Year: 2023
Type: conference-paper
Abstract: This paper focuses on constructing a Galois field of square matrices of order 2 and substantiates a theoretical basis for developing schemes of cryptographic transformation of information, key exchange, and digital signature. This research goal has been achieved by investigating a family of square matrices of order 2 with the commutative operation of matrix multiplication from the general linear group over the prime field of integers modulo. It has been proved that this commutative family of matrices is simultaneously diagonalized. The matrix that performs diagonalization has been calculated. This matrix is common to all matrices of the commutative family. The research has defined the family of matrices forming a Galois field of order with common operations of matrix multiplication and addition. The multiplicative cyclic group of this field has been shown.
Institution: Cherkasy State Technological University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7166325428