Block Matrix Linear Solver for Faster Digital Signature Generation
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Solution Overview
Problem
Existing multivariate quadratic cryptography systems face inefficiencies in computing solutions to linear systems, particularly when generating electronic signatures, due to the time-consuming process of computing inverse matrices, which is exacerbated by larger key sizes.
Innovation Solution
A device utilizing a block matrix decomposition method to compute solutions to linear systems by using inverse matrices of sub-block matrices, avoiding direct computation of the entire inverse matrix, and employing a central map based on multivariate quadratic polynomials for electronic signature generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the direct computation of inverse matrix is used to solve linear systems, then the solution can be obtained accurately, but the computation time increases significantly
Solution Approach 1:
The patent divides the k×k matrix into four (k/2)×(k/2) sub-block matrices and computes their inverses separately. This segmentation reduces the computational complexity from O(k³) to O((k/2)³), significantly decreasing the time required to solve the linear system while maintaining solution accuracy.
2Reliability
If the magnitude of secret key is increased to enhance security, then the security level is improved, but the time required to generate electronic signature increases
Solution Approach 1:
By segmenting the large secret key matrix into smaller sub-block matrices, the patent enables parallel computation of inverses for each sub-block. This approach maintains high security levels with larger key magnitudes while reducing the overall computation time through efficient block-wise processing.
3Loss of time
If the block matrix decomposition method is used to compute solution, then the computation time is reduced, but the device complexity increases
Solution Approach 1:
The patent implements block matrix decomposition by dividing the matrix into sub-blocks and computing their inverses separately. While this introduces additional structural organization requirements, the standardized block-wise computation流程 simplifies the overall algorithm management and reduces implementation complexity compared to direct inversion of large matrices.
Data Source
AI summary
Disclosed is an electronic device for computing a solution to a linear system using a block matrix. The electronic device includes a memory configured to store data, and a processor configured to perform a plurality of operations by executing instructions. The electronic device computes the solution to the linear system without directly computing an inverse matrix R−1 of a block matrix R, using an inverse matrix of at least one of a plurality of sub-blocks matrices A, B, C, and D that constitute a block matrix R representing the linear system, and an inverse matrix of at least one of combinations of the plurality of sub-block matrices A, B, C, and D. According, the solution to the linear system can be efficiently computed.