Abstract
Ultra-large-scale matrix inversion has been applied as the fundamental operation of numerous domains, owing to the growth of big data and matrix applications. Using cryptography as an example, the solution of ultra-large-scale linear equations over finite fields is important in many cryptanalysis schemes. However, inverting matrices of extremely high order, such as in millions, is challenging; nonetheless, the need has become increasingly urgent. Hence, we propose a parallel distributed block recursive computing method that can process matrices at a significantly increased scale, based on Strassen’s method; furthermore, we describe the related well-designed algorithm herein. Additionally, the experimental results based on comparison show the efficiency and the superiority of our method. Using our method, up to 140,000 dimensions can be processed in a supercomputing center.
Highlights
With the growth of computer applications, matrix inversion has become a basic operation that is widely used in various industries
Online video service providers use various types of the matrices to store user and item information [1]; in satellite navigation and positioning, matrix inversion is used to solve positioning equations [2]; triangular matrix inversion is used in the fast algorithm of radar pulse compression; and, matrices are used in multivariate public key encryption [3], etc
We have focused on the problem of large-scale matrix inversion, which has become increasingly fundamental, owing to the constant growth of the data in various fields
Summary
With the growth of computer applications, matrix inversion has become a basic operation that is widely used in various industries. Online video service providers (such as YouTube) use various types of the matrices to store user and item information [1]; in satellite navigation and positioning, matrix inversion is used to solve positioning equations [2]; triangular matrix inversion is used in the fast algorithm of radar pulse compression (based on reiterative minimum mean-square error); and, matrices are used in multivariate public key encryption [3], etc. The application of matrix in cryptography is described in detail. In some of existing cryptographic algorithms, a matrix is used to directly encrypt a message. When the process is duplicated, it is found that the encrypted message can be obtained by solving the inversion of the encryption matrix.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
