(untitled) (Sebha University Conference Proceedings, 2025)
The increasing data transformation through the network, the appearance of Bitcoin and alternative information over millions of miles, the need for new or more secure methods was found. The elliptic curve cryptography is widely used in encryption. However, there are a variety of attacks such as invalid curve which is the most popular attack that can be used to manipulate the safety of cryptosystem by nonprime group order, it would be connected with methods of cryptography such as asymmetric cryptography and according to the fact that elliptic curve ciphers are based in smartcards introduce a high level of secure data transformation due its advantage of requires less computational power memory. This paper assures the need for secure key exchange by combining elliptic curve cryptography with precomputation and simple continued fractions that help us to fix and observe new mathematical attacks.