Bézier Coefficients Matrix for ElGamal Elliptic Curve Cryptosystem

Abstract

It is well-known that cryptography is a branch of secrecy in science and mathematics, which usually preserves the confidentiality and authenticity of the information, where its growth is parallel with the rapid evolution of the internet and communication. As one of the prominent public key cryptosystems, the Elliptic Curve Cryptosystem (ECC) offers efficiency and complex mathematical operations with a smaller bit compared to other types of public key schemes. Throughout the evolution of cryptography, ElGamal Elliptic Curve Cryptosystem (ElGamal ECC) revolved from ElGamal public key scheme for user efficiency and privacy. In this study, an improved method will be introduced using ElGamal ECC as the foundation with the incorporation of the Bézier curve coefficient matrix, where the ElGamal ECC value is considered as the control point of the Bézier curve during the encryption and decryption processes. The proposed method is designed to develop a robust ciphertext system algorithm for better efficiency and to increase the level of protection in ElGamal ECC. In this paper, the performance of the proposed method is compared with the normal ElGamal ECC. The results of this study show that the proposed method offers no significant difference in terms of the implementation time during the encryption and decryption process. However, it does offer extra layers of protection when operated with complex mathematical operations.