Group theory plays a pivotal role in the field of cryptography, providing the mathematical underpinnings for various secure communication protocols and encryption algorithms. This study explores the applications of group theory in cryptographic algorithms, highlighting its significance in ensuring data confidentiality, integrity, and authenticity. Cryptographic systems can be broadly categorized into two types: symmetric and asymmetric (public key) cryptography. In symmetric key algorithms, such as the Advanced Encryption Standard (AES), group theory underlies operations performed in finite fields, facilitating efficient data transformation through structured mathematical properties. In contrast, asymmetric cryptography, including RSA, ElGamal, and elliptic curve cryptography (ECC), relies on group theory principles, particularly the discrete logarithm problem and the algebraic structures of elliptic curves, to establish secure key exchanges and encrypt sensitive information.