Applications of Group Theory in Cryptography

Abstract

Group theory is a branch of abstract algebra that studies the properties of groups, which are algebraic structures consisting of a set of elements and a binary operation that combines any two elements to form a third element. This paper will explore the applications of group theory in cryptography, a field concerned with securing communication and data. Specifically, we will discuss how groups are used to construct cryptosystems, which are systems for encrypting and decrypting messages. We will also explore the role of group theory in ensuring the security of these cryptosystems.