AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY

Protecting information that is being communicated between two parties overunsecured channels is of huge importance in today’s world. The use of mathematical concepts to achieve high levels of security when communicating over these unsecured platforms is cryptography. The world of cryptography is always expanding and growing. In this paper, we set out to explore the use of elliptic curves in the cryptography of today, as well as the cryptography of the future.We also offer our own original cryptosystem, CSDH. This system on its ownoffers some moderate level of security. It shares many similarities to the post-quantum, SIDH system. The parallels between these two systems can lead to a deeper understanding of the systems offered for our post-quantum world