Secure Matrix Multiplication via Dual Permutations for Lower Communication
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Solution Overview
Problem
Existing secure multi-party computation methods face inefficiencies in data communication and processing when calculating the product of a target matrix and a target column vector, particularly due to high communication overhead in operations like scalar or matrix multiplication, which hinders the efficiency of tasks such as SQL queries and machine learning.
Innovation Solution
A method involving two participants performing two rounds of secure permutation to generate permutation result shards for the product of an m*n target matrix and an n-dimensional target column vector, where each column of the target matrix is an m-dimensional one-hot vector, reducing communication volume by limiting it to n dimensions regardless of m, and improving processing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional secure multi-party computation methods are used for matrix multiplication, then computation functionality is achieved, but data communication volume and processing efficiency deteriorate
Solution Approach 1:
The patent segments the matrix multiplication computation into two independent rounds of secure permutation operations. Each round processes n dimensions independently, allowing the communication volume to be limited to O(n) rather than O(m*n). This segmentation enables parallel processing and reduces the dependency between communication volume and matrix size m.
Solution Approach 2:
The patent transforms the traditional matrix multiplication approach by changing the computational dimensionality. Instead of processing all m*n elements simultaneously, the method processes n dimensions at a time through permutation operations, effectively reducing the communication complexity from dependent on m to independent of m.
2Power
If scalar or matrix multiplication operations are performed in secure multi-party computation, then computation results are obtained, but communication overhead increases
Solution Approach 1:
The patent extracts the essential computation functionality by using secure permutation operations that process only the necessary n dimensions. The method takes out the core computational task from the full matrix multiplication, achieving the required computation results while eliminating unnecessary communication overhead related to m dimensions.
Solution Approach 2:
The patent introduces secure permutation operations as intermediary steps between data input and final computation results. These permutation operations act as mediators that reorganize data in a way that enables efficient computation with reduced communication, transforming the direct matrix multiplication into a two-step process with lower overhead.
Data Source
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AI summary
The present disclosure relates to a data processing method and apparatus for secure computation, a medium, and an electronic device. The method applied to a first participant includes: determining first permutation information and second permutation information according to a target matrix; jointly performing a first round of secure permutation with a second participant at least according to the first permutation information to obtain a first permutation result shard; jointly performing a second round of secure permutation with the second participant according to the first permutation result shard and the second permutation information to obtain a second permutation result shard; generating a first result shard according to the second permutation result shard; and performing a target data processing task based on the first result shard. The communication in the entire computing process is to call a secure permutation protocol in n dimensions twice, and the data communication volume of the two rounds of secure permutation is only related to n, but not related to m, and does not increase with the increase of m. Therefore, the data communication volume for calculating the product of the target matrix and the target column vector can be greatly reduced, and the service processing efficiency of the secure computation can be improved.