Open AccessBuilding matrixes of higher order to achieve the special commutative multiplication and its applications in cryptography: بناء مصفوفات تبديلية من مراتب عليا وتطبيقاتها في التشفير
Author(s) -
Mechal Fheed Alslman,
Nassr Aldin Ide,
Ahmad Zakzak Mechal Fheed Alslman,
Ahmad Zakzak
Publication year - 2021
Publication title -
mağallaẗ al-ʿulūm al-ṭabīʿiyyaẗ wa-al-ḥayātiyyaẗ wa-al-taṭbīqiyyaẗ
Language(s) - English
Resource type - Journals
ISSN - 2522-3356
DOI - 10.26389/ajsrp.c260521
Subject(s) - encryption , multiplication (music) , commutative property , cryptography , key exchange , key (lock) , matrix (chemical analysis) , mathematics , matrix multiplication , computer science , order (exchange) , property (philosophy) , theoretical computer science , public key cryptography , discrete mathematics , computer security , algorithm , combinatorics , philosophy , materials science , physics , finance , quantum mechanics , epistemology , economics , composite material , quantum
In this paper, we introduce a method for building matrices that verify the commutative property of multiplication on the basis of circular matrices, as each of these matrices can be divided into four circular matrices, and we can also build matrices that verify the commutative property of multiplication from higher order and are not necessarily divided into circular matrices. Using these matrixes, we provide a way to securely exchange a secret encryption key, which is a square matrix, over open communication channels, and then use this key to exchange encrypted messages between two sides or two parties. Moreover, using these matrixes we also offer a public-key encryption method, whereby the two parties exchange encrypted messages without previously agreeing on a common secret key between them.