Zero Knowledge Isogenies with Luca De Feo
Feb 19, 2020
Luca De Feo, a researcher at IBM and co-inventor of SIDH, delves into the fascinating world of isogenies and their role in cryptography. He explains how isogenies relate to public key encryption and supersingular curves, emphasizing their importance for post-quantum security. The discussion includes isogenies' connection with verifiable delay functions and their implications for randomness generation. De Feo also explores the unique challenges of isogeny graphs and the potential impact on blockchain technology, making complex mathematical concepts accessible and engaging.
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Understanding Isogenies Basics
- Isogenies are functions between elliptic curves that preserve group structure.
- They are special morphisms called isogenies, distinct from isomorphisms, with degree one defining isomorphisms.
Huge, Fast-Connected Isogeny Graphs
- Isogeny graphs contain huge numbers of elliptic curves linked by isogenies.
- Despite their size, these graphs have fast connectivity, allowing movement from any curve to another in a few steps.
Hard Pathfinding Enables Security
- The security of isogeny-based crypto relies on the hardness of finding paths between elliptic curves in isogeny graphs.
- This unique problem underpins isogeny post-quantum cryptography distinct from lattices or code-based crypto.