### Isogeny graphs of abelian surfaces

Linfoot Number Theory Seminar

20th March 2024, 11:00 am – 12:00 pm

Fry Building, 2.04

Isogeny-based cryptography is an active research area in post-quantum cryptography, and its security depends on variants of isogeny problems, namely the problem of finding an explicit isogeny between two abelian varieties. Although much of the research focused on isogenies of elliptic curves so far, it is mathematically interesting to understand isogeny graphs in dimension 2 in full generality, and the recent attacks using isogenies in higher dimensions switched the attention to dimension two. Unlike known methods, we use very geometrical and arithmetical objects, called refined Humbert invariants. We will propose possible promising applications of abelian surfaces with these invariants in the context of isogeny-based cryptography.

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