Efficient Computation of $(3^n , 3^n)$-Isogenies
| hal.structure.identifier | IMEC [IMEC] | |
| dc.contributor.author | DECRU, Thomas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | KUNZWEILER, Sabrina | |
| dc.date.accessioned | 2024-04-04T02:33:08Z | |
| dc.date.available | 2024-04-04T02:33:08Z | |
| dc.date.issued | 2023-07-13 | |
| dc.date.conference | 2023-07-19 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190446 | |
| dc.description.abstractEn | The parametrization of $(3, 3)$-isogenies by Bruin, Flynn and Testa requires over 37.500 multiplications if one wants to evaluate a single isogeny in a point. We simplify their formulae and reduce the amount of required multiplications by 94%. Further we deduce explicit formulae for evaluating $(3, 3)$-splitting and gluing maps in the framework of the parametrization by Bröker, Howe, Lauter and Stevenhagen. We provide implementations to compute $(3^n , 3^n)$-isogenies between principally polarized abelian surfaces with a focus on cryptographic application. Our implementation can retrieve Alice's secret isogeny in 11 seconds for the SIKEp751 parameters, which were aimed at NIST level 5 security. | |
| dc.description.sponsorship | Cryptographie, isogenies et variété abéliennes surpuissantes - ANR-19-CE48-0008 | |
| dc.language.iso | en | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.source.title | Lecture Notes in Computer Science | |
| dc.subject.en | Isogenies | |
| dc.subject.en | Post-quantum Cryptography | |
| dc.subject.en | Abelian surfaces | |
| dc.title.en | Efficient Computation of $(3^n , 3^n)$-Isogenies | |
| dc.type | Communication dans un congrès | |
| dc.identifier.doi | 10.1007/978-3-031-37679-5_3 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| bordeaux.page | 53-78 | |
| bordeaux.volume | 14064 | |
| 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 | AfricaCrypt 2023 | |
| bordeaux.country | TN | |
| bordeaux.title.proceeding | Lecture Notes in Computer Science | |
| bordeaux.conference.city | Sousse | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-04098198 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.end | 2023-07-21 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04098198v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Lecture%20Notes%20in%20Computer%20Science&rft.date=2023-07-13&rft.volume=14064&rft.spage=53-78&rft.epage=53-78&rft.au=DECRU,%20Thomas&KUNZWEILER,%20Sabrina&rft.genre=unknown |
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