or refuse to send the message; It is a public value representing the data held by all three parties. Everyone knows that if someone possesses data, a malicious party might tamper with it or refuse to send the message. Second step: Message reception Receive from ( (news) ,if from The message was received and the message was set to If no message is received, then set ; Receive from hash value :if from The message was received and the message was set to If no message is received, then set ; Step 3: Message Settings: If ,but set up ;if :if or ,but Ensure message accuracy and set If neither of the above two conditions is met, set .

7. The robust neural network training and inference method supporting output result guarantee according to claim 1, characterized in that, The application protocols include the PPML protocol and the unintentional data substitution protocol.

8. The robust neural network training and inference method supporting output result guarantee according to claim 7, characterized in that, The PPML protocol includes truncation protocol, dot product protocol, and... Bit random data generation protocol and data comparison protocol.

9. The robust neural network training and inference method supporting output result guarantee according to claim 3, characterized in that, Each participant, based on its own held data and the data it receives, utilizes the application protocol to perform neural network training and inference, including: During the training phase, the participants first share data through a data sharing protocol, and then use linear computation and multiplication protocols to perform linear computation, addition and multiplication operations. After encrypted linear computation and weighting, the ReLU activation function is used to process the data and output the encrypted weights and gradients to update the neural network model. During the inference phase, the participants share input data and convert it into an encrypted shared form through a secret sharing protocol. Then, they perform inference calculations on the trained neural network model to obtain the inference result. The participants jointly recover the inference result and ensure that the inference result is accurately received by all participants through the iJMP protocol.

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