Mathematics > Number Theory
[Submitted on 14 Jun 2024
(v1)
, last revised 1 Oct 2024 (this version, v2)]
Title: Extending class group action attacks via sesquilinear pairings
Title: 通过共轭双线性对扩展类群作用攻击
Abstract: We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the $\mathcal{O}$-module structure of an elliptic curve with CM by an imaginary quadratic order $\mathcal{O}$. We use these pairings to study the security of problems based on the class group action on collections of oriented ordinary or supersingular elliptic curves. This extends work of both (Castryck, Houben, Merz, Mula, Buuren, Vercauteren, 2023) and (De Feo, Fouotsa, Panny, 2024).
Submission history
From: Joseph Macula [view email][v1] Fri, 14 Jun 2024 23:17:48 UTC (32 KB)
[v2] Tue, 1 Oct 2024 02:13:48 UTC (37 KB)
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