Overview of Elliptic Curve Isogenies Based Public Key Cryptography Assumptions

Explore the foundations of elliptic curve isogenies in public key cryptography with David Jao from the University of Waterloo in this 43-minute lecture. Delve into the history and core concepts of elliptic curves, finite subgroups, and their applications in cryptographic systems. Examine the Supersingular Isogeny Diffie-Hellman (SIDH) and Isogeny-based Cryptographic Random Self-reducible Assumption (ICRSA) protocols. Investigate quantum cryptanalysis techniques, including the Quantum Fourier Transform and lattice approaches, as they relate to post-quantum cryptography. Gain insights into the random case scenario and control mechanisms within this advanced cryptographic framework.

Intro
What are elliptic curves
History
Venn Diagram
Examples
Finite Subgroup
SIDHI
CRS
Algorithm
Quantum Fourier Transform
Random Case
Control Not
Lattice Approach