Extending class group action attacks via sesquilinear pairings
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909331164758016 |
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| author | Macula, Joseph Stange, Katherine E. |
| author_facet | Macula, Joseph Stange, Katherine E. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extending class group action attacks via sesquilinear pairings Macula, Joseph Stange, Katherine E. Number Theory Cryptography and Security 11R65, 14H52, 94A60 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). |
| title | Extending class group action attacks via sesquilinear pairings |
| topic | Number Theory Cryptography and Security 11R65, 14H52, 94A60 |
| url | https://arxiv.org/abs/2406.10440 |