Quaternionic Moufang Loops: Algebraic Properties and Applications to Cryptography

Abstract

This work investigates the algebraic properties of quaternionic Moufang loops and their cryptosystems. We show that quaternionic Moufang loops are non associative, have high algebraic degree and are plaintext sensitive. These properties make them a good candidate for cryptosystems and an alternative to the traditional approach. The results show the potential of quaternionic Moufang loops to improve security in cryptosystems and we suggest further exploration of this area. The results contribute to the development of new cryptosystems using quaternionic Moufang loops.