Recorded 26 July 2022. Craig Costello of Microsoft Research presents "Post-quantum key exchange from supersingular isogenies" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This talk will give an overview of Supersingular isogeny Diffie-Hellman (SIDH): the post quantum key exchange scheme based on elliptic isogenies. The talk will be aimed at beginners, but a basic knowledge of elliptic curves will most certainly help. Suggested readings: Supersingular isogeny key exchange for beginners: https://eprint.iacr.org/2019/1321.pdf Mathematics of Isogeny Based Cryptography: https://arxiv.org/abs/1711.04062 Learn more online at: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-on-post-quantum-and-quantum-cryptography/?tab=overview