Matrix-embedded Diffie–Hellman key exchange and ElGamal encryption algorithms

The insistence on confidentiality in multimedia communication has never been as high as it is in the current era. Owing to the advancement of machine learning (ML) and artificial intelligence (AI), modern computers and advanced tools have created a huge threat to the prevailing digital security techniques. These modern tools play a noteworthy role in the cryptanalysis of some of the very well-established algorithms used for the secure key communication as well as authenticity and encryption purposes. This naturally motivates the problem of revisiting the existing techniques to enhance their security with the help of modern algebraic methods. The security frameworks that underpin the classical cryptographic system fundamentally rely on intricate properties of integers. In this paper, an enhancement to some protocols such as Diffie–Hellman key exchange protocol and ElGamal encryption algorithm is proposed by leveraging the conspicuous properties of matrices within the general linear group and matrix exponentiation, offering an improved persistence against the well-known attacks.