Computational Refinements for Post-Quantum Elliptic Curve Security

Computer security in a post-quantum world is a topic of great significance. The security of a vast number of public key encryption and key distribution techniques is dependent upon various number theoretic frameworks such as factoring, discrete logarithms and elliptic curves. Yet, variations on Shor’s algorithm have provided a theoretical basis for rendering such systems vulnerable to quantum attacks. In this work, we review quantum solutions for typical number theoretic problems. After leading up to elliptic curve systems, we highlight the relevance of computing modular inverses. Finally, refinements to quantum versions of the extended Euclidean algorithm are presented.