Applications of Group Theory in Cryptography
R. W. Asole1, S. P. Gaikwad2
Department of Mathematics, L. K. D. K. Banmeru Science College, Lonar, India.
Email: rajasole111@gmail.com, gaikwad1.618@gmail.com
Abstract
Group theory plays a vital role in modern cryptography by providing the mathematical framework essential for encryption, authentication, and secure communication. This paper explores the applications of group theory in cryptographic algorithms, including symmetric and asymmetric encryption, digital signatures, and key exchange mechanisms. Special emphasis is given to cyclic groups, finite fields, elliptic curve cryptography, and the complexity of computational problems such as the discrete logarithm problem and integer factorization. By understanding the algebraic properties of groups, we can ensure the security and efficiency of cryptographic protocols used in real-world applications.
Keywords: Group Theory, Cryptography, Discrete Logarithm Problem, RSA, Elliptic Curve
Cryptography
DOI link – https://doi.org/10.69758/GIMRJ/2504I5VXIIIP0036
Download