Exploring Quaternionic Moufang Loops in Error Detection Within Secure Communication System

Abstract

This paper presents the use of Moufang loops for error detection and how effective it is in secure communication. A set G with a binary operation ◦ is a Moufang loop if it has an identity element and satisfies:

By using their plaintext sensitivity and non-associative nature, we present in this paper a method for writing/encoding messages into quaternionic form and detecting errors using norm based thresholds. Furthermore, using theoretical analysis and simulated cyberattacks, we show that this approach is more effective than standard associative methods currently used in detecting subtle data changes.