Secure Conjugate Gradient Computation for Multiple Matrix Sets
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Solution Overview
Problem
Existing methods for secure computation of the conjugate gradient method require processing time to increase at O(N) when applied to multiple sets of symmetric positive definite matrices and vectors, necessitating efficient calculation for a plurality of sets.
Innovation Solution
A secure conjugate gradient method computation system with multiple secure computation apparatuses performs collective communication for matrix calculations, using initialization and calculation units to compute and update matrices and vectors efficiently, reducing communication requirements through element-wise multiplication and diagonal operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the conjugate gradient method is applied to multiple sets of symmetric positive definite matrices and vectors using prior art methods, then the conjugate gradient method can be computed for each set, but the processing time increases at O(N)
Solution Approach 1:
The patent merges N separate conjugate gradient computations into a single unified computation by stacking multiple matrix-vector pairs into a block matrix structure. The computation simultaneously solves for multiple solutions using matrix operations on consolidated data, reducing the total computation time from O(N) to approximately O(1) relative to the number of datasets.
Solution Approach 2:
The invention creates a universal computation framework that handles multiple different matrix-vector pairs through a single algorithm execution. By designing the computation to operate on block matrices and vectors that can accommodate multiple datasets, the system achieves multi-functionality without requiring separate computation routines for each dataset.
2Adaptability or versatility
If secure computation is performed for multiple sets of matrices and vectors, then comprehensive analysis is possible, but communication requirements increase
Solution Approach 1:
The patent combines communication operations for multiple datasets into a single communication round by structuring the data as block matrices. Instead of requiring separate communication for each matrix-vector pair, the system transmits consolidated block structures that can be processed collectively, significantly reducing communication overhead.
Solution Approach 2:
The invention transforms the problem from N separate computation tasks to a single higher-dimensional computation by stacking datasets into block matrix structures. This dimensional transformation allows the system to process multiple datasets simultaneously through operations on the extended matrix space, reducing the number of communication rounds required.
Data Source
AI summary
A method and circuitry to calculate a simultaneous linear equation with a plurality of symmetric positive definite matrices as coefficients. N symmetric positive definite matrices A˜ and N vectors B are input to input circuitry. Initialization circuitry initializes secret values of matrices X, R, and P and a vector γ→. First calculation circuitry collectively calculates N matrix calculations to generate a secret value of a vector α→. Second calculation circuitry updates the secret value of the matrix X. Third calculation circuitry collectively calculates N matrix calculations to update the secret value of the matrix R. Fourth calculation circuitry collectively calculates an inner product of N vectors to generate a secret value of the vector β→. Fifth calculation circuitry updates the secret value of the matrix P, and sixth calculation circuitry collectively calculates the inner product of the N vectors and updates the secret value of the vector γ→.