CWI Cryptology Group

Abstract: This talk will be an introduction to isogenies of elliptic curves and their (emerging) use in cryptography, particularly in post-quantum constructions. I will try to focus on the big picture, covering the elementary properties of isogeny graphs and how we can build cryptographic protocols from them, mainly demonstrating post-quantum key exchange as a fundamental example.

Abstract: Isogenies of elliptic curves have proven to be a powerful tool to construct cryptographic protocols, in particular quantum-resistant ones. The key encapsulation protocol SIKE is currently being considered for standardisation in the NIST post-quantum competition, while the younger primitive CSIDH is likely to find useful applications in more advanced protocols where a static-static key exchange is needed. At present, the picture of isogeny-based signature protocols is much less bright. While it is known how to derive various identification schemes and signatures from both SIKE and CSIDH, they are all inefficient in some regard. In this talk I will review the different protocols, both quantum-resistant and not, that have been devised to prove knowledge of a secret isogeny. I will explain their uses and limitations, report on ongoing work, and present some open questions.

Abstract: Isogeny-based cryptography using curves of genus 2 is still very much in an exploratory phase. In this talk I will report on some of the attempts undertaken thus far, while stating some open problems and discussing the potential gains and losses, when compared to genus 1 (= elliptic) curves. The focus will lie on hash functions à la CGL and key agreement à la SIDH.