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.

Syllabus

Intro
The threat of quantum computers
Outline
Supersingular curves and isogenies
Isogeny problems
Endomorphism rings
Isogeny graphs
Charles Goren-Lauter hash function
Strategy to break CGL hash function
Results in this paper
Key tools
Partial attack on CGL hash function
Remember CGL hash function
Equivalence of hard problems
Sketch (1) implies (2)
Conclusion and perspectives