Three-Party Matrix Multiplication Using Linear Secret Sharing
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Solution Overview
Problem
Existing privacy computing schemes face challenges in ensuring high computation speed and accuracy, particularly in matrix multiplication operations, with homomorphic encryption being computationally complex and differential privacy introducing noise that reduces accuracy.
Innovation Solution
A secure three-party multiplication method involving random matrix pairs and full rank decomposition to ensure data privacy and accuracy, where participants compute and share secret random matrices to obtain a product matrix without revealing intermediate results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption-based scheme is used, then security guarantee is strong, but computation complexity is high and computation speed is slow
Solution Approach 1:
The patent replaces the homomorphic encryption mechanism with a linear algebra-based secret sharing mechanism. Instead of using cryptographic modulo operations, the system uses matrix decomposition and linear combinations to achieve secure multi-party computation, thereby reducing computational complexity while maintaining security.
Solution Approach 2:
The patent changes the mathematical parameters from cryptographic modulo arithmetic to linear algebra operations. By transforming the computation domain from modular arithmetic to vector space operations, the system achieves faster computation while maintaining security through the randomness and linearity of the transformations.
2Reliability
If differential privacy-based scheme is used, then security against malicious nodes is high, but accuracy reliability of computation result is low due to noise introduction
Solution Approach 1:
The patent extracts the noise introduction mechanism from the differential privacy approach. Instead of adding noise to protect privacy, the system uses random matrix decomposition and secret sharing to achieve privacy protection without compromising computation accuracy. The randomness is used for security obfuscation rather than accuracy degradation.
3Reliability
If homomorphic encryption is used, then data privacy is protected, but computation resources required are large
Solution Approach 1:
The patent substitutes the resource-intensive homomorphic encryption system with a more efficient linear algebra-based approach. By replacing modular exponentiation and cryptographic operations with matrix multiplication and decomposition, the system significantly reduces computational resource requirements while maintaining data privacy through secret sharing.
Data Source
AI summary
The present disclosure provides a secure three-party multiplication method and system for privacy computing, involving the technical field of privacy computing. The method includes that an auxiliary compute node generates three groups of random matrix pairs randomly and transmits the random matrix pairs to three parties, and the three parties compute respective sum matrixes based on a sum of respective random matrixes and private matrixes, respectively Â, Ĉ and {circumflex over (B)}. A second party generates a matrix set according to a sum matrix, a first party obtains Ta based on the matrix set and its own secret matrix, the second party obtains Tb based on its own random secret matrix and Ta, and the third party generates its own random secret matrix based on Tb and the matrix set, and obtains a product matrix according to three random secret matrixes. The present disclosure can improve reliability of result accuracy.