The NIST post-quantum competition has started a race for post-quantum cryptography. As a result, we’ve seen a great deal of research into alternative hard mathematical problems to use as a basis for public-key cryptography schemes. Lattice-based cryptography! Error-correcting code based cryptography! And of course, isogeny-based cryptography, have all received enormous renewed interest as a result. While the NIST post-quantum competition recently announced that it’s favoring candidates founded on lattice-based cryptography, it also encouraged further research into isogeny-based cryptography. But what even is isogeny-based cryptography? Is it as intimidating as it sounds? And what’s keeping it behind on NIST’s list of post-quantum primitives? Today, it’s my pleasure to be joined by isogeny-based cryptography researchers Luca de Feo and Hart Montgomery, co-authors of a recent publication titled “Cryptographic Group Actions and Applications”, which Luca affectionately described as a “isogeny-based cryptography for dummies” paper. We’ll be discussing isogeny-based cryptography and more. Links and papers discussed in the show: Cryptographic Group Actions and Applications CSIDH Intro Music composed by Toby Fox and performed by Sean Schafianski. Special Guests: Hart Montgomery and Luca De Feo. Sponsored By: Symbolic Software: This episode is sponsored by Symbolic Software. Symbolic Software helps you bring in the experience and knowledge necessary to design, or prove secure, state-of-the-art cryptographic systems for new solutions. We've helped design and formally verify some of the world's most widely used cryptographic protocols.