Text encryption using Elliptic Curve Cryptography (ECC) over binary finite field and Elgamal Cryptosyste / Ahmad Asif Bakhtiar Noor Noor Hamid, Nor Syazwani Nor Zailan and Syaza Farlisa Ishak

Cryptography consists of some algorithms but the most common algorithms that had been used are Elliptic Curve Cyptography (ECC) and Rivest-Shamir-Adleman (RSA). ECC use very small keys, it is a way to be more effective computationally and makes it ideal for the smaller and less powerful devices that most people use to access network services. Due to small keys that had been offered by ECC, instead of RSA, ECC had been used widely in practical applications in embedded system such as mobile devices and IC card. finite field. ECC can be perfonn by using either finite field or binary field. Text encryption using ECC over bina1y finite ticld, G/(2"' ) has more advantage than Ctnitc field, Gf(p) but the previous study that use ECC and EIGamal for text encryption only represent the system using Gf(p). We observed that to implement Elgamal e1yptosystem in binaiy Cmite field, there are a few modification that need to be done to satisfy the properties of bina,y finite field. This is to ensure that the message that had been send can be decrypt successfully. The algorithm that will be used in this paper to complete the cnetyption and decryption process is EIGainal algorithm. Motivated from Natanael & Suryani in 2018, we represent the finite field using bina1y finite field Gf(2"' ) or ]Fr. Therefore, in this study, the implementation of ECC over lF, .., with the modification of EIGamal encryption ai1d decryption scheme work successfully where the original message or plaintext had been obtained after decryption process. For future studies, this method cai1 be further improves by using a larger value of m in IF)"' in order to increase the security of the text message. This method also can be implemented in GUI to make the calculation of encryption and decryption process faster instead of calculating manually.