Privacy protection function calculation method based on tropical algebraic neural network fitting
By using tropical algebraic neural network fitting and obfuscated circuit techniques, the efficiency and privacy protection issues in nonlinear function processing in multi-party secure computation are solved, achieving efficient, universal, and secure function computation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIAMEN UNIV
- Filing Date
- 2026-01-08
- Publication Date
- 2026-05-08
AI Technical Summary
Existing secure multi-party computation methods for nonlinear function processing suffer from high communication and computational complexity, poor scalability, severe customization requirements, and insufficient protection of function privacy.
A method based on tropical algebraic neural network fitting is adopted to fit continuous functions piecewise linearly into a tropical algebraic neural network model, which is then compiled into a garbled circuit. Encrypted calculations are performed through logic gate operations, and data privacy and function privacy are protected by an unintentional transmission protocol.
It reduces computational and communication complexity, improves scalability and applicability, and achieves end-to-end privacy protection for function models, providing an efficient and universal privacy-preserving function computation scheme.
Smart Images
Figure CN121997370A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of privacy protection technology, and in particular to a method for calculating a privacy protection function based on fitting a tropical algebraic neural network. Background Technology
[0002] In today's data-driven era, privacy protection has become a core issue that cannot be ignored in various computing tasks. With the rapid development of technologies such as artificial intelligence, big data, and cloud computing, various institutions and organizations urgently need to complete necessary computing tasks without disclosing the original data content or computational functions when collaboratively processing sensitive data (such as user behavior information, medical records, and financial data). This demand has spurred widespread attention and in-depth research into secure multi-party computation technologies.
[0003] Secure multi-party computation is a class of cryptographic methods that allows multiple participants to collaboratively compute a function while keeping their individual inputs confidential, ensuring the final result is correct and confidential to all parties. Two-party secure computation is the fundamental form of secure multi-party computation, suitable for scenarios with only two participants. It shows great promise in applications such as privacy-preserving search, joint machine learning, and cross-organizational data mining. Various implementations of secure multi-party computation have been developed, including secret sharing, homomorphic encryption, zero-knowledge proofs, and obfuscated circuits.
[0004] In practical applications, the fundamental building blocks used to construct secure multi-party computation protocols have relatively mature and efficient solutions for handling linear or near-linear functions (such as addition, scalar multiplication, and matrix multiplication). For example, by combining secret sharing with Beaver triplet preprocessing, parties can complete multiplication operations with only a small number of mask differences exchanged, effectively controlling communication and computational overhead. Many multi-party computation frameworks utilize this approach, decomposing linear computation into addition and multiplication, thus achieving efficient linear computation in practice.
[0005] However, when it is necessary to support nonlinear functions (such as activation functions, piecewise functions, logarithmic / exponential / regularization terms, etc.) while protecting privacy, the efficiency overhead of existing schemes skyrockets, which is one of the main bottlenecks in the application of secure multi-party computation in practical function computation. The following aspects are particularly prominent: 1. High communication and computational complexity Nonlinear functions typically require comparisons, conditional branching, approximate interpolation or higher-order polynomial expansions, table lookups, or obfuscated circuits. For example, implementing nonlinear gates (such as ReLU and sigmoid) in the Garbled Circuit approach requires more encryption gates, data transformations, and transmissions; in secret-sharing frameworks, additional protocols (such as secure comparison protocols) may be needed. Because these protocols involve many interaction steps, high encryption overhead, and require additional preprocessing or auxiliary servers, their overall efficiency is often far lower than that of linear gates.
[0006] 2. Poor scalability and excessive customization of solutions. For different nonlinear functions, different levels of precision / approximation methods, and different input domains / ranges of values, almost every case requires the design of a specific protocol or optimization strategy. In other words, there is currently no universal, black-box privacy-preserving computation framework that can efficiently and flexibly cover private computations for arbitrary functions or network structures. This makes it difficult to generalize or implement in engineering for each function fitting scenario, as a significant amount of customization work is required.
[0007] 3. Function privacy is not adequately protected. Current mainstream multi-party computation schemes almost all prioritize "protecting the inputs of all parties," while paying less attention to the confidentiality of the computation function itself (i.e., function model, parameters, structure, coefficients, etc.). In many real-world scenarios, the function model itself may contain trade secrets, algorithmic strategies, and trained parameters (such as weights and cost function forms in AI models). If function details are leaked while only data privacy is protected, core assets may be potentially exposed. Summary of the Invention
[0008] In view of this, the purpose of this invention is to propose a privacy protection function calculation method based on tropical algebraic neural network fitting, which can solve at least one of the technical problems mentioned in the background art.
[0009] According to one aspect of the present invention, a method for calculating a privacy-preserving function based on fitting a tropical algebraic neural network is provided, the method comprising: For continuous functions that require confidential computation, a tropical algebraic neural network is used to perform piecewise linear fitting on the continuous function; the fitted tropical algebraic neural network model is used as the function that needs to be protected, and the model holds the fitting parameters of the model. The model provider compiles the computation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypts and obfuscates the circuit, generates an obfuscated circuit, and sends it to the data provider. The data provider obtains its own private input data from the model provider. The corresponding encrypted tag; The data provider uses the obtained encrypted tags locally to evaluate the received obfuscation circuit layer by layer, and obtains the encrypted tags output by the fitted tropical algebraic neural network model. The data provider decrypts the output encrypted tag locally to obtain the final function calculation result y(x).
[0010] In the aforementioned technical solution, the introduction of tropical algebraic neural network fitting and obfuscated circuit techniques demonstrates significant advantages in privacy-preserving function computation, effectively addressing the core challenges of secure multi-party computation in nonlinear function processing. Specifically, First, this method uses a tropical algebraic neural network to perform piecewise linear fitting on continuous functions, transforming complex nonlinear functions into a series of linear segments. It only uses min, max, plus operations that are friendly to obfuscated circuits for calculation, thereby reducing the computational and communication complexity in obfuscated circuit implementation and improving overall efficiency.
[0011] Secondly, through a general fitting and compilation process, this approach reduces the need for customization for specific functions, enhancing scalability and applicability; the flexibility of tropical algebraic neural networks allows the model to adapt to approximations of different continuous functions, while the standardized compilation of obfuscated circuits supports black-box processing, reducing the complexity of engineering implementation.
[0012] Finally, during the computation process, the function model exists in encrypted form. The data party can only access the encryption tag and obfuscation circuit, and cannot infer the model parameters or structure, thus ensuring full protection of function privacy and overcoming the shortcomings of traditional schemes that may leak function details. In summary, this scheme has made positive progress in terms of efficiency, scalability, and function privacy protection, providing a feasible technical path for the promotion of secure multi-party computation in practical applications.
[0013] In some embodiments, the tropical algebraic neural network includes: a linear layer, a minimum addition layer, and a maximum addition layer; wherein, Linear layers are used to fit a given input data and output several linear basis functions; Minimum addition is used to perform a min-plus combination with bias on all linear basis functions; The maximum addition layer is used to perform a biased max-plus combination of all the linear basis functions resulting from the min-plus combination with bias.
[0014] In the aforementioned technical solution, the tropical algebraic neural network's reliance on comparison and addition operations synergizes efficiently with the encryption execution mode of the obfuscated circuit. Specifically, the network consists of linear layers, minimum-plus layers, and maximum-plus layers. The linear layers are responsible for generating multiple linear basis functions, the minimum-plus layers estimate the lower bound through biased min-plus operations, and the maximum-plus layers synthesize the upper bound through biased max-plus operations. This series of operations is mathematically equivalent to a complex piecewise linear function. When this model is compiled into a Boolean circuit, its computation process mainly consists of addition, comparison, and selection gates. Compared to circuits that require simulating higher-order polynomials or transcendental functions, the depth and number of gates in this circuit are significantly optimized, thereby directly reducing the communication and computational complexity in the generation, transmission, and evaluation processes of the obfuscated circuit.
[0015] Furthermore, tropical algebraic neural networks, as a general framework for function approximation, can adapt to various continuous nonlinear functions with a unified structure by adjusting the number of linear basis functions and bias parameters, avoiding the overhead of customizing a dedicated protocol for each specific function. This method of uniformly transforming any continuous function into a standard "linear layer - minimum layer addition - maximum layer addition" process enables highly automated subsequent circuit compilation and obfuscation processes, effectively overcoming the customization challenges caused by the diverse function forms in traditional solutions.
[0016] In terms of security, this scheme achieves end-to-end privacy protection throughout the computation process. The fitting parameters held by the model, namely the network weights and biases, remain encrypted throughout the entire computation. After obtaining the encrypted tags of the input data, the data provider only evaluates the obfuscated circuit layer by layer locally to obtain the final calculation result, without being able to access the function logic and parameters corresponding to the circuit structure. The model provider can only obtain the function logic and parameters, but cannot know the original input and corresponding function output of the data provider. This mechanism not only strictly protects data privacy but also ensures the confidentiality of the function model itself as a core intellectual property asset.
[0017] In some embodiments, the linear layer, given input data First layer output Linear basis functions:
[0018] In the formula, These are the first fitted parameters; Minimum layer, which contains Each kernel performs a biased min-plus combination of all linear basis functions:
[0019] In the formula, This is the second fitting parameter, used to control the bias of different kernels; Maximum layer, which contains Each core corresponds to all Perform a max-plus combination with bias:
[0020] In the formula, The third fitting parameter is used to control the bias of different kernels.
[0021] In the above technical solution, by precisely decomposing the computation process into linear matrix operations and paired min / max comparison operations, the solution achieves a significant reduction in computational complexity and a significant enhancement in security attributes at the cryptographic compilation level.
[0022] Specifically, the calculation of linear layers Essentially, it's matrix multiplication, an operation that falls under the category of linear computation in secure multi-party computation. In various paradigms, such as secret sharing or obfuscated circuits, linear computation can be efficiently performed using protocols with no or low interaction overhead. When this layer is compiled into a Boolean circuit, it primarily consists of arithmetic logic units, resulting in a well-structured and easily optimized architecture. Subsequent minimal layer additions... With maximum layer Although it introduces nonlinearity mathematically, its core operation is reduced to a series of paired "compare-select" operations. In the implementation of obfuscated circuits, a compare-select gate can be constructed from a constant number of encryption gates, with overhead far lower than the high-order polynomial approximations or table lookup operations required to implement transcendental functions such as sigmoid or exponential functions. This structure ensures that the Boolean circuits corresponding to the entire network have a relatively shallow depth and a controllable number of gates, directly translating into lower communication and computational latency in the obfuscated circuit scheme.
[0023] From the perspective of versatility and scalability, this network structure provides a parameterized function approximation template. The model only needs to adjust the dimensions and values of the fitting parameter matrices W, A, and C to adapt to different objective functions using the same computational framework, without changing the underlying secure computation protocol or circuit compilation logic. This "parameterized" rather than "structural" adjustment gives the solution near-black-box versatility, greatly reducing the cost of repeatedly designing customized protocols for different functions.
[0024] In terms of security, this hierarchical structure encapsulates the model's confidential information within three fitting parameter matrices. During the computational process, the data provider only has access to its encrypted input tags and obfuscated circuitry, remaining completely unaware of the specific values of parameters W, A, and C, thus ensuring the complete confidentiality of the function model. Simultaneously, the model provider only obtains the function model parameters throughout the process, unable to trace the computation results or deduce the data provider's original input. This achieves dual protection of data privacy and function privacy.
[0025] In summary, this scheme transforms complex nonlinear function fitting into a series of efficient and well-organized basic operations through the clear hierarchical computation graph of tropical algebraic neural networks. Thus, when compiled into obfuscated circuits, it achieves a balance between efficiency, versatility, and security, providing a highly promising technical path for privacy-preserving function computation.
[0026] In some embodiments, the data provider obtains its private input data from the model provider. The corresponding encrypted tags, specifically: The data provider obtains its private input data from the model provider through an unintentional transmission protocol. The corresponding encrypted tag.
[0027] In the above technical solution, the data provider obtains its private input data through an Oblivious Transfer (OT) protocol. The corresponding encrypted tags ensure that the model sender (the party sending the data) can input the data without knowing the specific choices made by the data receiver (the party receiving the data). Each bit of the input is securely transmitted to the data provider via one of two encrypted tags (corresponding to 0 and 1 respectively). This process perfectly balances the privacy needs of both parties: the data provider can only obtain its own input. The corresponding encrypted tag sequence is used, but the tags corresponding to other input values cannot be obtained, thus preventing the model from inferring model information through multiple rounds of queries; at the same time, the model cannot know the actual input from the data provider throughout the entire OT protocol execution process. This provides a safe foundation for subsequent evaluation of the obfuscated circuit, because if the data provider cannot obtain the correct input label, the entire circuit cannot be evaluated correctly.
[0028] This scheme achieves tight encapsulation and execution of computational logic through a two-way secure computation paradigm based on OT-based Garbled Circuit (GC). In terms of efficiency, modern unintentional transport extension techniques can generate a large number of OT instances at very low amortized cost, making it possible even for high-dimensional input data. Furthermore, the communication and computational overhead during the tag acquisition phase is within a controllable range. Compared to other security protocols that require complex interactions to prepare input, OT-GC, due to its clear division of responsibilities and optimized implementation library, typically offers superior overall performance in practice.
[0029] In summary, by introducing an unintentional transmission protocol, consistent and provable security guarantees are ensured for both data privacy and function privacy throughout the entire computational chain, from the initial data input to circuit evaluation and final result decryption. This constitutes a complete, efficient, and secure privacy-preserving function computation closed loop.
[0030] According to another aspect of the present invention, a privacy-preserving function calculation device based on tropical algebraic neural network fitting is provided, comprising: The fitting module is used to perform piecewise linear fitting of continuous functions that require confidential computation using a tropical algebraic neural network; the fitted tropical algebraic neural network model is used as the function that needs to be protected, and the model holds the fitting parameters of the model. The compilation and sending module is used by the model side to compile the calculation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypt and obfuscate the circuit, generate an obfuscated circuit, and send it to the data side. The receiving module is used by the data provider to obtain its private input data from the model provider. The corresponding encrypted tag; The solution module is used by the data provider to use the obtained encrypted tags locally to evaluate the received obfuscation circuit layer by layer, and obtain the encrypted tags output by the fitted tropical algebraic neural network model. The decryption module is used by the data party to decrypt the output encrypted tag locally to obtain the final function calculation result y(x).
[0031] In order to better utilize the above method, this application proposes a privacy-preserving function calculation device based on tropical algebraic neural network fitting. Each module corresponds to a step of the above method, and its specific principle has been described above and will not be repeated here.
[0032] According to another aspect of the present invention, a privacy-preserving function computation device based on tropical algebraic neural network fitting is provided, comprising: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described above.
[0033] In the above technical solution, to better operate and process the method, the method is stored in memory, and the processor executes the stored method. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here.
[0034] According to another aspect of the present invention, a computer-readable storage medium is provided storing a computer program, characterized in that the computer program implements the above-described method when executed by a processor.
[0035] In the above technical solution, to better operate and use the method, the method is stored in a computer-readable storage medium and implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here. Attached Figure Description
[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0037] Figure 1 This is a flowchart illustrating an embodiment of a privacy-preserving function calculation method based on tropical algebraic neural network fitting according to the present invention. Figure 2 This is a schematic diagram of a method for calculating a privacy-preserving function based on fitting a tropical algebraic neural network according to an embodiment of the present invention; Figure 3 This is a schematic diagram of an embodiment of a privacy-preserving function calculation device based on tropical algebraic neural network fitting according to the present invention. Detailed Implementation
[0038] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be particularly noted that the following embodiments are for illustrative purposes only and do not limit the scope of the invention. Similarly, the following embodiments are only some, not all, embodiments of the present invention, and all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0039] This invention proposes a function computation method based on tropical algebraic neural network fitting under privacy protection conditions. This method aims to address the core problems of existing schemes, such as the high cost of securely computing nonlinear functions, insufficient scalability of the computation schemes, and lack of function privacy protection, achieving efficient, secure, and scalable fitting and online evaluation of arbitrary continuous functions.
[0040] With the widespread adoption of cloud computing and federated computing, function computation on sensitive data faces severe privacy risks. This invention primarily addresses the dual problem of data privacy and function intellectual property leakage when performing secure function computation on sensitive data in a distributed collaborative environment. Specifically, when one party holds confidential private data and the other party holds proprietary computation functions that need protection (taking a model fitted by a tropical algebraic neural network as an example), this invention ensures that during the computation process, the input information of the data party will not be leaked to the function party, and the model parameters and business logic of the function party will not be discovered by the data party.
[0041] Using this invention in cloud-based model inference, enterprise clients can leverage cloud service providers' high-value predictive models to process their sensitive operational data, while neither party can access the other's assets. In cross-institutional collaborative diagnostics, multiple hospitals can jointly use advanced diagnostic models to analyze their confidential patient data, sharing only diagnostic conclusions rather than the original data or models. In the financial risk control field, financial institutions can complete secure credit assessments without exposing customer data and core risk control models. Furthermore, in scenarios such as critical infrastructure security assessments, regulatory authorities and enterprises can complete security status analysis without disclosing data or assessment functions. This invention provides a reliable technical solution for the aforementioned function computation requirements that demand bidirectional confidentiality by integrating the dual characteristics of tropical algebraic neural network fitting functions and obfuscated circuits.
[0042] Example 1 Tropical algebra is an unconventional algebraic structure whose operational rules differ significantly from classical linear algebra, yet it demonstrates powerful modeling capabilities in several practical applications. As a representative of idempotent semi-rings, tropical algebra is widely used in combinatorial optimization, graph theory, scheduling theory, automata theory, control systems, and the recently emerging fields of graph neural networks and algebraic geometry. In tropical algebra, traditional addition and multiplication are replaced with new operational rules. For example, tropical addition is defined as a "maximum value" operation in the traditional sense, and tropical multiplication is defined as a "addition" operation in the traditional sense. The algebraic system constructed under these operational rules is called a tropical semi-ring, possessing excellent mathematical structure and application value. Particularly in graph structure analysis and path planning, tropical operations can naturally represent the accumulation and selection operations of shortest paths, thus efficiently modeling practical problems.
[0043] In tropical algebra, traditional addition and multiplication are replaced with new operational rules: Tropical Addition ( This is defined as the traditional "maximum / minimum value" operation: or
[0044] Tropical multiplication ( This is defined as an addition operation in the traditional sense:
[0045] Therefore, common operations such as inner product and matrix multiplication can be redefined under tropical algebra. For example, two matrices of length 10 ... vector , The rules of tropical algebra are used to replace and reconstruct the above operations. Therefore, the dot product form under tropical algebra is:
[0046] Matrix multiplication in tropical algebra The calculation of each element becomes:
[0047]
[0048] With this structure, if privacy protection is achieved by combining obfuscation circuits, the time and communication overhead of calculating inner products and matrix multiplications can be greatly reduced.
[0049] Comparing the ordinary inner product and matrix multiplication based on obfuscated circuits under privacy protection with the inner product and matrix multiplication in tropical algebra, assuming one party has 'a' and the other party has 'b', the values are... Calculating the inner product on the ring with a vector length of n, comparing the time taken by the original method (without tropical algebra) and the method described above (using tropical algebra), the overall improvement is 5.69 to 13.78 times when b = 16, 32, 64 and n = 10, 500, 5000. The improvement becomes more significant as n increases (as shown in the table below).
[0050] In terms of communication volume, it increased by 8.60 times to 16.63 times (as shown in the table below):
[0051] Please see Figure 1 A method for calculating a privacy-preserving function based on tropical algebraic neural network fitting, the method comprising: S1. For the continuous function that needs to be computed confidentially, a tropical algebraic neural network is used to perform piecewise linear fitting on the continuous function; the tropical algebraic neural network includes sequentially composed linear layers, minimum addition layers, and maximum addition layers; the fitted tropical algebraic neural network model is used as the function that needs to be protected, and the model holds the fitting parameters of the model. In this embodiment, among the many structures of neural networks based on tropical algebra, we construct a model structure, LMM-NN (Linear–MaxPlus–MinPlus Neural Network), which consists of a linear layer, a max-plus layer, and a min-plus layer in sequence. This structure can approximate any continuous function with low computational complexity. Unlike traditional neural networks that rely on complex nonlinear activation functions, LMM-NN can theoretically approximate a wide family of functions using only "maximum / minimum" operations, "addition" operations, and a small number of "multiplication" operations, exhibiting high versatility and scalability.
[0052] In this embodiment, a Linear–Minplus–Maxplus Neural Network (LMM-NN) structure is used to perform piecewise linear fitting on the continuous function. The LMM-NN consists of three layers: a linear layer, a min-plus layer, and a max-plus layer; where... The linear layer, given input data First layer output Linear basis functions:
[0053] In the formula, These are the first fitted parameters; The minimum-plus layer contains Each kernel performs a biased min-plus combination of all linear basis functions:
[0054] In the formula, The second fitting parameter controls the bias of different kernels and determines how each kernel is combined. A linear feature.
[0055] Max-Plus Layer, which contains Each core corresponds to all Perform a max-plus combination with bias:
[0056] In the formula, The third fitting parameter is used to control the bias of different kernels.
[0057] When fitting a scalar function, k=1 is usually used, so the fitting formula for the entire LMM-NN is as follows:
[0058] Please see Figure 2 , Figure 2 It is a non-convex function An example of the curve fitting training results is shown using an LMM network with a single input node, 3 slope nodes, 5 hidden nodes, and a single output node, i.e., d=1, n=3, m=3. Figure 2 (a) shows the output of the linear layer, which is a linear function with three different slopes. Figure 2 (b) shows the output of the min-plus layer, which consists of five tropical min-plus positive terms, all of which are derived from the min and plus combinations of the three output linear functions of the linear layer. Figure 2 (c) is the final fitting result of the max-plus layer, which is the max and plus combination of the five minimum positive terms output by the min-plus layer.
[0059] In secure computing scenarios, the model holds the parameters ( The data provider holds the input. By using obfuscated circuits, inference can be completed without exposing model parameters and input data.
[0060] In this embodiment, unlike classic multi-party secure computation where customized protocols are required for different functions, LMM-NN transforms the fitting problem of any function into a set of parameterized Linear / Min-Plus / Max-Plus operations. This enables modeling of a wide range of function families within a unified framework, significantly improving the applicability and versatility of the solution. Furthermore, by parameterizing the objective function as the weights and biases of the neural network, this invention transforms the problem of function value calculation, which originally required point-by-point computation, into a fixed-structure, parameter-driven computation process. During the online inference phase, parameter privacy protection achieves function privacy. Due to the large number of logical operations involved in LMM-NN, obfuscated circuits exhibit unique advantages. Obfuscated circuits transform the entire computation process into a circuit composed of gates, offering significant advantages such as fixed communication rounds and low latency sensitivity. In obfuscated circuits, the implementation complexity of different types of operations on Boolean circuits varies significantly, especially for integer multiplication, where the Boolean circuit construction often becomes a performance bottleneck. Multiplication requires multiplying two n-digit numbers, and the Booleanization process necessitates the construction of multiple partial product generators and carry accumulators, resulting in a gate count of O(n^2). 2 The circuit depth of obfuscated operations is typically much greater than that of addition and comparison operations. For example, in 32-bit integers, a complete multiplier often contains more than 2,000 Boolean gates, while a comparator or adder only requires a few hundred gates. More importantly, obfuscated circuits require encryption, transmission, and evaluation of each Boolean gate during the evaluation process. Furthermore, due to the deeper layer of the multiplication circuit and the stronger dependency chains, the number of communication rounds, latency, and overall bandwidth usage of the protocol increase significantly. In a typical Yao protocol implementation, each non-XOR gate generates four garbled table entries, so the number of gates is linearly related to the communication volume, and multiplication operations significantly increase the overall communication and computational overhead. In addition, because multipliers contain multiple multiply-accumulate units, their circuit paths are long and their structures are complex, making parallel partitioning or modular reuse difficult, further limiting their practical efficiency in large-scale obfuscated computations.
[0061] In contrast, min / max operations are more compact and efficient when implemented in Boolean circuits. A min operation typically consists of a set of comparators and conditional selectors, requiring only one integer comparison (to generate the selection signal) and one bitwise selection logic. The overall gate count is O(n), resulting in a shallow structure with few dependencies and strong parallelism, making it suitable for streaming processing and modular reuse in obfuscated circuit execution models. Within the obfuscated circuit framework, this low-gate-count, shallow logic structure significantly reduces encryption communication overhead and alleviates the load on the decryption evaluation side, enabling the protocol to achieve better throughput and scalability in practical scenarios. Therefore, in obfuscated circuit computation tasks, refactoring the computation into a logic structure primarily based on min or max operations will fundamentally improve performance.
[0062] Traditional deep neural networks contain a large number of multiplications and nonlinear activations, resulting in excessively deep circuits and large encryption gates, making them difficult to execute efficiently in practice. In contrast, the core operations of LMM-NN mainly consist of min / max logic operations and addition. These operations can be represented compactly and efficiently in Boolean circuits, with shallow circuit depth and fewer gates, thus significantly improving the efficiency of privacy protection function computation.
[0063] Therefore, this invention combines the structural advantages of multiple logic operations and obfuscated circuits in logic gate computation of tropical algebraic neural networks to achieve efficient, safe, and scalable fitting and evaluation of generalized functions under privacy protection conditions, solving the three core problems of insufficient universality, high computational cost, and lack of protection of function privacy in the prior art.
[0064] S2. The model provider compiles the calculation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypts and obfuscates the circuit, generates an obfuscated circuit, and sends it to the data provider. In this embodiment, the model, acting as the circuit designer, transforms all operations of the LMM-NN network—including addition, comparisons (for min / max), and a small number of multiplications—into a Boolean circuit composed of logic gates. The model encrypts (i.e., "obfuscates") the truth table of each logic gate, obtaining a so-called obfuscated circuit, and sends it along with corresponding encrypted input tags to the data. Because the truth table of each logic gate is randomized after obfuscation, the data cannot deduce the specific values of the model parameters even if it obtains the entire circuit.
[0065] S3. The data provider obtains its own private input data from the model provider. The corresponding encrypted tag; In this embodiment, the data provider securely obtains its input via a protocol called Oblivious Transfer (OT). The corresponding encrypted tags ensure that the model provider cannot obtain them. The actual value of .
[0066] S4. The data provider uses the obtained encrypted tag locally to evaluate the received obfuscation circuit layer by layer, and obtains the encrypted tag output by the fitted tropical algebraic neural network model. S5. The data provider decrypts the output encrypted tag locally to obtain the final function calculation result. .
[0067] In this embodiment, the data provider cannot obtain the model parameters throughout the entire process. The model cannot know the input either. and This allows for the completion of complete neural network inference while ensuring privacy.
[0068] Example 2 Please see Figure 3 A privacy-preserving function computation device based on tropical algebraic neural network fitting, comprising: The fitting module is used to perform piecewise linear fitting of continuous functions that require confidential computation using a tropical algebraic neural network; the tropical algebraic neural network includes sequentially composed linear layers, minimum addition layers, and maximum addition layers; the fitted tropical algebraic neural network model is used as the function to be protected, and the model holds the fitting parameters of the model; The compilation and sending module is used by the model side to compile the calculation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypt and obfuscate the circuit, generate an obfuscated circuit, and send it to the data side. The receiving module is used by the data provider to obtain its private input data from the model provider. The corresponding encrypted tag; The solution module is used by the data provider to use the obtained encrypted tags locally to evaluate the received obfuscation circuit layer by layer, and obtain the encrypted tags output by the fitted tropical algebraic neural network model. The decryption module is used by the data provider to locally decrypt the output encrypted tag to obtain the final function calculation result. .
[0069] In order to better utilize the method described in one of the embodiments in the above technical solutions, this application proposes a privacy protection function calculation device based on tropical algebraic neural network fitting. Each module corresponds to each step of the above method, and its specific principle has been described above and will not be repeated here.
[0070] In this embodiment, the tropical algebraic neural network includes: a linear layer, a minimum addition layer, and a maximum addition layer; wherein, Linear layers are used to fit a given input data and output several linear basis functions; Minimum addition is used to perform a min-plus combination with bias on all linear basis functions; The maximum addition layer is used to perform a biased max-plus combination of all the linear basis functions resulting from the min-plus combination with bias.
[0071] In this embodiment, the linear layer is given input data. First layer output Linear basis functions:
[0072] In the formula, These are the first fitted parameters; Minimum layer, which contains Each kernel performs a biased min-plus combination of all linear basis functions:
[0073] In the formula, This is the second fitting parameter, used to control the bias of different kernels; Maximum layer, which contains Each core corresponds to all Perform a max-plus combination with bias:
[0074] In the formula, The third fitting parameter is used to control the bias of different kernels.
[0075] In this embodiment, the receiving module is specifically used for: The data provider obtains its private input data from the model provider through an unintentional transmission protocol. The corresponding encrypted tag.
[0076] Example 3 A privacy-preserving function computation device based on tropical algebraic neural network fitting, comprising: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in one of the embodiments.
[0077] In the above technical solution, in order to better operate and process the method described in one of the embodiments, the method is stored in a memory, and the stored method is executed by a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated further here.
[0078] Example 4 A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in one of the embodiments.
[0079] In the above technical solution, to better operate and use the method, the method is stored in a computer-readable storage medium and implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here.
[0080] The present invention has the following advantages: 1. High versatility and scalability Traditional privacy-preserving function computation schemes are typically designed for specific functions and lack general scalability. This invention, based on the LMM-NN model, approximates any continuous function through piecewise linear combinations. Theoretically, it can approximate any continuous function, thus possessing strong versatility and scalability, and is applicable to various practical scenarios such as finance, healthcare, and intelligent manufacturing.
[0081] 2. Low computational and communication overhead. The application of scrambled circuits in this invention fully leverages the structural features of LMM-NN. The linear, Min-Plus, and Max-Plus layer structures of LMM-NN naturally align with the Boolean circuits of scrambled circuits. The core operations of this network are mainly min, max, and addition operations. Its Boolean circuit depth is relatively shallow, and the number of communication rounds is fixed. Compared to the complex structures of traditional deep neural networks containing a large number of multiplications and nonlinear activation functions, the piecewise linear characteristics of LMM-NN give it a greater advantage in scrambled circuit computation scenarios.
[0082] 3. Dual privacy protection This invention protects the privacy of both model parameters and input data in a single inference iteration. The model side does not need to disclose function parameters, and the data side does not need to expose the input x. While ensuring computational accuracy, it strictly controls the risk of information leakage, making it particularly suitable for collaborative data computing needs across organizations and regions.
[0083] In summary, this invention, based on tropical algebraic neural networks and obfuscated circuits, constructs an efficient, universal, and secure comprehensive solution in the field of privacy-preserving function computation through the organic combination of its algorithm design and cryptographic primitives. Its core advantage lies in utilizing tropical algebra (max-plus and min-plus algebras) to perform piecewise linear fitting of continuous functions, transforming complex nonlinear computations into a regular computational graph composed of linear matrix operations and pairwise comparison-selection operations. This characteristic significantly reduces the number and depth of gates in the obfuscated circuit when compiled, thereby directly reducing the communication and computational complexity of secure computation. Simultaneously, this scheme securely transmits the data provider's input encryption tag by introducing an unintentional transmission protocol, achieving efficient synergy with the obfuscated circuit paradigm while ensuring input privacy, thus constructing a provably secure computational link.
[0084] The advantages of this scheme are reflected in the deep integration of three levels: In terms of computational efficiency, the clear hierarchical structure of the Tropical Algebraic Neural Network (linear layers, minimum addition layers, maximum addition layers) means that its Boolean circuit representation mainly consists of adders and multiplexers, avoiding the high-overhead operations required to implement transcendental functions and optimizing computational efficiency. In terms of generality and scalability, the model can adapt to different objective functions simply by adjusting the fitting parameter matrix without changing the underlying security protocol, providing a highly parameterized and near-black-box general computational framework, effectively overcoming the serious customization problems in traditional schemes. In terms of security attributes, this scheme achieves end-to-end privacy protection. Inadvertent transmission ensures the confidentiality of data input, while obfuscated circuits simultaneously hide the internal logic and parameters of the function, thus perfectly achieving the dual protection goals of data privacy and function privacy.
[0085] Therefore, this technical solution successfully solves the core bottleneck problem currently faced by secure multi-party computation in handling nonlinear functions, namely the dilemma of balancing efficiency, universality and function privacy protection, providing a strong theoretical basis and feasible engineering path for securely executing complex private function computations in the data-driven era.
[0086] The above description is only a part of the embodiments of the present invention and does not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made based on the content of the present invention specification and drawings, or direct or indirect application in other related technical fields, are similarly included within the patent protection scope of the present invention.
Claims
1. A method for calculating a privacy-preserving function based on tropical algebraic neural network fitting, characterized in that, The method includes: For continuous functions requiring confidential computation, a tropical algebraic neural network is used to perform piecewise linear fitting of the continuous function; the tropical algebraic neural network includes sequentially composed linear layers, minimum addition layers, and maximum addition layers; the fitted tropical algebraic neural network model is used as the function to be protected, and the model holds the fitting parameters of the model; The model provider compiles the computation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypts and obfuscates the circuit, generates an obfuscated circuit, and sends it to the data provider. The data provider obtains its own private input data from the model provider. The corresponding encrypted tag; The data provider uses the obtained encrypted tags locally to evaluate the received obfuscation circuit layer by layer, and obtains the encrypted tags output by the fitted tropical algebraic neural network model. The data provider decrypts the output encrypted tag locally to obtain the final function calculation result y(x).
2. The method for calculating a privacy-preserving function based on tropical algebraic neural network fitting as described in claim 1, characterized in that, The linear layer is used to fit a given input data and output several linear basis functions; The minimum addition layer is used to perform a min-plus combination with bias on all linear basis functions; The maximum addition layer is used to perform a biased max-plus combination of all the linear basis functions after the min-plus combination with bias.
3. The privacy-preserving function calculation method based on tropical algebraic neural network fitting as described in claim 2, characterized in that, The linear layer, given input data First layer output Linear basis functions: In the formula, These are the first fitted parameters; The minimum added layer contains Each kernel performs a biased min-plus combination of all linear basis functions: In the formula, This is the second fitting parameter, used to control the bias of different kernels; The maximum added layer contains Each core corresponds to all Perform a max-plus combination with bias: In the formula, The third fitting parameter is used to control the bias of different kernels.
4. The privacy-preserving function calculation method based on tropical algebraic neural network fitting as described in claim 1, characterized in that, The data provider obtains its own private input data from the model provider. The corresponding encrypted tags, specifically: The data provider obtains its private input data from the model provider through an unintentional transmission protocol. The corresponding encrypted tag.
5. A privacy-preserving function calculation device based on tropical algebraic neural network fitting, characterized in that, include: The fitting module is used to perform piecewise linear fitting of continuous functions that require confidential computation using a tropical algebraic neural network; the tropical algebraic neural network includes sequentially composed linear layers, minimum addition layers, and maximum addition layers; the fitted tropical algebraic neural network model is used as the function to be protected, and the model holds the fitting parameters of the model; The compilation and sending module is used by the model side to compile the calculation process of the fitted tropical algebraic neural network model into a Boolean circuit composed of logic gates, encrypt and obfuscate the circuit, generate an obfuscated circuit, and send it to the data side. The receiving module is used by the data provider to obtain its private input data from the model provider. The corresponding encrypted tag; The solution module is used by the data provider to use the obtained encrypted tags locally to evaluate the received obfuscation circuit layer by layer, and obtain the encrypted tags output by the fitted tropical algebraic neural network model. The decryption module is used by the data party to decrypt the output encrypted tag locally to obtain the final function calculation result y(x).
6. The privacy-preserving function calculation device based on tropical algebraic neural network fitting as described in claim 5, characterized in that, The tropical algebraic neural network includes: linear layers, minimum addition layers, and maximum addition layers; wherein... The linear layer is used to fit a given input data and output several linear basis functions; The minimum addition layer is used to perform a min-plus combination with bias on all linear basis functions; The maximum addition layer is used to perform a biased max-plus combination of all the linear basis functions after the min-plus combination with bias.
7. The privacy-preserving function calculation device based on tropical algebraic neural network fitting as described in claim 6, characterized in that, The linear layer, given input data First layer output Linear basis functions: In the formula, These are the first fitted parameters; The minimum added layer contains Each kernel performs a biased min-plus combination of all linear basis functions: In the formula, This is the second fitting parameter, used to control the bias of different kernels; The maximum added layer contains Each core corresponds to all Perform a max-plus combination with bias: In the formula, The third fitting parameter is used to control the bias of different kernels.
8. The privacy-preserving function calculation device based on tropical algebraic neural network fitting as described in claim 5, characterized in that, The receiving module is specifically used for: The data provider obtains its private input data from the model provider through an unintentional transmission protocol. The corresponding encrypted tag.
9. A privacy-preserving function calculation device based on tropical algebraic neural network fitting, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in any one of claims 1 to 4.
10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 4.