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Title:
Extending class group action attacks via pairings
Authors: Joseph Macula, Katherine E. Stange
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 field \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 [CHM+23] and [FFP24].
ePrint: https://eprint.iacr.org/2024/880
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