Post-quantum cryptography from isogenies and quaternions

• Applicant: Professor Dr. Lorenz Panny
• Subject Area: Security and Dependability, Operating-, Communication- and Distributed Systems ; Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554901831

Most of our current cyber security infrastructures will become completely insecure once large-scale quantum computers are built. Indeed, their security relies on the computational hardness of mathematical problems such as factoring that are intractable using today's computers but can be solved in polynomial time on quantum computers. To prevent this ''crypto-apocalypse'', new forms of cryptography must be developed, analyzed and deployed in all existing and future cyber security applications. Only a few plausible approaches have been identified; the most recent one is called isogeny-based cryptography. Compared to alternatives, isogeny-based cryptography has many appeals including a key exchange protocol that can serve as a direct replacement to the widely used Diffie-Hellman protocol, a signature protocol with very short keys, and algorithmic building blocks in common with elliptic curve protocols already in use. On the other hand, existing isogeny-based protocols are currently much too slow for many applications, and much more cryptanalysis effort is needed to gain confidence in their security. Until recently, most cryptographic protocols based on isogenies have been developed following two main frameworks, namely the cryptographic group action framework and the SIDH framework. Following early promising work by the PIs and co-authors, the CRYPTIQ project will aim to develop a third direction for isogeny-based cryptography, and exploit the connections between quaternion algebras and super-singular curves to design smaller, faster and more advanced protocols, and to shed new lights on security.

• DFG Programme: Research Grants
• International Connection: Belgium
• Cooperation Partner: Professor Dr. Christophe Petit