Treffer: Implementing a Key Exchange Protocol Using Isogenies on Elliptic Curves in Python

The study of Elliptic Curves continues to reveal more secure and efficient methods to encrypt information. For example, in De Feo, Jao, and Plˆut’s paper Towards Quantum- Resistant Cryptosystems From Supersingular Elliptic Curve Isogenies, they provide an abstract key exchange protocol using isogonies on supersingular elliptic curves. The main idea of this research is to present an accurate manifestation of the abstract protocol constructed by De Feo et al., which will be realized using Python. This protocol is founded in the Diffie-Hellman algorithm using isogenies on Elliptic Curves as its primary operation. Background on Elliptic Curve Cryptography will also be provided in order to fully understand the presented encryption process.