Inverse matrices with applications in public-key cryptography

作     者：Makoui, Farshid Haidary Gulliver, Thomas Aaron 

作者机构：Univ Victoria Dept Elect & Comp Engn POB 1700STN CSC Victoria BC V8W 2Y2 Canada 

出 版 物：《JOURNAL OF ALGORITHMS & COMPUTATIONAL TECHNOLOGY》 (J. Algorithms Comput. Technol.)

年 卷 期：2024年第18卷

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：The author(s) received no financial support for the research  authorship and/or publication of this article 

主　　题：Code-based cryptography inverse matrix error-correction coding blockchain post quantum cryptography public-key cryptosystem 

摘      要：The applications of non-square binary matrices span many domains including mathematics, error-correction coding, machine learning, data storage, navigation signals, and cryptography. In particular, they are employed in the McEliece and Niederreiter public-key cryptosystems. For the parity check matrix of these cryptosystems, a systematic non-square binary matrix H with dimensions m x n, n m, m = n - k, there exist 2m((n -m) )distinct inverse matrices. This article presents an algorithm to generate these matrices as well as a method to construct a random inverse matrix. Then it is extended to non-square matrices in arbitrary fields. This overcomes the limitations of the Moore-Penrose and Gauss-Jordan methods. The application to public-key cryptography is also discussed.