The fundamental focus of group theory is on structures known as groups. The combination of any two elements in a set with an operation (such as addition or multiplication) allows for the creation of a third member; this combination is known as a group. its quantum complexity was categorized as a cryptography group action, and its significance has been overlooked. A technique known as group-based cryptography is used when cryptographic primitives are constructed using groups. Because of their general algebraic features, groups find frequent use in cryptography. The Diffie-Hellman key exchange makes use of finite cyclic groups in particular. To guarantee its security, several cryptographic algorithms depend on complexity assumptions derived from group theory.