Pt.3 Supersingular Isogeny Graphs in Cryptography | Kristin Lauter, Meta (Facebook)
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 31/07/2022

With the advent of quantum computers, the mathematical community is under urgent pressure to work on proposing and attacking new hard problems for use in cryptography, which are not already broken in polynomial time by a quantum computer. Supersingular Isogeny Graphs were proposed for use in cryptography in 2006 by Charles, Goren, and Lauter. Supersingular Isogeny Graphs are examples of Ramanujan graphs, which are optimal expander graphs. These graphs have the property that relatively short walks on the graph approximate the uniform distribution, and for this reason, walks on expander graphs are often used as a good source of randomness in computer science. But the reason these graphs are important for cryptography is that finding paths in these graphs, i.e. routing, is hard: there are no known subexponential algorithms to solve this problem, either classically or on a quantum computer. For this reason, cryptosystems based on the hardness of problems on Supersingular Isogeny Graphs are currently under consideration for standardization in the NIST Post-Quantum Cryptography (PQC) Competition. This course will introduce these graphs, the cryptographic applications, and the various algorithmic approaches which have been tried to attack these systems.

IAS | PCMI 2022
https://www.ias.edu/pcmi/2022-graduate-summer-school-course-descriptions