Discrete Logarithmic Improvement for ElGamal Cryptosystem Using Matrix Concepts

The ElGamal cryptosystem is an asymmetric cryptosystem that works on abelian groups of integers. This study examines the improvement of the discrete logarithm of the matrix in the ElGamal cryptosystem. This system improvement involves using a square matrix as the private key. This research modifies the key pair generation algorithm, encryption, and description so that the proposed system can work properly. The results show that this system can work in a non-abelian group, which is claimed to be more resistant to quantum algorithms attacks. Furthermore, the private matrix key will make it more difficult for hackers to attempt a brute force attack. The proposed ElGamal cryptosystem also works well and is relatively safe at relatively small prime numbers. The strength of the proposed ElGamal cryptosystem lies in selecting prime numbers and the square matrix size. The larger the matrix size, the more likely it is to brute force attacks so that hackers will find it more difficult to carry out attacks.