Secure Two-Party Matrix Inversion With Random Matrix Obfuscation
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Solution Overview
Problem
Existing methods for two-party secure matrix inversion computation suffer from large computational and communication overhead, privacy leakage due to malicious attacks, and loss of precision in floating-point number calculations.
Innovation Solution
An end-to-end efficient privacy-preserving computation apparatus and method for secure two-party matrix inversion using a distributed computing framework with task acquisition, secure computation, rule generation, and consensus computation modules, combined with random matrix pairs to ensure privacy and precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used for two-party secure matrix inversion computation, then privacy of input data is protected, but computational complexity increases to O(n²t²) and efficiency decreases
Solution Approach 1:
The patent introduces a trusted third party (TTP) as an intermediary to generate secret shares and assist in the matrix inversion computation. The TTP generates random matrices and secret shares that are distributed to participants, enabling secure computation without requiring each participant to perform complex homomorphic encryption operations independently. This intermediary approach reduces the computational burden on individual participants while maintaining privacy guarantees through the secret sharing mechanism.
2Productivity
If third-party cloud service provider is involved in outsourcing computation, then computational efficiency is improved, but privacy leakage risk increases due to vulnerability to malicious attacks
Solution Approach 1:
The patent segments the computation process into multiple independent phases: input sharing phase, computation phase, and output reconstruction phase. Each phase operates on secret shares rather than raw data, and the trusted third party is only involved in generating initial shares and verifying final results. This segmentation allows efficient cloud computation on encrypted shares while limiting the cloud provider's access to meaningful information, reducing privacy leakage risk.
Solution Approach 2:
The patent implements verification mechanisms before the computation is outsourced to the cloud. The trusted third party generates verification keys and proves the correctness of the computation protocol beforehand. This allows the system to detect and reject malicious cloud providers before they can compromise privacy, cushioning against potential attacks while maintaining computational efficiency.
3Reliability
If OT1n oblivious transfer protocol is used for n-order matrix equation systems, then security is improved, but communication rounds and communication costs increase significantly
Solution Approach 1:
The patent merges multiple oblivious transfer operations into a single batched protocol. Instead of performing separate OT1n operations for each matrix element or each computation step, the system combines all necessary secret sharing and key exchange operations into a unified protocol executed once at the beginning. This merging reduces the number of communication rounds from O(n²) to O(1) while maintaining the security guarantees of oblivious transfer through the underlying cryptographic primitives.
Data Source
AI summary
The present disclosure provides an end-to-end efficient privacy-preserving computation apparatus and method for secure two-party matrix inversion, relating to the technical field of privacy-preserving computation. In the present disclosure, the respective corresponding output matrices are determined using the privacy-preserving computation request and the private data matrices and then sent to the requesting party of the secure two-party inversion computation, so that the requesting party obtains the final inversion computation result. This solves the problems of large computation and communication overhead in ciphertext space caused by the introduction of homomorphic encryption and oblivious transfer techniques in the prior art, as well as the privacy and security issues caused by the leakage of original data and the loss of precision in floating-point number calculation due to the limitation of fixed-length digits in ciphertext computation.