Isogeny Club Talk #3: [superlative]Solver: Attacking the General Isogeny Problem

Here is the discussion thread for the 3rd session of The Isogeny Club, where Maria presents her talk titled: [superlative]Solver: Attacking the General Isogeny Problem

The general supersingular isogeny problem is the foundational hardness assumption underpinning isogeny-based cryptography. Its conjectured classical and quantum hardness has cemented isogenies as a promising tool for building post-quantum secure protocols.

In this talk, we will look at the general isogeny problem in low dimensions. More specifically, we consider the hardness of finding an isogeny between two given supersingular elliptic curves or two superspecial abelian surfaces defined over \mathbb{F}_{p^2}. Viewing these as path-finding problems in a related isogeny graph, we introduce a general framework for solving these problems and present the state-of-the-art attacks against them. We will also discuss a strategy for improving their concrete complexity, based on joint work with Craig Costello, Sam Frengley and Jia Shi.

A link will appear here when the recording is available.

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