Supersingular Isogeny Graphs and Endomorphism Rings - Reductions and Solutions

Explore a comprehensive analysis of supersingular isogeny graphs and endomorphism rings in this 27-minute conference talk presented at Eurocrypt 2018. Delve into the threat of quantum computers, supersingular curves, isogeny problems, and the Charles Goren-Lauter hash function. Examine the strategy to break the CGL hash function, key tools, and the partial attack developed by the researchers. Gain insights into the equivalence of hard problems and their implications for cryptography. Conclude with perspectives on the future of isogeny-based cryptography and its potential applications in post-quantum security.