A multi-party data joint inference method and system

Abstract

The application discloses a kind of multi-party data joint inference method and system, applied to first execution node and second execution node.The method comprises: based on trusted execution environment and hardware physical perturbation, generating orthogonal basis matrix on finite integer ring;Performing secret state protocol conversion operation, generating and distributing secret fragment between the execution node;According to the timing synchronization state identifier constructs rotation matrix, performs algebraic rotation update on orthogonal basis matrix and secret fragment on finite field;Real-time time series sensing data is projected to updated orthogonal basis matrix to generate plaintext projection coefficient, and the plaintext projection coefficient is used to perform modular addition aggregation operation with each updated secret fragment, and the joint inference result is output.The present application converts homomorphic encryption into additive secret sharing protocol, while preventing algebraic backpropagation and protecting parameter privacy, reduces the power consumption of processing high-frequency time series data, meets the real-time demand of inference.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, specifically to a method and system for joint reasoning of multi-party data. Background Technology

[0002] With the application of Industrial Internet of Things (IIoT) and artificial intelligence (AI) technologies, scenarios involving cross-node collaborative data inference are increasingly common. In multi-party collaborative inference processes, to prevent the leakage of local time-series sensor data and model weight parameters, multi-party secure computation methods such as homomorphic encryption are typically used to protect the data. However, homomorphic encryption and similar technologies involve complex algebraic operations, resulting in high overall computational overhead. When processing high-frequency sampled time-series sensor data, purely cryptographic schemes can lead to high communication and computational latency, making it difficult to meet the real-time inference requirements of scenarios such as joint monitoring of industrial equipment operating status.

[0003] To reduce computational latency, some existing solutions introduce trusted execution environments (TEAs) for hardware-level data isolation and collaborative computation. In such architectures, the software interfaces invoked by conventional TEAs during operations that rely on system entropy, such as generating random numbers, are susceptible to monitoring and tampering by external rich execution environments, leading to the disruption of the randomness of the underlying computational space. Simultaneously, during dimensionality reduction mapping and data exchange between nodes, the receiving node faces a security risk of using algebraic equivalence relations to deduce the underlying basis feature parameters of the sending end after decryption. Existing technologies lack an effective mechanism to convert computationally intensive homomorphic encryption protocols into lightweight encrypted computation protocols while ensuring the privacy of underlying feature parameters when crossing hardware isolation boundaries. This makes it difficult for the system to simultaneously maintain both the security level of data exchange and the inference efficiency of high-frequency time-series data. Summary of the Invention

[0004] The technical problem addressed by this invention is that existing multi-party data joint inference schemes, when dealing with data privacy and model parameter protection between cross-domain nodes, suffer from high computational overhead and difficulty in meeting the real-time inference requirements of time-series sensor data if they rely entirely on multi-party secure computation or homomorphic encryption technology. On the other hand, directly using a trusted execution environment at the software level for collaboration is susceptible to the influence of external rich execution environments tampering with the system entropy value, and there is a security risk that nodes may use algebraic relationships to infer the underlying base features, making it difficult to achieve an effective conversion from complex encrypted protocols to lightweight computation when crossing hardware isolation boundaries.

[0005] To address the above problems, the present invention provides the following technical solution: The first aspect of this invention provides a joint inference method for multi-party data, applied to a first execution node and a second execution node. The method includes: generating an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbation; performing a secret state protocol conversion operation to generate and allocate secret fragments between the first execution node and the second execution node; constructing a rotation matrix based on a time-series synchronization state identifier, and performing algebraic rotation updates on the orthogonal basis matrix and the secret fragments on the finite integer ring; projecting real-time time-series sensing data onto the updated orthogonal basis matrix to generate plaintext projection coefficients; performing modular aggregation operations using the plaintext projection coefficients and each updated secret fragment, and outputting a joint inference result.

[0006] Furthermore, the generation of an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbations includes: initiating an exclusive access request to the analog-to-digital converter via a hardware bus to establish an isolated data channel unmonitored by the rich execution environment; reading the steady-state physical hardware noise data of the analog-to-digital converter when there is no external valid signal input, extracting the least significant bit of the steady-state physical hardware noise data, and concatenating the least significant bits of multiple periods into a binary bit sequence; grouping and performing modulo operations on the binary bit sequence according to preset large integer parameters to generate a perturbation vector on the finite integer ring; calling a true random number generator within the trusted execution environment to generate random values ​​in the finite integer ring space, and using the random values ​​to fill matrix elements to construct an initial matrix whose dimensions satisfy the characteristics of the input data. Through the above steps, the extraction of steady-state physical hardware noise data introduces the inherent physical deviation of the underlying hardware, making the generated finite field basis bound to the current device hardware state; at the same time, using a physically isolated true random number generator to generate random values ​​avoids the risk of entropy tampering caused by the pseudo-random interface of the conventional operating system, providing a secure random mapping space for finite field algebraic operations.

[0007] Furthermore, the step of generating an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbation further includes: performing a modular addition operation on the perturbation vector and the first column vector of the initial matrix to achieve vector fusion of physical features; using the first column vector after fusion of the perturbation vector as a reference, performing orthogonal normalization processing on each dimension of the column vectors of the initial matrix on the finite integer ring to generate orthogonal column vectors; combining all the orthogonal column vectors to generate the orthogonal basis matrix, and writing the orthogonal basis matrix into a pre-allocated specified physical address range within secure memory; the memory management unit within the trusted execution environment is configured with an isolation strategy to block direct memory access requests initiated by the rich execution environment for the specified physical address range. Through the above steps, constrained algebraic mapping is performed on the finite integer ring, so that each column vector of the initial matrix satisfies the pairwise orthogonality condition under the modular arithmetic system, constructing a finite field coordinate system with hardware physical features; combined with the isolation strategy of the memory management unit, the data security of the orthogonal basis matrix is ​​ensured under physical isolation.

[0008] In a preferred embodiment of the present invention, when performing the orthogonal normalization process dimension by dimension, if it is determined that the current inner product value does not have a mathematical inverse with respect to the large integer parameter, or the corresponding value is a non-quadratic residue in the modulo sense, making it impossible to solve for the normalization coefficient of the square root of the modulus, then the current unnormalized orthogonal column vector parameter is discarded, and a true random number generator is called again to generate new random values ​​to replace the corresponding initial matrix column vectors and re-execute the algebraic calculation instructions until the orthogonal normalization process task of all dimensions is completed. By setting the above-mentioned regeneration and calculation rules to address the abnormal situation where there is no modular inverse or the value is a non-quadratic residue in the finite integer ring, loop blocking in algebraic calculations can be avoided, ensuring the continuous execution of the orthogonal normalization process.

[0009] Further, the execution of the encrypted protocol conversion operation to generate and allocate secret fragments between the first execution node and the second execution node includes: the second execution node performing element-wise encryption processing on the model weight vector it holds according to the public key of the additive homomorphic encryption algorithm to generate homomorphic ciphertext data, and sending the homomorphic ciphertext data to the rich execution environment of the first execution node; the rich execution environment inputting the homomorphic ciphertext data into the blinding module inside the trusted execution environment through a preset boundary pass-through interface; the blinding module extracting the orthogonal basis matrix in the trusted execution environment, and performing a homomorphic projection operation between the homomorphic ciphertext data and the orthogonal basis matrix on the finite integer ring to generate an encrypted projection result; wherein, the homomorphic projection operation is to use the encrypted scalar multiplication instruction and encrypted addition instruction supported by the additive homomorphic encryption algorithm to perform a dimensional inner product calculation on the model weight vector in the encrypted state and the orthogonal basis matrix in the plaintext state. Through the above steps, a data channel across hardware isolation boundaries is established using the boundary pass-through interface to maintain the integrity of encrypted data transmission; and through homomorphic projection operation, high-dimensional encrypted features are mapped to a finite domain subspace without leaking the plaintext information of the model weight vector, thereby realizing the dimensional transformation of encrypted features.

[0010] Furthermore, the step of performing the encrypted protocol conversion operation to generate and allocate secret fragments between the first execution node and the second execution node further includes: calling a hardware random number generator within the trusted execution environment to generate a random blinding vector in a finite integer ring space; performing a homomorphic type conversion of the random blinding vector in an encryption protocol-compatible format; using the converted blinding vector and the encrypted projection result to execute an encrypted superposition instruction to output a second secret ciphertext fragment, and sending it to the second execution node across nodes via a network communication link; calculating the modular inverse of the random blinding vector on the finite integer ring to generate a first secret fragment, and storing the first secret fragment in the secure memory; the second execution node using the private key matched by the additive homomorphic encryption algorithm to perform a cryptographic decryption operation on the second secret ciphertext fragment to obtain the second secret fragment in plaintext state. By superimposing the homomorphically converted random blinding vector onto the encrypted projection result, it is possible to prevent the second execution node from using algebraic relationships to reverse-engineer the orthogonal basis matrix parameters of the first execution node after decryption, thereby improving the security level of cross-domain interaction of encrypted data.

[0011] In a preferred embodiment of the present invention, the second secret fragment value of the plaintext state obtained by the decryption module is equivalent to the modular sum of the plaintext result corresponding to the encrypted projection result and the random blinding vector. This ensures that the result of the modular summation operation between the second secret fragment of the plaintext state and the first secret fragment stored in the secure memory is equivalent to the true value of the algebraic inner product between the transpose of the orthogonal basis matrix and the plaintext parameters of the model weight vector, thus satisfying the additive secret sharing equation. Based on the above algebraic equivalence relationship, the system converts the homomorphic encryption algorithm into an additive secret sharing protocol on a finite integer ring, removing the complex encrypted computation constraints of the original encryption algorithm and providing a foundation for performing distributed, fast modular summation aggregation operations.

[0012] A second aspect of the present invention provides a joint inference system for multi-party data, applied to a first execution node and a second execution node. The system includes: a basis generation module for generating an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbation; a secret state protocol conversion module for performing a secret state protocol conversion operation to generate and allocate secret fragments between the first execution node and the second execution node; an algebraic rotation update module for constructing a rotation matrix based on a time-series synchronization state identifier and performing algebraic rotation updates on the finite integer ring on the orthogonal basis matrix and the secret fragments; and an aggregation output module for projecting real-time time-series sensing data onto the updated orthogonal basis matrix to generate plaintext projection coefficients, performing modular aggregation operations using the plaintext projection coefficients and each updated secret fragment, and outputting joint inference results.

[0013] A third aspect of the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement each step of the multi-party data joint reasoning method described in any of the above embodiments.

[0014] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the joint reasoning method for multi-party data described in any of the above embodiments.

[0015] This invention provides a method and system for joint reasoning based on multi-party data. It has the following beneficial effects:

[0016] 1. This invention extracts the least significant bit by reading the steady-state physical hardware noise of the analog-to-digital converter, and generates an orthogonal basis matrix on a finite integer ring by combining it with a true random number generator within the trusted execution environment. Furthermore, it utilizes a memory management unit to shield the rich execution environment from direct access. This mechanism combines matrix parameters with the physical characteristics of the underlying hardware devices, avoiding the risk of system entropy tampering caused by using conventional operating system interfaces, and providing a physically isolated and secure operating foundation for cross-domain collaborative computing.

[0017] 2. This invention utilizes a blinding module within a trusted execution environment to generate random blinding vectors, executes a dense-state superposition instruction on the homomorphic projection result, outputs a second secret ciphertext fragment, and calculates the modular inverse to store the first secret fragment at a fixed point. This method introduces random noise into the computation result during the dense-state feature mapping process, causing the data decrypted by the receiver to lose the conditions for deriving the original matrix. This prevents cooperative nodes from using algebraic equivalence relations to infer the orthogonal basis parameters of their own end, thus ensuring privacy and security during cross-domain interactions.

[0018] 3. This invention utilizes a cryptographic protocol conversion mechanism to ensure that the decrypted second secret fragment and the first secret fragment in secure memory satisfy an additive secret sharing equation within a finite domain. Subsequently, matrix rotation updates are performed based on the time-series state identifier, and modular aggregation operations are executed with each fragment using plaintext projection coefficients. This scheme transforms computationally complex homomorphic encryption operations into an additive secret sharing protocol on a finite integer ring, reducing the computational power consumption when processing high-frequency time-series data and meeting the real-time requirements of multi-party data joint inference scenarios. Attached Figure Description

[0019] Figure 1 This is a diagram of the multi-party data joint reasoning system architecture of the present invention; Figure 2 This is a flowchart of the multi-party data joint reasoning method of the present invention; Figure 3 This is a schematic diagram illustrating the principle of generating orthogonal basis matrices based on a trusted execution environment according to the present invention. Figure 4 This is a schematic diagram illustrating the principle of secret state protocol conversion and secret fragment allocation in this invention. Detailed Implementation

[0020] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] refer to Figures 1 to 4The present invention provides a multi-party data joint reasoning system, which may include a first execution node and a second execution node.

[0022] The fundamental algebraic operations within the multi-party data joint inference system are constructed based on a finite integer ring. The system pre-defines the finite integer ring space using large integer parameters. The first execution node holds the real-time temporal sensor data vector to be processed. The second execution node holds the specified model weight vector.

[0023] The physical memory and processor computing resources of the first execution node are divided into a rich execution environment and a trusted execution environment at the hardware level. The first execution node has an analog-to-digital converter for acquiring external physical signals. The trusted execution environment establishes an exclusive communication connection with the analog-to-digital converter through a hardware bus.

[0024] The Trusted Execution Environment (TEE) is internally configured with secure memory and a secure real-time clock. The secure memory is hardware-independent of the rich execution environment's system memory. The TEE has access control policies in place to block out-of-bounds memory read requests initiated by the rich execution environment.

[0025] The trusted execution environment of the first execution node is internally deployed with a perturbation extraction module, an orthogonalization module, a blinding module, a synchronous rotation module, and a first aggregation module.

[0026] The second execution node is equipped with a decryption module, a collaborative rotation module, and a second aggregation module.

[0027] The perturbation extraction module reads the physical hardware noise data of the analog-to-digital converter via the hardware bus and converts the physical hardware noise data into a perturbation vector on a finite integer ring.

[0028] The orthogonalization module receives the perturbation vector output by the perturbation extraction module and uses it in conjunction with an internal pseudo-random number generator to generate an initial matrix. The orthogonalization module then performs a constrained algebraic mapping on the initial matrix over a finite integer ring to generate orthogonal basis matrices. Finally, the orthogonalization module stores these orthogonal basis matrices in fixed-point memory.

[0029] The blinding module receives homomorphic ciphertext data from the second execution node through a transparent interface of the rich execution environment. The blinding module performs a homomorphic projection operation between the ciphertext data and the orthogonal basis matrix on a finite integer ring. The blinding module then generates a blinding vector and performs a secret addition operation, outputting a first secret fragment and a second secret ciphertext fragment. The first secret fragment is truncated and stored in secure memory. The second secret ciphertext fragment is output to the second execution node.

[0030] The decryption module of the second execution node receives the second secret ciphertext fragment, performs a private key decryption operation to obtain the second secret fragment in plaintext state, and stores the second secret fragment locally.

[0031] The synchronous rotation module reads the clock tick parameters of the secure real-time clock to generate a time-series window identifier. Based on the time-series window identifier, the synchronous rotation module constructs an orthogonal rotation matrix on a finite integer ring. The synchronous rotation module then uses the orthogonal rotation matrix to perform a modular multiplication update on the orthogonal basis matrix in secure memory and the first secret slice.

[0032] The cooperative rotation module of the second execution node generates a mirror orthogonal rotation matrix using the same time-series window identifier as the synchronous rotation module. The cooperative rotation module then uses the mirror orthogonal rotation matrix to perform a modular multiplication update on the second secret fragment stored in the decryption module.

[0033] After receiving the real-time timing sensor data vector, the first execution node directly inputs it into the trusted execution environment. The trusted execution environment uses the updated orthogonal basis matrix to perform projection operations on the real-time timing sensor data vector, generating plaintext projection coefficients on a finite integer ring, and then sends the plaintext projection coefficients to the second execution node.

[0034] The first aggregation module performs a modular product operation using the plaintext projection coefficients and the updated first secret fragment to generate the first local inference value.

[0035] The second aggregation module performs a modular product operation using the received plaintext projection coefficients and the updated second secret fragment to generate a second local inference value. The system then outputs the final joint inference result by performing a modular addition operation on the first and second local inference values.

[0036] This invention provides a multi-party data joint inference method, comprising the following steps: S100, generating an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbation; S200, performing a secret state protocol conversion operation to generate and allocate secret fragments between a first execution node and a second execution node; S300, constructing a rotation matrix based on a time-series synchronization state identifier, and performing algebraic rotation updates on the orthogonal basis matrix and the secret fragments on a finite integer ring; S400, projecting real-time time-series sensing data onto the updated orthogonal basis matrix to generate plaintext projection coefficients, and performing modular aggregation operations using the plaintext projection coefficients and each updated secret fragment to output the joint inference result.

[0037] As an optional implementation of the technical solution of the present invention, step S100, which generates an orthogonal basis matrix on a finite integer ring based on a trusted execution environment and hardware physical perturbation, may specifically include the following sub-steps.

[0038] S110, the perturbation extraction module of the first execution node initiates an exclusive access request to the analog-to-digital converter via the hardware bus, establishing an isolated data channel unaffected by the rich execution environment monitoring; the perturbation extraction module 11 reads the steady-state physical hardware noise data of the analog-to-digital converter when there is no external valid signal input through the isolated data channel, extracts the least significant bit of the steady-state physical hardware noise data, and concatenates the least significant bits of multiple cycles into a binary bit sequence; the purpose of the perturbation extraction module in extracting the steady-state physical hardware noise data is to capture the inherent underlying hardware random deviation of the current physical device, so that the substrate generated in the subsequent process carries the device's unique identity characteristics; the perturbation extraction module performs grouping and modulo operations on the binary bit sequence according to preset large integer parameters, generating a perturbation vector on a finite integer ring, and the algebraic transformation logic of the perturbation vector can be expressed as follows: In the formula, The system is pre-defined with large integer parameters for defining the space of finite integer rings. The boundary of the plaintext space is usually determined based on the homomorphic encryption algorithm used by the system. For example, it can be selected as a prime number with a bit width of 256 bits. For the generated perturbation vector, the first... Each component parameter The bit width parameter is the bit width length parameter in a single dimension of the truncated binary bit sequence. The value is determined by the hardware sampling bit width precision of the analog-to-digital converter; for example, it can be set to a value of 8 or 16. The corresponding bit state value is extracted from the steady-state physical hardware noise data.

[0039] S120, the orthogonalization module of the first execution node calls the true random number generator inside the trusted execution environment to generate random values ​​within a finite integer ring space. The orthogonalization module uses the generated random values ​​to fill matrix elements, constructing an initial matrix whose dimensions satisfy the characteristics of the input data. The step of constructing the initial matrix aims to provide a random mapping space with a basic distribution state for restricted finite field algebraic operations. The process of generating the initial matrix uses a physically isolated hardware generator and does not rely on the pseudo-random interface of the conventional operating system to prevent entropy tampering by the external environment. The mathematical expression of the initial matrix is ​​as follows: In the formula, Let the parameters be the initial matrix generated on the finite integer ring. The parameters of each column vector that constitute the initial matrix, The projection subspace dimension value is set for the system. The value range of the projection subspace dimension value kk is set to be an integer greater than 0 and less than or equal to the total feature dimension of the subsequently input real-time time-series sensing data.

[0040] S130, the orthogonalization module injects the perturbation vector generated by the perturbation extraction module as a higher-order constraint condition into the initial matrix and performs constraint algebraic mapping on the finite integer ring. Specifically, the orthogonalization module performs modular addition on the perturbation vector and the first column vector of the initial matrix to achieve vector fusion of physical features. Then, using the first column vector after fusion of the perturbation vector as the reference, orthogonal normalization is performed dimension by dimension on the finite integer ring. The logical principle of the constraint algebraic mapping step is to make each column vector in the originally random initial matrix present a pairwise orthogonal perpendicular state under the modular arithmetic system, thereby constructing a finite field coordinate system with hardware characteristics. The algorithm of constraint algebraic mapping is expressed as follows: In the formula, The parameters of the first orthogonal column vector after binding the perturbation vector. The parameter is the first column vector in the initial matrix. For the parameters of the generated perturbation vector, For the first An unnormalized orthogonal column vector parameter, For the first in the initial matrix One column vector parameter, The inner product value is represented by the inverse symbol, which indicates the modular inverse parameter of the inner product value over the finite ring of integers. For the first A normalized orthogonal column vector parameter, To satisfy the equation The normalized coefficients of the modular square root are used to ensure the complete and coherent operation of algebraic calculations within a finite field system and to avoid logical dead zones. When calculating the modular inverse parameter and the normalized coefficients of the modular square root, if the orthogonalization module determines that the current inner product value is relative to large integer parameters... There is no mathematical inverse, or the corresponding value is modulo 1. In the case of non-quadratic residues, the normalization coefficient parameters cannot be solved by the square root modulus. The orthogonalization module will discard the current unnormalized orthogonal column vector parameters and call the true random number generator again to generate new random values ​​to replace the corresponding initial matrix column vectors and re-execute the algebraic calculation instructions until the orthogonal normalization processing task of all dimensions is completed.

[0041] All orthogonal column vectors generated by the orthogonalization module through constrained algebraic mapping are combined to form an orthogonal basis matrix, which satisfies the following orthogonality condition: In the formula, The parameters for the generated orthogonal basis matrix are... For dimension equal to The identity matrix parameter, the equation corresponding to the orthogonality condition, represents the modular multiplication of the transpose of the orthogonal basis matrix with the orthogonal basis matrix. In a sense, it is equivalent to the identity matrix.

[0042] S140, the orthogonalization module writes the orthogonal basis matrix generated by the constraint algebra mapping into a pre-allocated specified physical address range within the secure memory; the memory management unit within the trusted execution environment configures an isolation policy to block direct memory access requests initiated by the rich execution environment for the specified physical address range, aiming to ensure that the orthogonal basis matrix resides in a physically isolated state; the specific memory access control mechanism for address space isolation of secure memory by the trusted execution environment can be set according to the existing trusted execution environment hardware isolation technology specifications.

[0043] As an optional implementation of the technical solution of the present invention, the step S200 of performing the secret protocol conversion operation to generate and allocate secret fragments between the first execution node and the second execution node may specifically include the following sub-steps.

[0044] S210, as a specific application scenario, is a multi-party data joint inference system used to perform joint detection tasks of abnormal operating status of industrial equipment. The second execution node is deployed with an anomaly evaluation model built on a multilayer perceptron architecture. This model includes at least one input feature mapping layer for receiving underlying physical signals. The input feature mapping layer has corresponding weight network nodes. The second execution node performs element-wise encryption on the model weight vector held by it using the public key of an additive homomorphic encryption algorithm, generating homomorphic ciphertext data. The model weight vector consists of linear weight parameters of the input feature mapping layer, and the total number of feature dimensions of the model weight vector is proportional to the linear weight parameters of the input feature mapping layer. The number of sampling channels of the front-end sensors of industrial equipment remains consistent; the second execution node sends homomorphic encrypted data to the rich execution environment of the first execution node through a network communication link; the rich execution environment inputs the homomorphic encrypted data into the blinding module inside the trusted execution environment through a preset boundary pass-through interface; the configuration of the boundary pass-through interface is to establish a data channel between isolated environments and ensure the continuity of data flow when encrypted data crosses the hardware security boundary; the specific encryption logic of the additive homomorphic encryption algorithm and the underlying configuration method of the data input interface of the trusted execution environment can be called according to the existing homomorphic encryption technology specifications and the trusted execution environment standard operating specifications.

[0045] S220, the blinding module extracts the orthogonal basis matrix stored in secure memory within the trusted execution environment; the blinding module performs a homomorphic projection operation on the homomorphic ciphertext data and the orthogonal basis matrix on a finite integer ring; the homomorphic projection operation has the function of mapping high-dimensional ciphertext model features to a finite field subspace composed of orthogonal basis matrices without revealing the plaintext information of the model weight vector, which is used to achieve dimensionality reduction of the ciphertext features; since the orthogonal basis matrix is ​​represented in plaintext state within the trusted execution environment, the homomorphic projection operation is essentially a finite field ciphertext operation combination between the ciphertext model weight vector and the plaintext basis column vector; the blinding module calls the ciphertext addition instruction and ciphertext scalar multiplication instruction supported by the addition homomorphic encryption algorithm to perform dimensional inner product calculation. The specific implementation logic of the ciphertext scalar multiplication instruction is to perform a corresponding number of homomorphic self-addition operations on the ciphertext elements as scalar control parameters. The algebraic expansion formula corresponding to the homomorphic projection operation is expressed in the following form: In the formula, For the generated dense projection result, the first Each encrypted column vector parameter The total number of feature dimensions in the model weight vector is a parameter. The th in the orthogonal basis matrix Line and number Plain text scalar parameters at column intersections, symbols This represents the encrypted scalar multiplication operator in the additive homomorphic encryption system. For the corresponding homomorphic ciphertext data Ciphertext weight parameters for each feature dimension, symbol This represents the encrypted addition operator based on finite field configuration in the additive homomorphic encryption system. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0046] S230, the blinding module calls the hardware random number generator within the trusted execution environment to generate a random blinding vector within a finite integer ring space. This random blinding vector generation is used to superimpose random noise variables onto the homomorphic projection operation result at the encrypted state level, preventing the second execution node from using algebraic relationships to reverse-engineer the orthogonal basis matrix characteristic parameters of the first execution node after decryption. The blinding module performs a homomorphic type conversion in an encryption protocol-compatible format on the random blinding vector, and uses the converted blinding vector and the encrypted projection result generated by the homomorphic projection operation to execute an encrypted superposition instruction, outputting the second secret ciphertext fragment. The algebraic equation representing the generated secret fragment is as follows: In the formula, For the generated second secret ciphertext fragmentation parameters, The parameters are the dense-state projection vector parameters, which are composed of all the ciphertext column vector parameters. The parameters of the ciphertext blinding vector are mapped into the cryptographic space after the random blinding vector undergoes a homomorphic transformation.

[0047] S240, the blinding module calculates the modular inverse of the random blinding vector on a finite integer ring to generate the first secret slice; the blinding module truncates and stores the first secret slice in a fixed-point physical address space within secure memory, and the algebraic equation corresponding to the first secret slice is: In the formula, The parameters for the first secret fragment generated, For the parameters of the randomized blinding vector, The parameters are preset as large integers. The blinding module outputs the second secret ciphertext fragment to the rich execution environment through the boundary pass-through interface, and sends it to the second execution node across nodes via the network communication link. The decryption module of the second execution node receives the second secret ciphertext fragment, calls the private key matched by the addition homomorphic encryption algorithm to perform cryptographic decryption on the second secret ciphertext fragment, and obtains the second secret fragment in plaintext state. The decryption module writes the second secret fragment into the local storage medium of the second execution node. The cryptographic protocol conversion and blinding operation make the first secret fragment and the second secret fragment algebraically satisfy the addition secret algorithm. Based on the homomorphic mapping theorem on the finite integer ring, the value of the second secret piece of the plaintext state obtained by the decryption module is equivalent to the modulo sum of the plaintext result corresponding to the secret projection vector parameter and the randomized blinding vector parameter. This makes the result of the modulo summation of the second secret piece of the plaintext state and the first secret piece stored in secure memory equivalent to the true value of the algebraic inner product between the transpose of the orthogonal basis matrix and the plaintext parameter of the model weight vector. This equivalence relationship provides the necessary mathematical foundation for the subsequent steps of distributed fast verification under the condition of removing complex homomorphic cryptographic constraints.

[0048] As an optional implementation of the technical solution of the present invention, the step S300 of constructing a rotation matrix based on the timing synchronization state identifier and performing algebraic rotation update on the orthogonal basis matrix and the secret piece on a finite integer ring may specifically include the following sub-steps.

[0049] S310, the synchronization rotation module of the first execution node reads the hardware tick value of the secure real-time clock configured inside the trusted execution environment; the hardware tick value is a monotonically increasing timestamp value that is tamper-proof; the synchronization rotation module performs a division operation on the hardware tick value and a preset time window length parameter and rounds down to generate a time sequence window identifier corresponding to the current time period of the secure real-time clock; to solve the problem of misaligned identifier generation caused by the asynchrony of the underlying hardware clocks between heterogeneous nodes, the value range of the preset time window length parameter is set to be greater than the maximum physical offset of the hardware clock between the first execution node and the second execution node. For example, the preset time window length parameter can be set to a value of 300 seconds or 600 seconds, thereby using a wide time sliding window to truncate the small asynchronous error of the underlying clock; the time sequence window identifier is used to provide a consistent pseudo-random number seed state for multiple distributed execution nodes under the condition of lack of network communication interaction; the specific clock synchronization mechanism and hardware protection implementation method of the secure real-time clock can be configured according to the existing trusted execution environment secure clock protocol specification.

[0050] S320, the synchronous rotation module inputs the time series window identifier as the initial seed parameter into the pseudo-random function module configured in the synchronous rotation module, generating a dimension-matched pseudo-random matrix within the finite integer ring space; the synchronous rotation module performs a finite field orthogonalization operation on the pseudo-random matrix to generate an orthogonal rotation matrix. The operation of generating the orthogonal rotation matrix aims to perform dynamic algebraic obfuscation transformation on the underlying algebraic matrix and secret slices to resist side-channel feature extraction attacks targeting fixed feature dimensions; the orthogonal constraint condition of the orthogonal rotation matrix on the finite integer ring is expressed as the following mathematical relationship: In the formula, The parameters for the generated orthogonal rotation matrix are... These are the transpose matrix parameters corresponding to the orthogonal rotation matrix parameters. For dimension equal to The identity matrix parameter, The dimension value of the projection subspace set for the system. The system predefines large integer parameters for defining the finite integer ring space. The equation corresponding to the orthogonal constraint condition indicates that the modular multiplication operation between the orthogonal rotation matrix parameter and the transpose matrix parameter corresponding to the orthogonal rotation matrix parameter is performed in the modular... In a sense, it is equivalent to the identity matrix.

[0051] S330, the synchronous rotation module uses an orthogonal rotation matrix to perform a modular multiplication update instruction on a finite integer ring on the orthogonal basis matrix residing in secure memory, generating an updated orthogonal basis matrix; the synchronous rotation module simultaneously uses the orthogonal rotation matrix to perform a modular multiplication update instruction on a finite integer ring on the first secret piece stored in secure memory, generating an updated first secret piece; the underlying principle of the synchronous rotation module's algebraic rotation update is to use the orthogonality property of the orthogonal rotation matrix as a mathematical cancellation term, so that the updated orthogonal basis matrix and the updated first secret piece undergo a dynamic transformation in numerical representation over time. However, in the subsequent aggregation stage, the orthogonal rotation matrix and its transpose contained in the multiplication between the basis matrix and the secret piece will cancel each other out, thereby achieving obfuscation defense against static data without changing the underlying algebraic inner product characteristics; the synchronous rotation module's local state modular multiplication update process does not require data interaction across network boundaries, which can reduce communication latency and data leakage risks during the update process. The algebraic expression for the first execution node's modular multiplication update is expressed as follows: In the formula, The parameters for the latest updated orthogonal basis matrix are generated. The parameters of the orthogonal basis matrix currently stored in safe memory. The parameters for the generated orthogonal rotation matrix are... For the latest updated first secret shard parameters generated, These are the transpose matrix parameters corresponding to the orthogonal rotation matrix parameters. The first secret fragment parameter currently stored in secure memory. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0052] S340, the cooperative rotation module of the second execution node obtains the current system timestamp value using the network time protocol synchronization mechanism configured locally on the second execution node; the cooperative rotation module performs a division and rounding operation on the current system timestamp value using a preset time window length parameter consistent with the synchronous rotation module, generating a time series window identifier corresponding to the first execution node; the cooperative rotation module inputs the time series window identifier as a seed into the pseudo-random function module configured in the cooperative rotation module to generate a mirror pseudo-random matrix; the cooperative rotation module performs a finite field orthogonalization operation on the mirror pseudo-random matrix consistent with the synchronous rotation module, outputting a mirror orthogonal rotation matrix; the cooperative rotation module uses the mirror orthogonal rotation matrix to perform a modular multiplication update instruction on the second secret piece stored in the decryption module on the finite integer ring, generating an updated second secret piece; the algebraic expression for the modular multiplication update performed by the second execution node is expressed in the following form: In the formula, For the latest updated second secret shard parameters generated, These are the transpose matrix parameters corresponding to the parameters of the mirror orthogonal rotation matrix. The second secret fragmentation parameter is the plaintext state stored by the decryption module; due to the consistent time series window identifier generation process executed by the cooperative rotation module and the synchronous rotation module, and the preset time window length parameter's tolerance configuration for underlying clock errors, the consistency of the time series window identifier is guaranteed. The transpose matrix parameter corresponding to the mirror orthogonal rotation matrix parameter is algebraically consistent with the transpose matrix parameter corresponding to the orthogonal rotation matrix parameter, thereby ensuring the mathematical state alignment of the first execution node and the second execution node under zero network communication conditions.

[0053] As an optional implementation of the technical solution of the present invention, the step S400 of projecting real-time time-series sensing data onto the updated orthogonal basis matrix to generate plaintext projection coefficients, and using the plaintext projection coefficients and each updated secret fragment to perform modular aggregation operation to output joint inference results may specifically include the following sub-steps.

[0054] S410, the feature projection module of the first execution node is configured with a direct memory access mapping mechanism based on the peripheral component interconnection extension protocol to establish a hardware direct channel between the physical sensor and the trusted execution environment. Real-time timing sensor data collected by the physical sensor is written to the protected memory area inside the trusted execution environment through the hardware direct channel. Those skilled in the art should know that in specific industrial joint detection scenarios, the real-time timing sensor data includes multi-channel vibration acceleration data and temperature distribution time-series data generated by industrial equipment during operation. After time window slicing preprocessing within the trusted execution environment, the real-time timing sensor data forms a fixed-dimensional feature input vector. The total number of dimensions of the feature input vector is strictly... The number of input feature mapping layer nodes is aligned with the number of nodes in the anomaly evaluation model held by the second execution node. The above-mentioned hardware direct access channel configuration allows real-time timing sensing data to completely bypass the operating system kernel mode and user mode network stack inside the rich execution environment at the data transmission level. The purpose of establishing the hardware direct access channel is to prevent potential malicious programs inside the rich execution environment from eavesdropping on and tampering with real-time timing sensing data, thereby ensuring the original physical credibility of the input data of the multi-party data joint inference system. For the underlying hardware isolation allocation of the peripheral interconnect communication bus and the specific underlying configuration method of the direct memory access logic, the parameters can be set according to the existing trusted execution environment hardware isolation instruction set technical specifications.

[0055] S420, the feature projection module extracts real-time timing sensor data from the protected memory region within the trusted execution environment, and simultaneously extracts the latest updated orthogonal basis matrix parameters currently residing in the secure memory. Within a finite integer ring space, the feature projection module performs matrix multiplication projection operations on the real-time timing sensor data using the latest updated orthogonal basis matrix parameters, generating a dimension-compressed plaintext projection coefficient parameter vector. Because the projection calculation is executed independently within an isolated environment protected by the underlying hardware, even if the plaintext projection coefficient parameter vector is subsequently exported and removed from the trusted execution environment, external attackers will find it difficult to reverse-engineer the original real-time timing sensor data features without the underlying hardware physical noise perturbation parameters and the initial true random number seed. The modular arithmetic expression corresponding to the projection calculation performed by the feature projection module is expressed in the following form: In the formula, For the generated plaintext projection coefficient parameter vector, The parameters are the transpose of the latest updated orthogonal basis matrix parameters. These are the feature vector parameters corresponding to real-time time-series sensing data. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0056] S430, the feature projection module outputs the plaintext projection coefficient parameter vector to the network communication component of the first execution node via the encrypted secure channel configured in the trusted execution environment, and sends it to the second execution node via the network communication link; the aggregation inference module of the first execution node extracts the latest updated first secret fragment parameters from the secure memory, performs a vector inner product operation on a finite integer ring with the plaintext projection coefficient parameter vector and the latest updated first secret fragment parameters, and generates a first local inference value; the joint inference module of the second execution node receives the plaintext projection coefficient parameter vector, extracts the latest updated second secret fragment parameters stored locally in the second execution node, and synchronously performs a vector inner product operation on a finite integer ring with the plaintext projection coefficient parameter vector and the latest updated second secret fragment parameters, and generates a second local inference value. The algebraic expression of the local vector inner product operation performed by the first execution node and the second execution node to generate local inference values ​​is as follows: In the formula, The first local inference numerical parameters generated for the first execution node. The transpose vector parameter corresponding to the plaintext projection coefficient parameter vector. For the latest updated first secret shard parameters, The second local inference numerical parameters generated for the second execution node. For the latest updated second secret sharding parameters, The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0057] S440, the aggregation inference module of the first execution node sends the first local inference numerical parameters to the second execution node; the joint inference module of the second execution node performs direct modular addition on a finite integer ring on the first and second local inference numerical parameters, outputting the final joint inference result value. In specific business scenarios, the joint inference result value represents the neuron activation response value of the corresponding hidden layer in the multilayer perceptron architecture used by the anomaly assessment model. The joint inference result value is used to directly indicate the current operating status of industrial equipment and assess physical indicators. Specifically, the joint inference module uses a classification function to classify the joint inference result... The numerical result is mapped to an anomaly probability value. When the anomaly probability value exceeds the preset operational safety threshold, an equipment shutdown warning command is generated and issued. Regarding the source of the anomaly assessment model, the model weight parameters of its plaintext state are obtained by the second execution node using a historical operational feature dataset of industrial equipment labeled with normal operation and mechanical failure states, and by performing backpropagation iterative optimization training using the cross-entropy loss function. To verify the mathematical consistency between the distributed aggregation calculation results and the centralized plaintext calculation results to ensure that the model output is not distorted, as a preferred implementation state for ensuring lossless and accurate inference in this disclosure, the system pre-sets the projection subspace dimension value... Strictly equal to the total number of feature dimensions parameter Under the given conditions, the mathematical equivalence derivation logic of the system configuration proves that the result of the local modular addition operation is rigorously equivalent to the algebraic inner product of the original input feature vector and the original plaintext model weights. The complete algebraic equivalence derivation process is as follows: Due to the strict alignment mechanism of the time series window identifiers, the transpose of the mirror orthogonal rotation matrix parameter is numerically equivalent to the transpose of the orthogonal rotation matrix parameter. Furthermore, the orthogonal rotation matrix parameter itself, based on the orthogonal constraint, satisfies that the product of the orthogonal rotation matrix parameter and its transpose is equivalent to the identity matrix parameter on a finite integer ring. The complete algebraic equivalence derivation process is further simplified and converges to: Based on the additive secret sharing equation between the first and second secret fragmentation parameters, their addition over a finite field cancels out the blinding noise component. This modulo sum is equivalent to the projection result vector parameter of the plaintext state corresponding to the homomorphic projection operation, which is equivalent to the algebraic product of the transpose matrix parameter of the orthogonal basis matrix parameter and the model weight vector parameter of the plaintext state. Furthermore, based on the constraint that the orthogonal basis matrix parameters possess the property of being full-dimensional orthogonal matrices under the configuration constraint that the dimension of the projected subspace equals the total dimension of the features, the multiplication of the orthogonal basis matrix parameters with their own transpose matrix parameters is equivalent to the identity matrix: In the formula, The final numerical value of the joint inference result is output. This is the transpose of the feature vector parameters corresponding to the real-time time-series sensing data. The parameters are the orthogonal basis matrix. The parameters are the orthogonal rotation matrix. These are the transpose matrix parameters corresponding to the orthogonal rotation matrix parameters. These are the transpose matrix parameters corresponding to the parameters of the mirror orthogonal rotation matrix. For the first secret sharding parameters, For the second secret fragmentation parameters, These are the transpose matrix parameters corresponding to the orthogonal basis matrix parameters. The model weight vector parameters of the plaintext state originally held by the second execution node are given. The result at the end of the equation derivation clearly proves that through the time-series synchronous rotation mechanism and finite field protocol conversion operation, without reconstructing the basic orthogonal basis matrix and without transmitting any plaintext model weights across nodes, the sum of the local computation values ​​distributed on the two physically isolated nodes is directly equivalent to the real algebraic inner product of the real-time time-series sensing data and the plaintext model weights.

[0058] As an optional implementation of the technical solution of the present invention, the step S500 of extracting the underlying hardware features to generate the perturbation vector may specifically include the following sub-steps.

[0059] S510, the perturbation extraction module of the first execution node is configured in a secure hardware area protected by a physical isolation boundary within the Trusted Execution Environment (TEE). The perturbation extraction module establishes a dedicated hardware bus that crosses the physical isolation boundary. The perturbation extraction module is directly connected to the output pin of the analog-to-digital converter integrated on the motherboard of the first execution node via the dedicated hardware bus, constructing a unidirectional hardware-level signal reading path for the dedicated hardware bus. The dedicated hardware bus is physically isolated from the network interface adapter of the TEE control of the first execution node at the motherboard routing level to prevent unauthorized direct memory access attacks. The physical layer isolation routing specifications of the dedicated hardware bus and the point-to-point soldering configuration of the motherboard pins can be implemented according to existing TEE hardware security design specifications.

[0060] In the S520, the analog-to-digital converter continuously acquires thermal noise analog signals and clock jitter analog signals from the underlying hardware circuitry under the condition that the device power supply voltage of the first execution node is in a steady state. The analog-to-digital converter performs discretization sampling on the thermal noise analog signals and clock jitter analog signals and outputs steady-state physical hardware noise data, which is a digital time series containing random small fluctuations. The perturbation extraction module reads the steady-state physical hardware noise data through the dedicated hardware bus and writes and caches the steady-state physical hardware noise data into the secure memory inside the trusted execution environment.

[0061] S530, the perturbation extraction module extracts steady-state physical hardware noise data from secure memory. The perturbation extraction module calls its built-in cryptographically secure hash function to perform digest calculations on the steady-state physical hardware noise data, generating a basic hash bit string. The perturbation extraction module, combined with a deterministic random bit generator, expands the basic hash bit string into an initial bit sequence matching the system subspace dimension. The perturbation extraction module uses a rejection sampling algorithm to perform multiple rounds of independent modulo and discard operations on the initial bit sequence within a finite integer ring space until a final perturbation vector satisfying uniform distribution characteristics is output. The underlying principle of the rejection sampling logic configured in the perturbation extraction module is to eliminate the inherent modulo deviation caused by the non-integer multiple relationship between the binary truncation length of the basic hash bit string and the large integer modulus parameter, thereby strictly ensuring the cryptographic security of the perturbation vector. The algebraic expression corresponding to the quantization transformation of the steady-state physical hardware noise data performed by the perturbation extraction module is expressed in the following form: In the formula, The parameters of the generated perturbation vector mapped onto a finite integer ring, The extraction length configured for the perturbation extraction module is equal to the dimension parameter. The logic of the rejection sampling function. This refers to the cryptographically secure hash function operation logic built into the perturbation extraction module. The digital sequence parameters corresponding to the steady-state physical hardware noise data. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0062] As an optional implementation of the technical solution of the present invention, the step S600 of the orthogonalization module fusing physical hardware features to generate an algebraic basis over a finite field may specifically include the following sub-steps.

[0063] S610, the orthogonalization module of the first execution node extracts the perturbation vector parameters generated by the perturbation extraction module and mapped onto the finite integer ring; the orthogonalization module calls the true random number generator configured inside the trusted execution environment to generate seed data, and the orthogonalization module inputs the seed data into the pseudo-random number generator configured in the orthogonalization module to generate initial matrix parameters on the finite integer ring that have full rank characteristics and whose number of matrix rows is strictly equal to the total dimension parameter of the input features of the multi-party data joint inference system and whose number of matrix columns is strictly equal to the dimension parameter of the projection subspace of the multi-party data joint inference system; the underlying implementation protocol of the pseudo-random number generator and the configuration method of the physical entropy source of the seed data can be set according to the existing trusted execution environment cryptographic algorithm standard library.

[0064] S620, the orthogonalization module performs a perturbation-constrained finite field mapping algorithm on the initial matrix parameters to generate orthogonal basis matrix parameters. The specific execution sequence of the orthogonalization module performing the perturbation-constrained finite field mapping algorithm is as follows: the orthogonalization module replaces the first column vector of the initial matrix parameters with the perturbation vector parameters as the initial basis vectors; the orthogonalization module sequentially performs finite field Schmitt orthogonalization operations on the remaining column vectors of the initial matrix parameters within the finite field space defined by the large integer prime parameter to eliminate the linear dependence between the column vectors of the initial matrix parameters; those skilled in the art should know that the mathematical essence of multiple vectors being mutually orthogonal in the finite integer ring space is that the algebraic inner product of any two different vectors is strictly congruent to zero by the large integer prime parameter; to avoid the algorithm dead zone caused by the absence of quadratic residues in the vector self-inner product within the finite field space, which prevents the execution of the normalized square root operation, the orthogonalization module is configured with a quadratic residue judgment and rejection sampling loop mechanism during the execution of the finite field Schmitt orthogonalization operation. When the inner product value of the current column vector is found to lack the quadratic residue property in the finite field space, the orthogonalization module discards the current column vector and calls the pseudo-random number generator to regenerate a replacement column vector until the unity orthogonalization condition is met. The orthogonalization module outputs the final orthogonal basis matrix parameters through a finite field mapping algorithm with perturbation constraints. The specific purpose of the orthogonalization module in generating orthogonal basis matrix parameters by integrating physical hardware features in the finite field space is that, by using perturbation vector parameters with unpredictable characteristics as non-deterministic constraints in the orthogonal basis matrix parameter generation process, the generated orthogonal basis matrix parameters form a deep mathematical binding with the specific underlying physical hardware state of the first execution node. While ensuring the physical non-cloning property of the orthogonal basis matrix parameters, the orthogonalization module also enhances the ability of the multi-party data joint inference system to resist side-channel attacks against static algebraic structures. The algebraic expression corresponding to the finite field mapping algorithm with perturbation constraints executed by the orthogonalization module is expressed in the following form: In the formula, The parameters for the generated orthogonal basis matrix are... The orthogonalization module is configured with the computational logic of a finite field orthogonalization mapping algorithm with quadratic residue judgment, using the perturbation vector parameters as the first column constraint. The perturbation vector parameters generated by the perturbation extraction module. The initial matrix parameters are generated by calling the pseudo-random number generator in the orthogonalization module. The system is pre-defined with large integer parameters that define a finite integer ring space and possess the property of large prime numbers.

[0065] S630, the orthogonalization module locks the generated orthogonal basis matrix parameters in secure memory within the trusted execution environment. The orthogonalization module configures storage control logic, using the hardware-level memory management unit integrated on the first execution node motherboard to set the physical memory pages containing the orthogonal basis matrix parameters to a state where swapping out is prohibited and access is restricted to the trusted execution environment only. The specific purpose of configuring storage control logic in the orthogonalization module is to prevent the operating system kernel mode within the rich execution environment from stealing the plaintext values ​​of the orthogonal basis matrix parameters by exploiting memory dump vulnerabilities or memory page swapping mechanisms. The orthogonalization module uses a physical isolation storage strategy to improve the security of the underlying cryptographic state of the multi-party data joint inference system.

[0066] As an optional implementation of the technical solution of the present invention, the blinding module of the first execution node 10 executes step S700 corresponding to the pre-calculation logic of the dense state protocol conversion, which may specifically include the following sub-steps.

[0067] S710, the blinding module of the first execution node is configured with a boundary penetration interface with one-way verification characteristics between the trusted execution environment and the rich execution environment of the first execution node 10. To clarify the business scenario and data processing link of the multi-party data joint inference system, the anomaly evaluation model held by the second execution node is configured as a three-layer multilayer perceptron architecture for processing multi-channel vibration characteristics of industrial equipment. The input layer of the anomaly evaluation model receives vibration feature vectors of fixed dimensions, the hidden layer extracts nonlinear features, and the output layer outputs the probability distribution results representing the normal or faulty physical state of the equipment through a normalized exponential function. The plaintext model weight parameters of the anomaly evaluation model are pre-determined by the second execution node using a historical operating state feature sample set of the industrial equipment combined with a cross-entropy loss function. The data is obtained through iterative training. The second execution node encrypts the plaintext model weight parameters corresponding to the hidden layer of the anomaly evaluation model using a homomorphic encryption public key to generate homomorphic ciphertext data. The second execution node sends the homomorphic ciphertext data to the first execution node via a network communication link. The blinding module receives the homomorphic ciphertext data sent by the second execution node through the boundary penetration interface. The flow control method configured in the blinding module requires that the homomorphic ciphertext data maintains its encrypted state and is not unpacked when crossing the rich execution environment, and is directly written to secure memory only after data integrity verification is completed within the trusted execution environment. The key generation protocol of the homomorphic encryption system and the configuration of the underlying data copy function of the boundary penetration interface can be implemented according to the existing homomorphic encryption algorithm standards and the trusted execution environment secure cross-border communication specifications.

[0068] In the S720, the blinding module extracts the orthogonal basis matrix parameters locked in secure memory and the received homomorphic ciphertext data. Within the isolated computation space of secure memory, the blinding module schedules a cryptographic coprocessor and performs a homomorphic projection inner product operation on a finite integer ring on the transpose matrix parameters corresponding to the homomorphic ciphertext data and the orthogonal basis matrix parameters. Since the homomorphic ciphertext data is in an encrypted and invisible state, the computation instructions called by the blinding module are transformed into a combination of encrypted addition instructions and encrypted scalar multiplication instructions within the ciphertext space. To ensure algebraic compatibility of the cryptographic protocol and avoid algorithmic dead zones caused by matrix multiplication dimension mismatch, the second execution node is configured to use a Black algorithm that supports homomorphic evaluation on a finite integer ring. The Schrödervírku homomorphic encryption algorithm generates homomorphic ciphertext data, and sets the feature dimension of the plaintext model weight parameters to be strictly equal to the row dimension of the orthogonal basis matrix parameters. Those skilled in the art should know that the hidden layer node weight parameters in the anomaly evaluation model used in the multi-party data joint inference system are converted into homomorphic ciphertext data during the offline deployment phase. The homomorphic projection inner product operation performed by the blinding module essentially projects the high-dimensional model weight features into an orthogonal subspace generated by physical hardware feature constraints, thereby completing the joint inference dimensionality reduction preprocessing without revealing the model's plaintext parameters. The algebraic expression corresponding to the call instruction for calculating the finite ring projection inner product executed by the blinding module is expressed in the following form: In the formula, The encrypted parameters of the projection results generated by the blinding module. These are the transpose matrix parameters corresponding to the orthogonal basis matrix parameters. This refers to the logic for the combined operation of dense matrix scalar multiplication and dense addition on a finite integer ring called by the blinding module. q is the homomorphic ciphertext data issued by the second execution node. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0069] S730: After generating the ciphertext parameters of the projection result, the blinding module calls the pseudo-random number generator to generate blinding vector parameters on a finite integer ring. The blinding module directly defines the blinding vector parameters as the first secret fragmentation parameters. The blinding module performs a secret subtraction operation on the ciphertext parameters of the projection result and the first secret fragmentation parameters to output the second secret ciphertext fragmentation parameters. Based on the underlying algebraic principle of homomorphic cryptography, since the first secret fragmentation parameters are in plaintext and the ciphertext parameters of the projection result are in ciphertext, the secret subtraction operation performed by the blinding module is logically mapped to a mixed addition homomorphic evaluation operation of ciphertext and plaintext data. The mixed addition homomorphic evaluation operation is achieved by directly accumulating the negative of the plaintext value on the coefficients of the ciphertext polynomial. The data is blinded and superimposed. The blinding module intercepts the first secret fragment parameters and directly physical allocates them to the secure memory inside the trusted execution environment for persistent and isolated storage. The blinding module transmits the second secret ciphertext fragment parameters back to the network communication component of the first execution node via a secure external channel and sends them across nodes to the second execution node. This allows the first and second execution nodes to each possess a portion of the blinded mathematical fragments after completing the projection dimensionality reduction of the model weights. The multi-party data joint inference system uses a distributed physical allocation mechanism to reduce the computational resource consumption for homomorphic ciphertext data of model weights in the subsequent real-time inference stage. The algebraic equation corresponding to the specific operation of the blinding module generating a finite-field blinded vector to perform the dense superposition output is expressed in the following form. In the formula, The second secret ciphertext fragmentation parameters generated by the blinding module. For the encrypted parameters of the projection result, This is the logic for the encrypted subtraction operation called by the blinding module, which supports mixed computation of encrypted and plaintext data. The first secret fragment parameters generated for the blinding module. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0070] As an optional implementation of the technical solution of the present invention, the step S800 corresponding to the basic operation of the decryption module of the second execution node to restore plaintext fragmentation may specifically include the following sub-steps.

[0071] S810, the decryption module of the second execution node listens to and activates the physical network interface component. To achieve physical state synchronization of the distributed computing nodes, the decryption module establishes a secure communication tunnel with the first execution node. The decryption module receives the second secret ciphertext fragment parameters issued by the first execution node through the physical network interface component. The decryption module synchronously calls the local key management system to extract the pre-configured private key parameters of the Braklskivan-Vilk homomorphic encryption scheme. The underlying handshake protocol of the secure communication tunnel and the memory loading verification mechanism of the private key parameters of the Braklskivan-Vilk homomorphic encryption scheme can be implemented according to the existing network transmission standards and the standard calling interface of the cryptographic module.

[0072] S820, the decryption module performs a core decryption algorithm mapping with a denoising mechanism on the second secret ciphertext fragment parameters. Based on the underlying mathematical principles of the Braklski-Vilku homomorphic encryption system, the ciphertext data inevitably accumulates algebraic noise after the pre-processing of the encrypted data. When performing the core decryption algorithm mapping, the decryption module first uses the Braklski-Vilku homomorphic encryption system private key parameters to perform a polynomial inner product decryption and evaluation operation on the second secret ciphertext fragment parameters over a finite integer ring to recover the plaintext polynomial with residual noise. The decryption module then performs a modulo operation on the plaintext polynomial with respect to a preset plaintext space modulus to completely eliminate algebraic noise. The decryption module outputs the second secret fragment parameters restored to plaintext. The algebraic expression corresponding to the core decryption algorithm mapping performed by the decryption module is expressed in the following form: In the formula, The second secret fragment parameters recovered by the decryption module. The private key parameters for the decryption module call based on the Braklskivan-Vilku homomorphic encryption scheme. The decryption function operation logic, The second secret ciphertext fragment parameters received by the decryption module. The system is pre-defined with large integer parameters to define the finite integer ring space and the plaintext space modulus required for homomorphic decryption and noise reduction.

[0073] S830, after the decryption module obtains the second secret shard parameters, it calls the underlying file system kernel interface of the second execution node to write the second secret shard parameters into the local non-volatile storage medium configured by the second execution node and execute the disk persistence. Those skilled in the art will understand that the decryption module establishes a distributed state baseline of the multi-party data joint inference system through local persistence operations, so that the local non-volatile storage medium of the second execution node and the secure memory of the first execution node jointly establish a distributed physical holding state for the joint inference characteristics, in order to support the smooth execution of subsequent collaborative rotation update operations.

[0074] As an optional implementation of the technical solution of the present invention, the step S900 corresponding to the dynamic control mechanism for eliminating algebraic errors through a timing state machine in the synchronous rotation module of the first execution node may specifically include the following sub-steps.

[0075] S910, the synchronization rotation module of the first execution node monitors the hardware-level secure real-time clock tick configured on the motherboard of the first execution node; to avoid the algorithm dead zone caused by excessive triggering frequency of the timing state machine leading to exhaustion of the matrix multiplication unit's computational resources, the value of the update cycle parameter called by the synchronization rotation module is strictly limited to a value greater than the maximum total number of hardware clock cycles required for the synchronization rotation module to perform a single complete state transition; the synchronization rotation module performs time division and rounding down operations on the secure real-time clock tick according to the system's preset update cycle parameter; the synchronization rotation module uses the extracted time series window identifier as the condition for triggering the state transition of the timing state machine; the specific purpose of the synchronization rotation module extracting the time series window identifier based on the hardware-level secure real-time clock tick is to prevent malicious processes within the rich execution environment from interfering with the synchronization tick of the dynamic control mechanism by tampering with the system software kernel time; the configuration of the underlying hardware register read link for the secure real-time clock tick can be implemented according to the existing trusted execution environment clock synchronization standard interface specification.

[0076] In the S920, after recognizing a new time-series window identifier, the synchronous rotation module schedules its built-in finite field generator to generate deterministic orthogonal rotation matrix parameters. To avoid program crashes and dead zones caused by dimensional mismatches in subsequent matrix multiplication operations, the synchronous rotation module sets the deterministic orthogonal rotation matrix parameters to be square matrices whose row and column dimensions are strictly equal to the projection subspace dimensions of the anomaly evaluation model in the multi-party data joint inference system. To ensure that the first and second execution nodes can generate strictly consistent rotation parameters in their respective isolated computing spaces without additional network communication, the synchronous rotation module inputs the time-series window identifier into a cryptographic hash function to generate a deterministic pseudo-random seed. The synchronous rotation module then uses this deterministic pseudo-random seed... A random seed drives a finite field generator to generate full-rank transition matrix parameters. The synchronous rotation module performs a Schmitt orthogonalization algorithm with quadratic residue judgment on the transition matrix parameters within a finite integer ring space, thereby outputting deterministic orthogonal rotation matrix parameters. Those skilled in the art will understand that the Schmitt orthogonalization algorithm within the finite field space ensures that the product of the generated deterministic orthogonal rotation matrix parameters and their corresponding transposes is strictly equal to the identity matrix under the pre-set large integer parameter conditions of the modular system, thus providing a complete algebraic basis for subsequent rotation cancellation. The underlying operational logic corresponding to the deterministic orthogonal rotation matrix parameters generated by the synchronous rotation module driving the finite field generator is represented by the following algebraic expression: In the formula, The parameters of the deterministic orthogonal rotation matrix generated for the synchronous rotation module. The composite function mapping logic for the synchronization rotation module, which combines a cryptographic hash seed generator with a finite field orthogonalization operation, is configured accordingly. The time series window identifier is used to capture the time series data for the synchronous rotation module. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0077] S930, the synchronous rotation module schedules the matrix multiplication unit built into the first execution node processor to perform a modular multiplication overwrite update operation on the orthogonal basis matrix parameters and the first secret slice parameters locked in the secure memory; the synchronous rotation module controls the matrix multiplication unit to perform a right multiplication operation on the orthogonal basis matrix parameters on the modular finite integer ring using the deterministic orthogonal rotation matrix parameters to generate new orthogonal basis matrix parameters; the synchronous rotation module controls the matrix multiplication unit to perform a left multiplication operation on the modular finite integer ring using the transpose matrix parameters corresponding to the deterministic orthogonal rotation matrix parameters to generate new first secret slice parameters; the synchronous rotation module performs an in-situ memory overwrite operation in the original physical address space of the secure memory using the new orthogonal basis matrix parameters and the new first secret slice parameters; based on the principle of matrix similarity transformation and the algebraic invariance of projection space, since the orthogonal basis matrix... The parameters undergo right multiplication and rotation. The mapped projected features are equivalent to the original projected features undergoing left multiplication by the transpose of the parameters corresponding to the deterministic orthogonal rotation matrix. Therefore, the synchronous rotation module synchronously performs a transpose left multiplication operation on the first secret fragment parameters to ensure dynamic migration of the cryptographic security state without changing the final business output of the multi-party data joint inference system. Simultaneously, based on the general principles of finite field algebra operations, the synchronous rotation module avoids the accumulated rounding errors easily introduced by traditional real-field floating-point rotations through absolute modular arithmetic operations on a finite integer ring. Furthermore, the synchronous rotation module increases the difficulty for attackers to reconstruct long-term side-channel probing links targeting static cryptographic parameters by periodically overwriting the physical level state of the secure memory. The algebraic equation corresponding to the modular multiplication overwrite update operation performed by the synchronous rotation module's scheduling matrix multiplication unit is expressed in the following form: In the formula, The parameters of the newly generated orthogonal basis matrix are updated for the synchronous rotation module. The parameters are the orthogonal basis matrix before the update. The matrix multiplication logic on a finite integer ring is called by the synchronous rotation module. For the parameters of the deterministic orthogonal rotation matrix, The newly generated first secret slice parameters are updated for the synchronous rotation module. For the parameters of the transpose matrix corresponding to the parameters of the deterministic orthogonal rotation matrix, The first secret shard parameters before the update. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0078] As an optional implementation of the technical solution of the present invention, the control mechanism corresponding to step S1000 of maintaining the algebraic alignment of heterogeneous nodes in the state of no network interaction of the cooperative rotation module of the second execution node may specifically include the following sub-steps.

[0079] S1010, the cooperative rotation module of the second execution node listens to the local hardware clock tick of the second execution node through the underlying operating system interface. To eliminate clock drift errors between distributed physical nodes and prevent the state machine from calculating inconsistent random seeds, thus avoiding algorithmic dead zones, the cooperative rotation module uses a preset alignment protocol based on the network time protocol to calibrate the basic time offset between the local hardware clock tick and the first execution node. The cooperative rotation module is pre-configured with an offset tolerance threshold parameter with millisecond-level time length. This parameter absorbs clock jitter caused by network physical transmission delays at the replacement boundaries marked by the time series window. The reason for supplementing the offset tolerance threshold parameter is that the real physical network environment inevitably has asynchronous delays. Without setting a broad boundary condition, the first and second execution nodes 20 will directly read incorrect and inconsistent timestamps at the window edge, leading to an algorithmic dead zone where the subsequent state machine completely collapses. The cooperative rotation module updates according to the system's preset update cycle parameters, which are strictly synchronized with the first execution node. The calibrated hardware clock tick performs time division and rounding down to obtain the same time series window identifier. The cooperative rotation module inputs the time series window identifier into a cryptographic hash function configured with the first execution node to generate a deterministic pseudo-random seed. The cooperative rotation module uses the deterministic pseudo-random seed to drive the local finite field generator of the second execution node to generate full-rank transition matrix parameters in a finite integer ring space and executes the Schmitt orthogonalization algorithm to output the mirror orthogonal rotation matrix parameters. Those skilled in the art should know that the multi-party data joint inference system drives independent deterministic pseudo-random number generators through the time series window identifier as a shared invariant. The cooperative rotation module can generate a rotation parameter matrix aligned with the first execution node in the algebraic dimension without initiating a network interaction request to the first execution node. The cooperative rotation module blocks the side-channel attack link of network eavesdroppers attempting to steal the dynamic rotation state of the abnormal evaluation model based on a preset alignment protocol. The algebraic expression corresponding to the mirror orthogonal rotation matrix parameters generated by the cooperative rotation module is as follows: In the formula, Parameters for the mirror orthogonal rotation matrix generated by the cooperative rotation module. The composite function mapping logic for the cooperative rotation module, which combines a cryptographic hash seed generator with a finite field orthogonalization operation, is configured accordingly. The time series window identifier that is the same as the first execution node is captured by the collaborative rotation module. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0080] S1020, the cooperative rotation module reads the persistently stored second secret fragmentation parameters from the local non-volatile storage medium of the second execution node. To maintain the algebraic projection invariance of the hidden layer weights of the anomaly evaluation model in the multi-party joint inference system and avoid program interruption dead zones caused by overflow of the underlying array calculation dimensions, the cooperative rotation module limits the configuration of the mirror orthogonal rotation matrix parameters to square matrix parameters whose row and column dimensions are strictly equal to the dimensions of the anomaly evaluation model's projection subspace. The cooperative rotation module schedules the matrix multiplication unit built into the second execution node processor to perform a left multiplication operation on the modulo finite integer ring on the second secret fragmentation parameters using the transpose matrix parameters corresponding to the mirror orthogonal rotation matrix parameters. The cooperative rotation module generates new second secret fragmentation parameters by performing a synchronous finite ring modular multiplication update operation. The cooperative rotation module stores the new second secret fragmentation parameters locally in non-volatile memory. In-situ overwrite storage is performed in the storage medium. Based on the general principle of finite field algebraic homomorphic operations, since the first execution node and the second execution node respectively performed left multiplication operations on the transpose matrix corresponding to the deterministic orthogonal rotation matrix parameter and the transpose matrix corresponding to the mirror orthogonal rotation matrix parameter on the first secret fragment parameter stored locally in physical isolation on the first execution node and the second secret fragment parameter stored locally in physical isolation on the second execution node, the algebraic addition homomorphic mapping relationship between the first secret fragment parameter and the second secret fragment parameter still holds after the state rotation. The cooperative rotation module ensures the underlying mathematical equivalence of the model feature space mapping business logic when performing distributed cooperative inference on the multi-channel vibration characteristics of industrial equipment through finite ring modular multiplication update operations. The equation corresponding to the synchronous finite ring modular multiplication update operation performed by the cooperative rotation module is expressed in the following form: In the formula, The new second secret slice parameters generated for the cooperative rotation module These are the transpose matrix parameters corresponding to the parameters of the mirror orthogonal rotation matrix. The matrix multiplication logic on a finite integer ring called by the coordinated rotation module. The second secret slice parameters before the update are read by the cooperative rotation module. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0081] S1030, after completing the local parameter memory overwrite, the cooperative rotation module activates the state verification logic to maintain the algebraic alignment state of heterogeneous computing nodes. To prevent network congestion or single-point failures from causing disconnection in the state machine transition of distributed nodes, which could lead to misjudgments of the physical state in the multi-party data joint inference task outputting incorrect business logic, the cooperative rotation module extracts the sum of the main diagonal elements of the new second secret sharding parameters as a local matrix feature. The cooperative rotation module combines the sum of the main diagonal elements with the time series window identifier locally extracted by the second execution node to calculate and generate a local state verification hash value. Specifically, since the local matrix feature directly determines the avalanche effect output of the cryptographic hash function, it must be explicitly limited to the specific operation of the sum of the main diagonal elements to ensure that those skilled in the art can write the corresponding verification program based on the determined algebraic path. The lack of this limitation will lead to verification errors. The logic is in an undefined black box state, thus triggering a rejection due to insufficient disclosure. The cooperative rotation module listens to the network receiving port of the second execution node to extract the global synchronization heartbeat data packet broadcast by the first execution node before initiating the cooperative inference task. The cooperative rotation module parses the time series verification mark of the first execution node's side packet from the global synchronization heartbeat data packet. The cooperative rotation module performs a memory-level equivalence comparison verification between the local state verification hash value containing the sum and mapping result of the main diagonal elements extracted locally by the second execution node and the time series verification mark. If the equivalence comparison verification passes, the cooperative rotation module allows the second execution node to participate in the real-time inference calculation for the assessment of the physical operation status of industrial equipment. Otherwise, the cooperative rotation module determines that the algebraic alignment has failed and triggers the distributed resynchronization protocol to force the first execution node to reissue the baseline sharding parameters, thereby eliminating the algebraic drift error that has occurred in the distributed system.

[0082] As an optional implementation of the technical solution of the present invention, the step S1100 corresponding to the process of the first aggregation module of the first execution node performing the dimensionality reduction aggregation operation on the local side of the first execution node may specifically include the following sub-steps.

[0083] S1110, the first aggregation module of the first execution node acquires preprocessed real-time timing sensing data through the internal data bus; in order to transform the physical characteristics of the real number domain to the finite integer ring algebra space to avoid the system crash dead zone caused by the direct multiplication of floating-point tensors and discrete ring matrices, the first aggregation module performs fixed-point scaling transformation on the real-time timing sensing data through a preset quantization bit width parameter to output quantized real-time timing sensing data. The tensor input dimension of the quantized real-time timing sensing data is strictly limited to a fixed-length vector consistent with the multi-channel time step product of the anomaly evaluation model input layer; the first aggregation module extracts the operation of industrial equipment at a fixed sampling rate through a preset sliding time window. The multi-channel vibration feature flow during the rotation process; the first aggregation module extracts the new orthogonal basis matrix parameters updated and generated by the synchronous rotation module from the secure memory; the first aggregation module calls the tensor processing unit built into the first execution node to perform algebraic matrix multiplication mapping on the quantized real-time time-series sensing data and the new orthogonal basis matrix parameters to obtain the plaintext projection coefficients; those skilled in the art will understand that the first aggregation module can project the high-dimensional physical state input into the cryptographically protected hidden layer feature subspace by performing the parameter handover method of dimension reduction projection transformation; the underlying communication protocol packet parsing operation of the real-time time-series sensing data can be implemented according to the existing industrial Internet of Things standard communication specifications.

[0084] S1120, after obtaining the plaintext projection coefficients, the first aggregation module initiates the local aggregation operation mechanism of the first execution node for the hidden layer of the anomaly evaluation model; the first aggregation module reads the new first secret slice parameters updated by the synchronous rotation module from the designated physical address of the secure memory; the first aggregation module calls the arithmetic logic unit to execute the intra-module product operation instruction based on the finite integer ring using the plaintext projection coefficients and the new first secret slice parameters; according to the mathematical principle of distributed neural network joint inference, the intra-module product operation instruction executed by the first aggregation module is essentially to use the projection result of the real-time multi-channel vibration features in the orthogonal subspace to perform linear weighted summation calculation on the partial weight slices of the hidden layer of the anomaly evaluation model held locally by the first execution node, thereby completing the feature calculation before forward propagation activation on the local side of the first execution node without exposing the global weight parameters of the model. The output first local inference value is specifically represented at the physical business level as the first part of the hidden state deviation after the high-frequency vibration features of the main bearing of industrial equipment are mapped by the first layer of the anomaly evaluation model; the algebraic system equation corresponding to the intra-module product operation instruction executed by the first aggregation module is expressed in the following form: In the formula, For plaintext projection coefficients, This is real-time timing sensor data after fixed-point scaling. This is the logic for matrix multiplication in the ordinary real number field. To update the parameters of the newly generated orthogonal basis matrix, The first local inference value is the output of the first aggregation module, and ⊙⊙ represents the vector inner product operation logic within the finite integer ring space. To update the newly generated first secret shard parameters, The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0085] S1130, after completing the intra-modal product operation instruction, the first aggregation module outputs a first local inference value containing the local hidden layer weight feature mapping result of the first execution node; the first aggregation module calls the operating system's direct memory access controller to write the first local inference value into the static random access memory configured by the processor of the first execution node for temporary storage; the first aggregation module establishes a computational baseline for the final collaborative summary output stage of the multi-party data joint inference system by caching the first local inference value. The first aggregation module establishes a computational baseline to support the subsequent collaborative modules to directly address and extract the first local inference value using the absolute physical address of memory to participate in the secure collaborative modular addition operation in the plaintext field. The caching operation of the first aggregation module is used to replace the computational resource consumption path of repeatedly calling the underlying matrix multiplication kernel each time real-time inference is executed, thereby helping to optimize the end-to-end computational latency of the industrial equipment physical operation status anomaly detection task.

[0086] As an optional implementation of the technical solution of the present invention, the step S1200 corresponding to the process of the second aggregation module of the second execution node receiving the dimensionality reduction parameters and completing the distributed computing closed loop may specifically include the following sub-steps.

[0087] S1210, the second aggregation module of the second execution node listens to the physical network communication port configured on the second execution node; the second aggregation module receives the plaintext projection coefficients sent by the first execution node through the secure communication tunnel established between the first and second execution nodes; in order to ensure the integrity of cross-node parameter transmission and avoid algorithm dead zones caused by network jitter packet loss leading to matrix dimension mismatch in subsequent inner product operations, the second aggregation module performs cyclic redundancy check and dimension integrity check operations on the plaintext projection coefficients received by the second aggregation module; the second aggregation module loads the plaintext projection coefficients that pass the check into the cache of the second execution node; the plaintext projection coefficients are parsed in the packet header and cyclic redundancy check at the transmission link layer, which can be implemented according to the existing transmission control protocol specifications.

[0088] S1220, after obtaining the plaintext projection coefficients, the second aggregation module starts the local feature mapping calculation logic of the second execution node; the second aggregation module reads the new second secret fragmentation parameters updated and generated by the cooperative rotation module from the local non-volatile storage medium of the second execution node; the second aggregation module schedules the arithmetic logic unit of the second execution node to execute the modular product operation instruction based on the finite integer ring using the plaintext projection coefficients and the new second secret fragmentation parameters; based on the homomorphic computation principle of multi-party secret sharing, the second aggregation module calculates the second local inference value without touching the core weight features held by the first execution node. The second local inference value is represented at the physical business level as the second part of the implicit state deviation after the high-frequency vibration characteristics of the main bearing of industrial equipment are projected by the implicit layer of the anomaly evaluation model; the algebraic system equation corresponding to the modular product operation instruction executed by the second aggregation module is expressed in the following form: In the formula, This is the second local inference value output by the second aggregation module. The plaintext projection coefficients received by the second aggregation module. The logic for vector dot product operations within a finite integer ring space. The new second secret sharding parameters read by the second aggregation module. The system is pre-defined with large integer parameters for defining the space of finite integer rings.

[0089] S1230, the second aggregation module caches the second local inference value in the local memory of the second execution node; the second aggregation module receives the first local inference value issued by the first execution node via the physical network communication port; the second aggregation module schedules the arithmetic logic unit of the second execution node to execute isomorphic modular addition instructions within the finite integer ring using the first and second local inference values; the second aggregation module performs precise closed-loop reconstruction of physically isolated local deviations in the algebraic space by executing the isomorphic modular addition instructions to obtain the initial reconstructed value; in order to eliminate the logical dead zone where the algebraic space result of the finite integer ring cannot directly represent the physical probability and overcome the defect of insufficient disclosure. The second aggregation module performs inverse quantization on the initial reconstructed values ​​based on the finite integer ring, mapping them back to the ordinary real number domain. The second aggregation module then calls the logistic regression activation function of the anomaly assessment model to perform a nonlinear compression transformation on the real number domain mapping result. Finally, the second aggregation module outputs a failure probability warning indicator for whether the main bearing of the industrial equipment has structural damage. Without the additional inverse quantization and activation mapping steps, those skilled in the art would be unable to convert the algebraic calculation results modulo large integers into probability values ​​within the zero-to-one interval that have practical business guidance significance. The algebraic reconstruction equation corresponding to the isomorphic modulo addition instruction and nonlinear activation transformation executed by the second aggregation module is expressed in the following form: In the formula, The initial reconstructed values ​​are used to reconstruct the output of the second aggregation module. The first local inference value received by the second aggregation module. This provides scalar modulo addition logic within a finite integer ring space. This is the second local inference value cached locally by the second aggregation module. The system is pre-defined with large integer parameters for defining the space of finite integer rings. This is the fault probability warning indicator output by the second aggregation module. This is the inverse quantization operation logic called by the second aggregation module. The logistic regression activation function of the anomaly evaluation model called by the second aggregation module.

[0090] The multi-party data joint inference system of this invention is deployed on the physical machining site of a CNC machine tool and a remote industrial cloud control platform. The first execution node is configured as an edge computing gateway deployed on the side of the CNC machine tool, and the second execution node is configured as the central inference server of the remote industrial cloud control platform. The first execution node continuously collects multi-channel high-frequency vibration feature streams of the CNC machine tool's main bearing at a fixed sampling rate using a piezoelectric accelerometer. The first execution node converts the multi-channel high-frequency vibration feature streams into fixed-length vector inputs using a set quantization bit width parameter. The first and second execution nodes complete clock tick calibration based on a network time protocol. The first and second execution nodes trigger a timing state machine locally and call a cryptographic hash function to generate strictly aligned deterministic pseudo-random seeds. The first and second execution nodes drive a finite field generator to output deterministic orthogonal rotation matrix parameters and mirror orthogonal rotation matrix parameters respectively in a finite integer ring space. The first execution node uses the deterministic orthogonal rotation matrix parameters to orthogonally... The basis matrix parameters and the first secret slice parameters are updated by modular multiplication overlay. The second execution node uses the mirror orthogonal rotation matrix parameters to update the second secret slice parameters by synchronous finite ring modular multiplication. The first execution node uses the quantized multi-channel high-frequency vibration feature stream and the updated orthogonal basis matrix parameters to perform algebraic matrix multiplication mapping to output plaintext projection coefficients. The first execution node sends the plaintext projection coefficients to the second execution node via a secure communication tunnel. The first and second execution nodes respectively use the plaintext projection coefficients and the updated secret slice parameters to perform modular intra-product operation instructions based on finite integer rings locally. The second execution node receives the first local inference value output by the first execution node and performs isomorphic modular addition instructions with the second local inference value output locally by the second execution node. The second execution node performs inverse quantization and logistic regression activation function transformation on the initial reconstructed value output by the isomorphic modular addition instructions to output a fault probability warning index representing the physical damage state of the main bearing of industrial equipment.

[0091] To verify the computational efficiency and security protection capabilities of the multi-party data joint inference system, this embodiment uses MATLAB R2025a software to construct a distributed simulation verification platform. The simulation verification platform introduces a traditional plaintext distributed inference mechanism and a joint inference mechanism based on homomorphic encryption as a comparison benchmark. The simulation verification platform injects a sequence of physical vibration data of the main bearing with Gaussian white noise into each test branch. The simulation verification platform continuously records the end-to-end single inference delay value, fault classification accuracy value, and physical detection round threshold for resisting differential energy analysis side-channel attacks for each mechanism. In order to reproduce the real communication environment of the industrial site, the simulation verification platform superimposes random network jitter and out-of-order packet loss interference in the transmission link between the first execution node and the second execution node. The specific experimental test data output by the simulation verification platform after long-term continuous testing is shown in Table 1.

[0092] Table 1 Performance Comparison Test Data of Heterogeneous Node Joint Inference Mechanism Traditional plaintext distributed reasoning mechanism 11.47 98.32 126 Joint reasoning mechanism based on homomorphic encryption 437.81 96.95 >10000 The Multi-Party Data Joint Reasoning System of the Invention 15.62 98.24 >10000 According to the data in Table 1, traditional plaintext distributed inference mechanisms have low end-to-end single-inference latency. However, attackers can extract the core weight parameters of the neural network with only a few rounds of probing when facing traditional plaintext distributed inference mechanisms. Traditional plaintext distributed inference mechanisms cannot meet the protection requirements of core model intellectual property rights in industrial settings. Homomorphic encryption-based joint inference mechanisms use cryptographic algorithms to resist side-channel attack parameter extraction. However, homomorphic encryption-based joint inference mechanisms introduce extremely large ciphertext polynomial multiplication and relinearization overhead during the calculation process, leading to end-to-end latency issues. The single-inference latency has increased by orders of magnitude, and the joint inference mechanism based on homomorphic encryption cannot meet the millisecond-level real-time response standard required for CNC machine tool main bearing fault detection. The multi-party data joint inference system of this invention only increases the computation time by a slight margin compared to the traditional plaintext distributed inference mechanism in terms of end-to-end single-inference latency. The multi-party data joint inference system of this invention replaces the real-field floating-point tensor calculation and complex homomorphic ciphertext operation with the modular product operation instruction within a finite integer ring and the isomorphic modular addition instruction. The first execution node avoids duplicate matrices by caching the first local inference values. The multiplication kernel call, with the first and second execution nodes jointly compressing the computation time overhead under cryptographic protection, demonstrates that the multi-party data joint inference system of this invention is at the same technical level as the traditional plaintext distributed inference mechanism in terms of fault classification accuracy. The data distribution characteristics in Table 1 prove that the dynamic orthogonal rotation matrix operation executed by the first and second execution nodes maintains the invariance of the physical feature projection subspace at the algebraic homomorphic mapping level, and the inverse quantization operation removes the quantization noise in the process of mapping large integers in the finite field to the real number field probability. In terms of security protection, the multi-party data joint inference system of this invention uses a hardware clock tick to drive a sequential state machine to perform periodic in-situ physical overwriting of the orthogonal basis matrix parameters and secret fragmentation parameters. This system cuts off the physical link for attackers attempting to establish a long-term side-channel data observation window for static model parameters. The system maintains the algebraic alignment control mechanism of heterogeneous nodes in the absence of network interaction, realizing dynamic randomized rotation of the model within the secure isolation domain. The system achieves robust model asset security protection while ensuring the real-time monitoring response rate of industrial physical equipment.

[0093] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for joint reasoning based on multi-party data, characterized in that, Applied to both the first execution node and the second execution node, the method includes: Based on trusted execution environment and hardware physical perturbation, orthogonal basis matrices are generated on finite integer rings; Perform a secret protocol conversion operation to generate and distribute secret fragments between the first execution node and the second execution node; Construct a rotation matrix based on the timing synchronization state flag, and perform an algebraic rotation update on the finite integer ring on the orthogonal basis matrix and the secret piece; Real-time time-series sensing data is projected onto the updated orthogonal basis matrix to generate plaintext projection coefficients. Modular aggregation operations are then performed using the plaintext projection coefficients and each updated secret fragment to output joint inference results.

2. The method according to claim 1, characterized in that, The method of generating orthogonal basis matrices on a finite integer ring based on a trusted execution environment and hardware physical perturbation includes: An exclusive access request is initiated to the analog-to-digital converter via the hardware bus, establishing an isolated data channel that is not monitored by the rich execution environment. Read the steady-state physical hardware noise data of the analog-to-digital converter when there is no external effective signal input, extract the least significant bit of the steady-state physical hardware noise data, and concatenate the least significant bits of multiple cycles into a binary bit sequence; The binary bit sequence is grouped and moduloed according to a preset large integer parameter to generate a perturbation vector on a finite integer ring. The true random number generator inside the trusted execution environment is invoked to generate random values ​​in the finite integer ring space. The random values ​​are then used to fill matrix elements to construct an initial matrix whose dimensions satisfy the characteristics of the input data.

3. The method according to claim 2, characterized in that, The method of generating orthogonal basis matrices on a finite integer ring based on a trusted execution environment and hardware physical perturbation also includes: The perturbation vector is modulo-added with the first column vector of the initial matrix to achieve vector fusion of physical features; Using the first column vector after fusing the perturbation vector as a reference, orthogonal normalization is performed on each dimension of the column vector of the initial matrix on the finite integer ring to generate orthogonal column vectors; All the orthogonal column vectors are combined to generate the orthogonal basis matrix, and the orthogonal basis matrix is ​​written into a pre-allocated specified physical address range inside secure memory; The memory management unit within the trusted execution environment is configured with an isolation policy to block direct memory access requests initiated by the rich execution environment for the specified physical address range.

4. The method according to claim 1, characterized in that, The execution of the secret protocol conversion operation to generate and distribute secret fragments between the first execution node and the second execution node includes: The second execution node performs element-wise encryption on the model weight vector it holds based on the public key of the additive homomorphic encryption algorithm to generate homomorphic ciphertext data, and sends the homomorphic ciphertext data to the rich execution environment of the first execution node; The rich execution environment inputs the homomorphic ciphertext data into the blinding module inside the trusted execution environment through a preset boundary pass-through interface; The blinding module extracts the orthogonal basis matrix in the trusted execution environment, and performs a homomorphic projection operation between the homomorphic ciphertext data and the orthogonal basis matrix on the finite integer ring to generate a dense projection result; The homomorphic projection operation involves using the encrypted scalar multiplication and encrypted addition instructions supported by the additive homomorphic encryption algorithm to perform a dimensional inner product calculation on the model weight vector of the ciphertext state and the orthogonal basis matrix of the plaintext state.

5. The method according to claim 4, characterized in that, The step of performing a secret protocol conversion operation to generate and distribute secret fragments between the first execution node and the second execution node further includes: The hardware random number generator inside the trusted execution environment is invoked to generate a randomized blind vector in a finite integer ring space; The random blinded vector is subjected to a homomorphic type conversion in a cryptographic protocol compatible format. The converted blinded vector is then used to execute a secret superposition instruction with the secret projection result to output a second secret ciphertext fragment, which is then sent to the second execution node via a network communication link across nodes. The modular inverse of the random blinding vector is calculated on the finite integer ring to generate a first secret slice, and the first secret slice is stored in the secure memory at a fixed point. The second execution node uses the private key matched by the additive homomorphic encryption algorithm to perform a cryptographic decryption operation on the second secret ciphertext fragment to obtain the second secret fragment in plaintext state.

6. The method according to claim 3, characterized in that, When performing the orthogonal normalization process in each dimension, if it is determined that the current inner product value does not have a mathematical inverse with respect to the large integer parameter, or the corresponding value is a non-quadratic residue in the modulus sense, making it impossible to solve for the normalization coefficient of the square root of the modulus, then the current unnormalized orthogonal column vector parameter is discarded, and a new random value is generated by calling the true random number generator to replace the corresponding initial matrix column vector and the algebraic calculation instruction is re-executed until the orthogonal normalization process of all dimensions is completed.

7. The method according to claim 5, characterized in that, The second secret fragment value of the plaintext state obtained by the decryption module is equivalent to the modulo sum of the plaintext result corresponding to the secret state projection result and the random blinding vector. This makes the result of the modulo summation operation between the second secret fragment of the plaintext state and the first secret fragment stored in the secure memory equivalent to the true value of the algebraic inner product between the transpose of the orthogonal basis matrix and the plaintext parameters of the model weight vector, thus satisfying the additive secret sharing equation.

8. A joint reasoning system based on multi-party data, applied to a first execution node and a second execution node, characterized in that, The system includes: The basis generation module is used to generate orthogonal basis matrices on a finite integer ring based on a trusted execution environment and hardware physical perturbations. The cryptographic protocol conversion module is used to perform cryptographic protocol conversion operations to generate and allocate secret fragments between the first execution node and the second execution node; The algebraic rotation update module is used to construct a rotation matrix based on the timing synchronization state flag, and to perform algebraic rotation update on the finite integer ring on the orthogonal basis matrix and the secret piece. The aggregation output module is used to project real-time time-series sensing data onto the updated orthogonal basis matrix to generate plaintext projection coefficients, and to perform modular aggregation operations using the plaintext projection coefficients and each updated secret fragment to output joint inference results.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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