Supersingular Isogeny-Based Cryptography
In the near future the way that we encrypt and authenticate information online may not be safe. For this reason, we need to create new tools that will enable secure communication for many coming years. The proposed research is to create such tools from a certain algebraic object called isogenies. These are functions that take one elliptic curve to another. Breaking isogeny-based encryption is thought to be difficult, and so we will be able to create other cryptographic tools from them besides encryption. In addition to constructing such tools, the proposed research includes making them have fast performance on computers and mobile devices without any loss of security.