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Extending class group action attacks via sesquilinear pairings
June 14, 2024 Β· Declared Dead Β· π International Conference on the Theory and Application of Cryptology and Information Security
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Authors
Joseph Macula, Katherine E. Stange
arXiv ID
2406.10440
Category
math.NT
Cross-listed
cs.CR
Citations
3
Venue
International Conference on the Theory and Application of Cryptology and Information Security
Last Checked
4 months ago
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).
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