On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves
| hal.structure.identifier | Computer Security and Industrial Cryptography [KU Leuven] [ESAT-COSIC] | |
| dc.contributor.author | CASTRYCK, Wouter | |
| hal.structure.identifier | Computer Security and Industrial Cryptography [KU Leuven] [ESAT-COSIC] | |
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| dc.contributor.author | HOUBEN, Marc | |
| hal.structure.identifier | Computer Security and Industrial Cryptography [KU Leuven] [ESAT-COSIC] | |
| dc.contributor.author | VERCAUTEREN, Frederik | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | WESOLOWSKI, Benjamin | |
| dc.date.accessioned | 2024-04-04T02:40:13Z | |
| dc.date.available | 2024-04-04T02:40:13Z | |
| dc.date.created | 2022-08-08 | |
| dc.date.issued | 2022-08-08 | |
| dc.date.conference | 2022-08-08 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191045 | |
| dc.description.abstractEn | We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order $\mathcal O$ in an unknown ideal class $[\mathfrak a] \in \mathrm{Cl}(\mathcal O)$ that connects two given $\mathcal O$-oriented elliptic curves $(E, \iota)$ and $(E' , \iota') = [\mathfrak a](E, \iota)$. When specialized to ordinary elliptic curves over finite fields, our method is conceptually simpler and often somewhat faster than a recent approach due to Castryck, Sotáková and Vercauteren, who rely on the Tate pairing instead. The main implication of our work is that it breaks the decisional Diffie-Hellman problem for practically all oriented elliptic curves that are acted upon by an even-order class group. It can also be used to better handle the worst cases in Wesolowski's recent reduction from the vectorization problem for oriented elliptic curves to the endomorphism ring problem, leading to a method that always works in sub-exponential time. | |
| dc.language.iso | en | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.identifier.arxiv | 2210.01160 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.conference.title | Fifteenth Algorithmic Number Theory Symposium, ANTS-XV | |
| bordeaux.country | GB | |
| bordeaux.conference.city | Bristol | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03805601 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03805601v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2022-08-08&rft.au=CASTRYCK,%20Wouter&HOUBEN,%20Marc&VERCAUTEREN,%20Frederik&WESOLOWSKI,%20Benjamin&rft.genre=unknown |
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