Extensible distributed privacy-preserving fft method based on secret sharing and mac tag

Abstract

The application relates to an expandable distributed privacy protection FFT method and system based on secret sharing and MAC tags, which comprises the following steps: input original data is divided into multiple data shares by adopting a three-party replication secret sharing technology, a corresponding MAC tag is generated for each data share, and the secret sharing is performed to each participant cluster; each computing node in each participant cluster performs one-dimensional fast Fourier transform on each row of the held data share to obtain an intermediate matrix; a rotation factor is multiplied with the intermediate matrix to obtain a rotation matrix; each computing node divides the rotation matrix into multiple section shares in the column direction, and sends each section share to a corresponding group leader according to the serial number of the section share; the computing node calculates the fast Fourier transform in the column direction to obtain an output matrix, and a principal verifies the output matrix; while resisting malicious attacks, the communication complexity is reduced from O(M) to O(M / N), the MAC verification overhead is reduced to less than 8% of the total time consumption, and the expandability of the system is greatly improved.

Description

Technical Field

[0001] This invention relates to the intersection of privacy computing and high-performance computing, and in particular to a scalable distributed privacy-preserving FFT method and system based on secret sharing and MAC tagging. Background Technology

[0002] As a core algorithm in fields such as digital signal processing, image processing, scientific computing, and machine learning, the computational efficiency of the Fast Fourier Transform (FFT) directly impacts the overall performance of related applications. With the explosive growth of data volume (such as astronomical data processing, genome sequence analysis, and large-scale IoT signal processing), single-machine FFT can no longer meet the processing demands of massive amounts of data, making distributed FFT an inevitable choice. However, how to achieve efficient FFT computation while protecting data privacy in a distributed environment has become a critical technical challenge that urgently needs to be addressed.

[0003] In the field of MPC (Multi-Party Computation), the SPDZ protocol is one of the most practical and proactively secure general-purpose MPC protocols (i.e., capable of resisting malicious attackers). SPDZ employs a preprocessing model (generating random multiplication triples offline and using these triples to compute functions online), enabling it to withstand any number of malicious corrupted nodes. However, existing SPDZ protocols primarily target general-purpose arithmetic circuit design, directly applying them to distributed FFT. Existing technologies suffer from the following drawbacks: First, there's the conflict between communication overhead and security mechanisms. Distributed FFT (especially the matrix transpose stage) requires global data rearrangement (All-to-All communication). Achieving this global communication in a secret-sharing state necessitates introducing numerous consistency check protocols (MAC checks), causing communication complexity to increase quadratically. As the node scales, communication overhead quickly becomes a system bottleneck.

[0004] Second, there is the computational bottleneck issue of tag verification. The MAC (Message Authentication Code) mechanism used in SPDZ for tamper-proofing requires MAC verification after each multiplication operation. However, FFT involves a large number of butterfly operations (multiplication operations), and directly applying this mechanism would lead to excessive computational overhead in the online phase. Experiments show that when processing 1TB of data on a 16-node cluster, MAC verification overhead can account for more than 35% of the total FFT computation time.

[0005] Third, there is the problem of undifferentiated node roles. Existing distributed FFT schemes typically treat all nodes as peers, without considering the possibility of introducing a hierarchical structure in the security protocol to optimize communication patterns. This flat architecture forces all nodes to participate in global communication, making it impossible to leverage data locality to optimize communication paths.

[0006] Fourth, there is the complexity of cross-domain collaboration. In practical applications, data is often held by a single entity (such as the data owner), but computation may be performed jointly by multiple untrusted cloud service providers (CSPs). Currently, there is no mature solution for how to securely distribute computational tasks to multiple participating clusters and efficiently complete distributed FFT after the data owner has completed the secret sharing. Summary of the Invention

[0007] This invention addresses the technical problems existing in the prior art by providing a scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging. It adopts a distributed authentication private FFT scheme based on a three-level network architecture, combining layered communication and batch verification mechanisms to achieve an optimal balance between communication complexity and security strength, while supporting secure collaboration between data owners and multiple computing service providers.

[0008] According to a first aspect of the present invention, a scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging is provided, comprising: Step 1: The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generates a corresponding MAC tag for each data share, and then secretly shares it with each participating cluster. Step 2: The computing nodes within each participating party's cluster perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; the intermediate matrix is ​​then multiplied by a rotation factor to obtain a rotation matrix. Step 3: Set the computing nodes with even indices as group leaders and the computing nodes with odd indices as group members; after each computing node divides the rotation matrix into multiple segments according to the column direction, it sends each segment to the corresponding group leader according to the segment number. Each group leader aggregates the received segment segments to obtain two column vectors, performs a transpose operation on the two column vectors, and sends them to the corresponding group members. Step 4: Each computing node performs a Fast Fourier Transform in its local computing column direction to obtain an output matrix, and the client verifies the output matrix.

[0009] Based on the above technical solution, the present invention can also be improved as follows.

[0010] Optionally, step 1 includes: Step 101: Reshape the input raw data into a matrix. The matrix The element in the j-th row and k-th column is ; Step 102, the delegator determines the cluster to be assigned to any i-th participating party. Data share is ; Step 103, the principal generates a global MAC key. The MAC tag is generated as follows: .

[0011] Optionally, the intermediate matrix in step 2 is: ; Cluster The intermediate matrix obtained through collaborative computation by internal servers The line, number The frequency domain output is: in, Represents the finite field The primary unit root; The MAC tags are synchronously updated during the calculation of the intermediate matrix as follows: .

[0012] Optionally, step 2, which involves performing a rotation factor multiplication on the intermediate matrix to obtain the rotation matrix, includes: Define the rotation factor matrix The element in the j-th row and k-th column is: ; This represents the total number of elements in the matrix; Each participating cluster on the intermediate matrix The rotation matrix is ​​obtained by performing element-wise multiplication. for: Among them, symbols This indicates Hadamard element-wise multiplication, where i represents the index of the participating cluster.

[0013] Optionally, step 3 includes: Step 301, each computing node will use the rotation matrix The data is divided into N / 2 segments along the column direction, and each segment contains two consecutive columns of data; N represents the total number of computing nodes. Step 302: Each computing node sends the share of each segment to the corresponding group leader. The computing node of the group leader corresponding to any k-th segment share... If the group leader corresponding to the segment share is itself, then the copy is completed through local memory. Step 303, calculate nodes for any group leader It receives the k-th segment data sent by all computing nodes in parallel and assembles it into a set of segment shares for two complete column vectors.

[0014] Optionally, step 3 may further include: In step 304, each group leader transposes the two aggregated column vectors locally to obtain two rows of data; the first row of data obtained after transposition is kept locally, and the second row of data obtained after transposition is sent to the paired group member computing node through a point-to-point secure link. .

[0015] Optionally, step 4 includes: Step 401, each computing node performs a length-based operation on its held column shares. The Fast Fourier Transform (FFT) of the i-th participating cluster is used to compute the FFT in the column direction, resulting in the following output matrix: in, Represents the output matrix The element in the m-th row and k-th column; This refers to the element in the j-th row and k-th column of the matrix after the transpose operation.

[0016] Optionally, step 4 further includes: Step 401: The client flattens the output matrix and combines it with the MAC tags to form a data pair. For length of Perform batch aggregation on sequences: in, This represents the output sequence after the output matrix is ​​aggregated. This represents the output sequence after MAC tag aggregation. This is a randomly selected number.

[0017] Step 402, the principal uses the global MAC key Verify the aggregation results and determine the equality. Is it valid? If the equation is true, it confirms that all shares have not been tampered with; if the equation is false, it is determined that at least one data share has been tampered with, and the process is rolled back to verify each share in order to locate the malicious computing node.

[0018] Optionally, step 4 further includes: The client rearranges the data that passes the equality verification in order to obtain the target one-dimensional sequence as the final one-dimensional output result; the strict mapping relationship of the rearrangement process is defined as: in, , Let be the index of the element in the target one-dimensional sequence. , ; Let i represent the l-th element in the target one-dimensional sequence, and let i represent the index of the participating cluster.

[0019] According to a second aspect of the present invention, a scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging is provided, comprising: a delegator, a participant cluster, and computing nodes; The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generate a corresponding MAC tag for each data share, and then secretly share it with each of the participating party clusters. The computing nodes are deployed within the clusters of each participating party. The computing nodes within the clusters perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; and perform a rotation factor multiplication on the intermediate matrix to obtain a rotation matrix. The computation nodes with even indices are designated as group leaders, and the computation nodes with odd indices are designated as group members. Each computation node divides the rotation matrix into multiple segments along the column direction, and then sends each segment to the corresponding group leader according to its sequence number. Each group leader aggregates the received segments to obtain two column vectors, performs a transpose operation on the two column vectors, and then sends them to the corresponding group members. Each computation node performs a Fast Fourier Transform in the column direction locally to obtain the output matrix. The client verifies the output matrix.

[0020] This invention provides a scalable distributed privacy-preserving FFT method and system based on secret sharing and MAC tagging. Through a three-tier network architecture, it separates the data owner from the computing nodes, constructing a lightweight private computing outsourcing model. The delegator only needs to complete the secret sharing and tag generation once to go offline; all subsequent complex calculations are handled by a cluster of multiple participants, greatly reducing the computational burden on the data owner, making it particularly suitable for resource-constrained terminal devices. Simultaneously, the delegator and computing nodes are physically isolated, and the original data always exists in the form of a secret share, fundamentally eliminating the risk of data leakage.

[0021] This invention introduces a privacy protection mechanism based on three-party replication and secret sharing to ensure the confidentiality of data throughout its entire lifecycle. The original data is segmented using three-party replication and secret sharing, preventing any single node from obtaining any plaintext information. Any two nodes can collaborate to reconstruct the secret, and this threshold characteristic provides a flexible balance between security and availability. Data remains secret throughout transmission, storage, and computation, ensuring that no single node (including the group leader) can access the original data.

[0022] This invention integrates the SPDZ-MAC tagging scheme to achieve data integrity protection under a malicious security model. Each secret share is tagged with a tag protected by a global MAC key; any tampering with the share will cause MAC verification to fail. For the numerous parallel multiplication operations in FFT computation, a dedicated MAC batch verification protocol is designed. This protocol combines the MAC checks of multiple shares into a single verification operation through random linear combination, reducing verification overhead from... Reduce to Meanwhile, by embedding the generation, updating, and verification of MAC tags into the FFT operation process, parallel processing of computation and integrity protection is achieved, reducing the MAC verification overhead from 35% of the total FFT time to less than 8%.

[0023] By employing a hierarchical communication topology of group leader and group members, global all-to-all communication is transformed into a two-stage mode of local aggregation and point-to-point scattering, completely resolving the communication bottleneck problem. This invention designates even-numbered index nodes as group leaders and odd-numbered nodes as group members. All nodes first aggregate data to their corresponding group leader, then scatter it to their paired group members after the group leader's transpose. When the target column index matches a node index, the data is directly retained locally, maximizing data locality. This mechanism reduces communication complexity from... Reduce to This allows the speedup to remain nearly linear (efficiency ≥ 82%) when the node size is expanded from N=4 to N=64.

[0024] It possesses extremely high versatility and scalability, making it suitable for various high-security and privacy-preserving computing scenarios. This invention does not rely on specific underlying hardware or network infrastructure, and is applicable to multiple clusters within a single cloud service provider, as well as collaborative computing across multiple cloud service providers. By configuring different secret-sharing parameters and MAC security parameters, the system can adapt to different security requirements, ranging from semi-honest security to malicious security, and can be widely applied in fields requiring secure spectrum analysis of large-scale data, such as financial risk control, medical data analysis, and privacy-preserving machine learning. Attached Figure Description

[0025] Figure 1A flowchart illustrating an embodiment of a scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging provided by the present invention; Figure 2 A three-level architecture diagram of an embodiment of a scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging provided by the present invention; Figure 3 This is a schematic diagram illustrating the interactions of various roles in an embodiment of a scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging provided by the present invention. Detailed Implementation

[0026] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0027] Figure 1 The flowchart illustrates an embodiment of a scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging provided by the present invention. Figure 1 This describes the complete process from client data distribution, row-wise FFT computation, rotation factor multiplication and global transpose to column-wise FFT and result output, demonstrating the core steps of hierarchical communication and MAC batch verification, combined with... Figure 1 It can be seen that the FFT method includes: Step 1: The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generates a corresponding MAC tag for each data share, and then secretly shares it with each participating cluster.

[0028] The principal distributes the share to each computing node via a secure channel. Once distribution is complete, the principal can immediately go offline and no longer participate in subsequent computations, achieving a truly lightweight outsourcing model.

[0029] Step 2: The computing nodes within each participating cluster perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; the intermediate matrix is ​​then multiplied by a rotation factor to obtain a rotation matrix.

[0030] In practice, each computing node performs the first-stage FFT calculation on its data share, which is to perform a one-dimensional fast Fourier transform on each row of the matrix.

[0031] Step 3: Set the computation nodes with even indices as group leaders and the computation nodes with odd indices as group members; after each computation node divides the rotation matrix into multiple segments according to the column direction, it sends each segment to the corresponding group leader according to the segment number. Each group leader aggregates the received segment segments to obtain two column vectors, performs a transpose operation on the two column vectors, and then sends them to the corresponding group members.

[0032] Step 4: Each computing node performs a Fast Fourier Transform in the column direction of its local computing node to obtain the output matrix, which the client then verifies.

[0033] To address the high computational complexity bottleneck and inability to handle malicious security issues inherent in existing Fast Fourier Transform (FFT) methods, and to overcome the shortcomings of existing privacy-preserving distributed computing schemes such as high communication overhead, high verification costs, poor scalability, and complex cross-domain collaboration, this invention provides a scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging. The aim is to upgrade traditional FFT with privacy protection and tamper-proof capabilities under malicious security models, reducing communication complexity from O(M) to O(M / N) and MAC verification overhead from over 35% to below 8%, achieving an optimal balance between security, communication efficiency, and computational efficiency. Example 1

[0034] Embodiment 1 provided by this invention is an embodiment of a scalable distributed privacy-preserving FFT based on secret sharing and MAC tagging, as provided by this invention. Figure 2 and Figure 3 The figures shown are a three-level architecture diagram and an interaction diagram of each role in an embodiment of a scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging provided by the present invention. Figure 2 This demonstrates the overall role architecture of the algorithm. Figure 3 This demonstrates the algorithmic structure consisting of the principal, participating clusters, and computing nodes, clarifying the internal composition of each role and their interaction relationships within the three-level network topology. Figures 1-3 It can be seen that the embodiments of this FFT method include: Step 1: The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generates a corresponding MAC tag for each data share, and then secretly shares it with each participating cluster.

[0035] In one possible embodiment, step 1 includes: Step 101: Reshape the input raw data into a matrix. ,matrix The element in the j-th row and k-th column is .

[0036] In practice, the input data is: To improve the efficiency of FFT computation, the input vector is first reshaped into a matrix: ,in M represents the total amount of data. Representation matrix the number of rows, Representation matrix The number of columns.

[0037] Step 102: The delegator determines the cluster to be assigned to any i-th participating party. Data share is .

[0038] In one possible implementation, the principal first secretly shares the input data by splitting it into multiple fragments and distributing them to various computing nodes.

[0039] In one embodiment of the present invention, the system consists of three independent participant clusters: Each participating cluster Contains Each computing server, or N computing nodes, is used to execute secret shared computing tasks in parallel. The three clusters logically correspond to the parties involved in the protocol. Specifically, the delegator generates three additive secret shares: Step 103: To ensure the correctness of subsequent calculations, the principal generates a global MAC key. Global MAC key Used to verify the integrity of the entire calculation process.

[0040] And this MAC value is also secretly shared, obtaining... .

[0041] The principal sends the data share and MAC share to the corresponding participant clusters, respectively. Within each cluster, the data is further distributed among the cluster's participants. Multiple computing nodes are used to support parallel computing.

[0042] Step 2: The computing nodes within each participating cluster perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; the intermediate matrix is ​​then multiplied by a rotation factor to obtain a rotation matrix.

[0043] The core of this step is to independently perform row-wise FFTs within each node, while ensuring all operations are performed on the secret-shared domain and maintaining MAC tag consistency. For each multiplication operation, a node needs to interact with its associated parties to complete the computation. Under the three-party replication secret-shared setup, each participant holds two shares, and multiplication operations can be correctly executed through communication between the participants. Importantly, MAC tags need to be updated synchronously throughout the computation. After each multiplication, the node needs to update the corresponding MAC tag share based on the MAC key share and the newly calculated result share, ensuring that the final result includes not only the data share but also the correct MAC tag. After completing the FFT of all rows, each node obtains a result vector with the same row size as the input matrix, where each element is a secret-shared value with a MAC tag. These results will serve as input for the next stage.

[0044] In distributed FFT, after row transformations, a twiddle factor multiplication and matrix transpose are required before performing a column-direction FFT. The twiddle factor is an inherent complex constant in the FFT algorithm; for each matrix element, its twiddle factor depends on the element's row and column indices. Since the twiddle factor is publicly known, each node can directly multiply its local share by the corresponding twiddle factor. In the secret-sharing domain, multiplication with the public constant is a simple scalar multiplication; each node independently performs the multiplication operation on its locally held share, without involving inter-node communication.

[0045] In one possible embodiment, the intermediate matrix in step 2 is: .

[0046] Cluster The intermediate matrix obtained through collaborative computation by internal servers The line, number The frequency domain output is: in, Represents the finite field The primary unit root.

[0047] The MAC tags are updated synchronously when calculating the intermediate matrix as follows: .

[0048] In practice, since FFT is a linear operation, MAC tags can be updated in the same way. In this way, each cluster can complete row-wise FFT calculations and obtain the corresponding MAC tag values ​​without recovering the plaintext data.

[0049] In one possible embodiment, step 2, which involves multiplying the intermediate matrix by a rotation factor to obtain the rotation matrix, includes: Define the rotation factor matrix The element in the j-th row and k-th column is: ; This represents the total number of elements in the matrix.

[0050] Each participating cluster on the intermediate matrix Perform element-wise multiplication to obtain the rotation matrix for: Among them, symbols Indicates Hadamard element-wise multiplication, where i is the index of the participating cluster.

[0051] Step 3: Set the computation nodes with even indices as group leaders and the computation nodes with odd indices as group members; after each computation node divides the rotation matrix into multiple segments according to the column direction, it sends each segment to the corresponding group leader according to the segment number. Each group leader aggregates the received segment segments to obtain two column vectors, performs a transpose operation on the two column vectors, and then sends them to the corresponding group members.

[0052] After performing the rotation factor multiplication, the node needs to divide the current matrix into multiple segments along the column direction, each segment containing two consecutive columns of data. The number of segments is exactly equal to the number of group leader nodes (i.e., N / 2), and the target receiver for each segment is a fixed group leader node: the k-th segment will be sent to the group leader numbered 2k. After receiving the corresponding segment data from the entire network in parallel, the group leader node assembles it locally and performs a matrix transpose operation; subsequently, the group leader node keeps the first row of data after transpose (corresponding to a complete column of data) locally, and sends the second row of data to its paired member nodes through point-to-point directional scattering. Through this aggregation method, the originally globally synchronized All-to-All communication is decomposed into multiple parallel "many-to-one" communications, distributing the communication pressure from the entire network to each group leader node, significantly reducing the overall communication complexity.

[0053] In one possible embodiment, step 3 includes: Step 301, each computing node rotates the matrix The data is divided into N / 2 segments along the column direction, and each segment contains two consecutive columns of data; N represents the total number of computing nodes.

[0054] Step 302: Each computing node sends the share of each segment to the corresponding group leader. The computing node of the group leader corresponding to any k-th segment share... If the group leader corresponding to a segment share is itself, then it is completed through local memory copying; in specific implementation, each segment contains two consecutive columns of data, and the column index corresponding to the k-th segment is... .

[0055] Step 303, calculate nodes for any group leader It receives the k-th segment data sent by all computing nodes in parallel and assembles it into a set of segment shares in two complete column vectors (i.e., the 2k-th column and the 2k+1-th column of the original matrix).

[0056] In one possible embodiment, step 3 further includes: In step 304, each group leader performs a local transpose on the two aggregated column vectors to obtain two rows of data. The transpose operation is as follows: The first row of data obtained after transposition (corresponding to the 2kth column of the final output matrix) is kept locally, and the second row of data obtained after transposition (corresponding to the 2k+1th column) is sent to the paired member computing node via a point-to-point secure link. .

[0057] Step 4: Each computing node performs a Fast Fourier Transform (FFT) in its local column direction to obtain the output matrix, which the client then verifies. The computing nodes complete the final calculation, and the client reconstructs and verifies the result.

[0058] Each node holds a complete column of transposed data (shared in secret) and can begin the second phase of local computation of column-direction FFT.

[0059] Each node performs a Fast Fourier Transform (FFT) on its column vectors. Similar to the row-oriented FFT, each operation in the column-oriented FFT is performed on the secret-sharing domain. Additions and subtractions are calculated directly, while multiplications are performed according to the three-way copy secret-sharing multiplication protocol, with MAC tags updated synchronously. This process is entirely local. After the column-oriented FFT is complete, each node receives one column of the resulting matrix. The resulting columns from all nodes are combined to form the secret-sharing representation of the complete FFT result matrix. Subsequently, each node flattens the result matrix, restoring it to a one-dimensional output share vector.

[0060] At this point, the client is responsible for data recovery and verification. The client collects result shares and their corresponding MAC tags from at least a threshold number of nodes. To avoid the enormous overhead of comparing each node individually, the client uses compressed batch verification technology for integrity verification: the client randomly selects a set of public challenge coefficients (or verification points), aggregates the massive number of collected result shares and tags into a single verification equation, and performs a one-time comparison using its offline-stored global MAC key. If the aggregated equation holds true, it is confirmed with a very high probability that all data has not been tampered with. The client uses a reconstruction algorithm to recover and rearrange the output of the final plaintext FFT result; if the verification fails, it indicates malicious tampering. The client refuses to output the result and triggers an alarm mechanism, thus efficiently ensuring the reliability of the output.

[0061] In one possible embodiment, step 4 includes: Step 401, each computing node performs a length-based operation on its held column shares. The Fast Fourier Transform (FFT) of the i-th participating cluster is used to compute the FFT in the column direction, resulting in the following output matrix: in, Represents the output matrix The element in the m-th row and k-th column; This refers to the element in the j-th row and k-th column of the matrix after the transpose operation.

[0062] Similarly, the corresponding labels are calculated, and after the calculation is completed, each cluster returns the result share to the delegator. In one possible embodiment, step 4 further includes: Step 401: The client flattens the output matrix and combines it with MAC tags to form a data pair. For length of Perform batch aggregation on sequences: in, This represents the output sequence after the output matrix is ​​aggregated. This represents the output sequence after MAC tag aggregation. This is a randomly selected number.

[0063] Step 402, the principal uses the global MAC key Verify the aggregation results and determine the equality. Whether it is valid or not.

[0064] If the equation holds true, then according to the Schwartz-Zippel lemma, it can be confirmed with a very high probability that all shares have not been tampered with; if the equation does not hold true, then it is determined that at least one data share has been tampered with, and in this case, it is necessary to backtrack to verify one by one to locate the malicious computing node.

[0065] In practical implementation, due to finite fields Large enough (e.g.) The probability of compression verification errors is almost negligible.

[0066] In one possible embodiment, step 4 further includes: The client rearranges the data that passes the equality verification in order to obtain the target one-dimensional sequence as the final one-dimensional output result; the strict mapping relationship of the rearrangement process is defined as: in, , Let be the index of the element in the target one-dimensional sequence. Its index can be uniquely determined by the row index and column index in the matrix, that is... ; Let i represent the l-th element in the target one-dimensional sequence, and let i represent the index of the participating cluster.

[0067] The above process achieves lightweight offline outsourcing for clients through a three-tier network architecture, transforms global all-to-all communication into a two-stage aggregation-scattering mode through hierarchical communication between team leaders and team members, minimizes integrity check overhead through MAC batch verification, and finally achieves efficient and scalable distributed FFT computation under a malicious security model.

[0068] The core concept of this invention lies in using a three-party replication secret sharing (RSS) and message authentication code (MAC) tagging mechanism as the security foundation of the system, and deeply integrating it with a three-tier network architecture of "delegator-participant cluster-computing node". Specifically, this invention utilizes the RSS mechanism to achieve "usable but invisible" massive amounts of data, and uses MAC tags based on global keys to give the system proactive defense capabilities against malicious node tampering. To overcome the communication and computational explosion brought about by the introduction of RSS and MAC, this invention innovatively introduces a "regional coordination node (group leader)" mechanism within the secret sharing domain, dividing the roles of group leader and group members according to node index, transforming the originally expensive global all-to-all communication in the encrypted state into a two-stage dimensionality reduction process of local aggregation and directional scattering; at the same time, combined with a MAC tag batch verification strategy based on random linear combination optimized for the characteristics of FFT butterfly operation, the encrypted computation and integrity verification are completely decoupled. Example 2

[0069] Embodiment 2 of this invention provides an example of a scalable distributed privacy-preserving FFT system based on secret sharing and MAC tags. To support secure computation logic based on third-party replicated secret sharing (RSS) and message authentication code (MAC) tags, this system abandons the traditional flat peer-to-peer network and constructs a three-level asymmetric interaction system consisting of "delegator-participant cluster layer-computing node end". Combined with... Figures 1-3 It is known that the implementation of this FFT system includes: a principal, a cluster of participants, and computing nodes.

[0070] The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generate a corresponding MAC tag for each data share, and then secretly share it with each participating cluster.

[0071] The delegator, acting as both the initiator of the computation task and the recipient of the final result, runs on a trusted physical terminal. It undertakes the following dedicated computational logic: Offline preprocessing and data distribution: During the task initialization phase, the delegator generates a global MAC key. The method employs a three-party replication and secret sharing technique to divide each element of the original data matrix and its corresponding global MAC key into multiple secret shares, and calculates a corresponding MAC tag for each data share. Subsequently, the delegator distributes the secret shares and tags to each computing node via a secure channel. After distribution is complete, the delegator can disconnect from the network, achieving lightweight offline operation.

[0072] Online Collection and Result Verification Reconstruction: When computation results are needed, the client re-logins and initiates reconstruction requests to at least a threshold number of computation nodes, collecting result shares and MAC tags. Subsequently, the client uses a compressed batch verification technique based on random linear combinations to perform integrity verification on all shares (i.e.,... The complexity of the verification is compressed into a single aggregation equation verification. After the verification is passed, the plaintext FFT result is recovered using the secret sharing reconstruction algorithm and rearranged in order.

[0073] The computing nodes are deployed within the clusters of each participating party. The computing nodes within the cluster perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; the intermediate matrix is ​​then multiplied by a rotation factor to obtain a rotation matrix.

[0074] The computation nodes with even indices are designated as group leaders, and the computation nodes with odd indices are designated as group members. Each computation node divides the rotation matrix into multiple segments along the column direction, and then sends each segment to the corresponding group leader according to its sequence number. Each group leader aggregates the received segments to obtain two column vectors, performs a transpose operation on the two column vectors, and then sends them to the corresponding group members. Each computation node obtains the output matrix after performing a Fast Fourier Transform in the column direction locally.

[0075] The participating clusters consist of at least three independent, non-colluding participating clusters, each representing a logical participant in a secure multi-party computation (MPC). Each participating cluster is responsible for providing network isolation and resource scheduling for the computing nodes within it, upholding the underlying trust assumptions of the three-party replication secret-sharing protocol. Clusters exchange encrypted data via a wide area network; if any single cluster is compromised, no plaintext information of the original data can be obtained.

[0076] The compute nodes are physical or virtual servers deployed within the clusters of each participating party, responsible for carrying the FFT arithmetic logic in encrypted state. To overcome the global All-to-All communication bottleneck, the system dynamically assigns compute nodes to two sub-roles with different network interaction protocols based on the node index (such as the parity of IP or unique ID) during initialization, and establishes a point-to-point secure channel.

[0077] Ordinary compute nodes (group members, such as odd-indexed nodes): Local computation: Performs secret-shared-domain computations for row-wise and column-wise FFTs. During multiplication operations, it interacts with associated nodes according to the communication protocol and synchronously updates MAC tags.

[0078] Coordinated rearrangement: After the row-wise FFT is completed, instead of global broadcasting, the matrix it holds is divided into segments by column, and the specific segment data is accurately sent to the corresponding target "group leader" node; then, it is in listening state, receiving the transposed column data directionally scattered back from the paired "group leader" node, and then enters the column-wise FFT stage.

[0079] Regional coordination node (group leader, e.g., even-indexed node): Local computation: Just like a normal compute node, it performs secret-shared domain arithmetic operations for row-wise FFT and column-wise FFT, as well as MAC tag updates.

[0080] Regional aggregation and directional scattering (core dimensionality reduction routing): After the row-wise FFT is completed, in addition to its own data partitioning, the group leader node needs to open a parallel listening port to receive segment data sent from all nodes in the network with the target index pointing to itself (i.e., regional aggregation); the group leader node independently completes the matrix transpose of the aggregated data locally; after the transpose is completed, according to the role allocation protocol, the first row of data is kept locally, and the second row of data is directionally scattered to its paired "group member" node through a dedicated point-to-point link.

[0081] Through the collaborative work of the three entities mentioned above, this system successfully offloads the expensive global transpose communication to specific "group leader" nodes for local routing, reconstructing the originally disordered, flat network into an ordered topology of "local aggregation-directional scattering." This achieves efficient and scalable distributed authentication private Fast Fourier Transform under a malicious security model. This system and the aforementioned methods are based on the same inventive concept; the physical responsibilities of each executing role correspond one-to-one with the logical steps of the aforementioned methods, together forming a complete privacy computing solution.

[0082] It is understood that the scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging provided by this invention corresponds to the scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging provided in the foregoing embodiments. The relevant technical features of the scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging can be referred to the relevant technical features of the scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging, and will not be repeated here.

[0083] To address the high computational complexity and vulnerability to malicious security issues inherent in existing Fast Fourier Transform (FFT) methods, this invention upgrades traditional FFT to a distributed system with malicious security defense capabilities by introducing three-party replication secret sharing (RSS) and Message Authentication Code (MAC) tagging technologies. It also innovatively constructs a three-tiered network topology of "delegator-participant cluster-computing node". Before computation, the delegator segments the original data using the three-party replication secret sharing mechanism and generates MAC tags using a global key, enabling lightweight data distribution and secure offline execution. During the secret sharing domain computation phase, this invention introduces a role-based hierarchical mechanism, designating even-indexed nodes as group leaders and odd-indexed nodes as group members. After each node completes a row-wise FFT locally, it partitions the data by column and locally aggregates it to the corresponding group leader. The group leader performs matrix transposition locally, retaining the first row and then scattering the next row directionally to paired group members, transforming the global data rearrangement into a two-stage dimensionality-reduced communication mode of "local aggregation-directional scattering". After the node performs a column-wise FFT, the delegator uses a compressed batch verification mechanism based on random linear combinations to efficiently verify the results and reconstruct the plaintext. This invention, while resisting malicious attacks, reduces communication complexity from O(M) to O(M / N) and reduces MAC verification overhead to less than 8% of the total time, significantly improving system scalability. It can be widely applied to high-security scenarios such as medical data analysis, zero-knowledge proofs, financial risk control, and privacy-preserving machine learning.

[0084] This invention provides a scalable distributed privacy-preserving FFT method and system based on secret sharing and MAC tagging. Through a three-tier network architecture, it separates the data owner from the computing nodes, constructing a lightweight private computing outsourcing model. The delegator only needs to complete the secret sharing and tag generation once to go offline; all subsequent complex calculations are handled by a cluster of multiple participants, greatly reducing the computational burden on the data owner, making it particularly suitable for resource-constrained terminal devices. Simultaneously, the delegator and computing nodes are physically isolated, and the original data always exists in the form of a secret share, fundamentally eliminating the risk of data leakage.

[0085] This invention introduces a privacy protection mechanism based on three-party replication and secret sharing to ensure the confidentiality of data throughout its entire lifecycle. The original data is segmented using three-party replication and secret sharing, preventing any single node from obtaining any plaintext information. Any two nodes can collaborate to reconstruct the secret, and this threshold characteristic provides a flexible balance between security and availability. Data remains secret throughout transmission, storage, and computation, ensuring that no single node (including the group leader) can access the original data.

[0086] This invention integrates the SPDZ-MAC tagging scheme to achieve data integrity protection under a malicious security model. Each secret share is tagged with a tag protected by a global MAC key; any tampering with the share will cause MAC verification to fail. For the numerous parallel multiplication operations in FFT computation, a dedicated MAC batch verification protocol is designed. This protocol combines the MAC checks of multiple shares into a single verification operation through random linear combination, reducing verification overhead from... Reduce to Meanwhile, by embedding the generation, updating, and verification of MAC tags into the FFT operation process, parallel processing of computation and integrity protection is achieved, reducing the MAC verification overhead from 35% of the total FFT time to less than 8%.

[0087] By employing a hierarchical communication topology of group leader and group members, global all-to-all communication is transformed into a two-stage mode of local aggregation and point-to-point scattering, completely resolving the communication bottleneck problem. This invention designates even-numbered index nodes as group leaders and odd-numbered nodes as group members. All nodes first aggregate data to their corresponding group leader, then scatter it to their paired group members after the group leader's transpose. When the target column index matches a node index, the data is directly retained locally, maximizing data locality. This mechanism reduces communication complexity from... Reduce to This allows the speedup to remain nearly linear (efficiency ≥ 82%) when the node size is expanded from N=4 to N=64.

[0088] It possesses extremely high versatility and scalability, making it suitable for various high-security and privacy-preserving computing scenarios. This invention does not rely on specific underlying hardware or network infrastructure, and is applicable to multiple clusters within a single cloud service provider, as well as collaborative computing across multiple cloud service providers. By configuring different secret-sharing parameters and MAC security parameters, the system can adapt to different security requirements, ranging from semi-honest security to malicious security, and can be widely applied in fields requiring secure spectrum analysis of large-scale data, such as financial risk control, medical data analysis, and privacy-preserving machine learning.

[0089] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0090] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0091] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0092] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0093] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0094] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0095] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A scalable distributed privacy-preserving FFT method based on secret sharing and MAC tagging, characterized in that, The FFT method includes: Step 1: The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generates a corresponding MAC tag for each data share, and then secretly shares it with each participating cluster. Step 2: The computing nodes within each participating party's cluster perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; the intermediate matrix is ​​then multiplied by a rotation factor to obtain a rotation matrix. Step 3: Set the computing nodes with even indices as group leaders and the computing nodes with odd indices as group members; after each computing node divides the rotation matrix into multiple segments according to the column direction, it sends each segment to the corresponding group leader according to the segment number. Each group leader aggregates the received segment segments to obtain two column vectors, performs a transpose operation on the two column vectors, and sends them to the corresponding group members. Step 4: Each computing node performs a Fast Fourier Transform in its local computing column direction to obtain an output matrix, and the client verifies the output matrix.

2. The FFT method according to claim 1, characterized in that, Step 1 includes: Step 101: Reshape the input raw data into a matrix. The matrix The element in the j-th row and k-th column is ; Step 102, the delegator determines the cluster to be assigned to any i-th participating party. Data share is ; Step 103, the principal generates a global MAC key. The MAC tag is generated as follows: .

3. The FFT method according to claim 2, characterized in that, The intermediate matrix in step 2 is: ; Cluster The intermediate matrix obtained through collaborative computation by internal servers The line, number The frequency domain output is: in, Represents the finite field The primary unit root; The MAC tags are synchronously updated during the calculation of the intermediate matrix as follows: 。 4. The FFT method according to claim 1, characterized in that, The process of obtaining the rotation matrix by performing a rotation factor multiplication on the intermediate matrix in step 2 includes: Define the rotation factor matrix The element in the j-th row and k-th column is: ; This represents the total number of elements in the matrix; Each participating cluster on the intermediate matrix The rotation matrix is ​​obtained by performing element-wise multiplication. for: Among them, symbols This indicates Hadamard element-wise multiplication, where i represents the index of the participating cluster.

5. The FFT method according to claim 1, characterized in that, Step 3 includes: Step 301, each computing node will use the rotation matrix The data is divided into N / 2 segments along the column direction, and each segment contains two consecutive columns of data; N represents the total number of computing nodes. Step 302: Each computing node sends the share of each segment to the corresponding group leader, and the computing node of the group leader corresponding to any k-th segment share... If the group leader corresponding to the segment share is itself, then the copy is completed through local memory. Step 303, calculate nodes for any group leader It receives the k-th segment data sent by all computing nodes in parallel and assembles it into a set of segment shares for two complete column vectors.

6. The FFT method according to claim 1, characterized in that, Step 3 also includes: In step 304, each group leader transposes the two aggregated column vectors locally to obtain two rows of data; the first row of data obtained after transposition is kept locally, and the second row of data obtained after transposition is sent to the paired group member computing node through a point-to-point secure link. .

7. The FFT method according to claim 3, characterized in that, Step 4 includes: Step 401, each computing node performs a length-based operation on its held column shares. The Fast Fourier Transform (FFT) of the i-th participating cluster is used to compute the FFT in the column direction, resulting in the following output matrix: in, Represents the output matrix The element in the m-th row and k-th column; This refers to the element in the j-th row and k-th column of the matrix after the transpose operation.

8. The FFT method according to claim 7, characterized in that, Step 4 also includes: Step 401: The client flattens the output matrix and combines it with the MAC tags to form a data pair. For length of Perform batch aggregation on sequences: in, This represents the output sequence after the output matrix is ​​aggregated. This represents the output sequence after MAC tag aggregation. The selected random number; Step 402, the principal uses the global MAC key Verify the aggregation results and determine the equality. Is it valid? If the equation is true, it confirms that all shares have not been tampered with; if the equation is false, it is determined that at least one data share has been tampered with, and the process is rolled back to verify each share in order to locate the malicious computing node.

9. The FFT method according to claim 8, characterized in that, Step 4 also includes: The client rearranges the data that passes the equality verification in order to obtain the target one-dimensional sequence as the final one-dimensional output result; the strict mapping relationship of the rearrangement process is defined as: in, , Let be the index of the element in the target one-dimensional sequence. , ; Let i represent the l-th element in the target one-dimensional sequence, and let i represent the index of the participating cluster.

10. A scalable distributed privacy-preserving FFT system based on secret sharing and MAC tagging, characterized in that, The FFT system includes: a principal, a cluster of participants, and computing nodes; The principal uses a three-party replication secret sharing technology to divide the input raw data into multiple data shares, generate a corresponding MAC tag for each data share, and then secretly share it with each of the participating party clusters. The computing nodes are deployed within the clusters of each participating party. The computing nodes within the clusters perform a one-dimensional fast Fourier transform on each row of the data share they hold to obtain an intermediate matrix; and perform a rotation factor multiplication on the intermediate matrix to obtain a rotation matrix. The computation nodes with even indices are designated as group leaders, and the computation nodes with odd indices are designated as group members. Each computation node divides the rotation matrix into multiple segments along the column direction, and then sends each segment to the corresponding group leader according to its sequence number. Each group leader aggregates the received segments to obtain two column vectors, performs a transpose operation on the two column vectors, and then sends them to the corresponding group members. Each computation node performs a Fast Fourier Transform in the column direction locally to obtain the output matrix. The client verifies the output matrix.

Images