This award supports research into the security of a new family of cryptosystems based on a mathematical structure called isogenies of elliptic curves. The research will also include the development of new isogeny-based protocols. These protocols are among the front runners in the process of replacement of the current public key primitives by alternatives that will be secure against attacks by quantum computers. The transition towards a quantum-safe cyberspace is an immediate priority for the cryptography community. Indeed, quantum-safe primitives will need to be ready and deployed long before the construction of large scale quantum computers to account for the shelf life of encrypted data. This research has broader impacts to industry which will need to follow recommendations for a secure use of isogeny cryptosystems. It also impacts education through the development of new cybersecurity curriculum at the university and high school level. This project will involve the analysis of the hardness of the task of finding an isogeny between two given elliptic curves over a finite field. In particular, new quantum algorithms will be developed for computing isogenies. The careful analysis of the performances of these algorithms is the indicator of the security of isogeny-based schemes. It will permit the identification of an appropriate size for keys that keep users out of the reach of quantum attacks. The project will also explore new applications of cryptographic primitives based on isogenies. Efficient solutions for static-static key exchange protocols will be investigated. These primitives also have potential for ring signatures that can have many practical applications including anonymous transactions on the blockchain, and quantum-safe anonymous cryptocurrencies.
EAGER: Quantum-Safe Cryptosystems Based on Isogenies