The special case of cyclotomic fields in quantum algorithms for unit groups
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | BARBULESCU, Razvan | |
| hal.structure.identifier | Alice & Bob | |
| hal.structure.identifier | Corps Royal des Mines | |
| dc.contributor.author | POULALION, Adrien | |
| dc.contributor.editor | Nadia El Mrabet | |
| dc.contributor.editor | Luca de Feo | |
| dc.contributor.editor | Sylvain Duquesne | |
| dc.date.accessioned | 2024-04-04T02:35:29Z | |
| dc.date.available | 2024-04-04T02:35:29Z | |
| dc.date.created | 2023-02-27 | |
| dc.date.issued | 2023-07-21 | |
| dc.date.conference | 2023-07-18 | |
| dc.identifier.isbn | 0302-9743 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190642 | |
| dc.description.abstractEn | Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is Õ(m 5). In this work we propose a modification of the algorithm for which the number of qubits is Õ(m 2) in the case of cyclotomic fields. Moreover, under a recent conjecture on the size of the class group of $ \mathbb{Q}(ζ_m + ζ _m^{−1})$, the quantum algorithms is much simpler because it is a hidden subgroup problem (HSP) algorithm rather than its error estimation counterpart: continuous hidden subgroup problem (CHSP). We also discuss the (minor) speed-up obtained when exploiting Galois automorphisms thanks to the Buchmann-Pohst algorithm over OK-lattices. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.source.title | Progress in cryptology -- AFRICACRYPT 2023Lecture notes in computer science (LNCS) | |
| dc.subject.en | Quantum algorithms | |
| dc.subject.en | unit groups | |
| dc.subject.en | Cyclotomic fields | |
| dc.subject.en | lattices | |
| dc.title.en | The special case of cyclotomic fields in quantum algorithms for unit groups | |
| dc.type | Communication dans un congrès | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 2303.03978 | |
| bordeaux.page | 229 | |
| 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 | Progress in cryptology -- AFRICACRYPT 2023Lecture notes in computer science (LNCS) | |
| bordeaux.conference.city | Soussa | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-04012986 | |
| hal.version | 1 | |
| hal.invited | non | |
| hal.proceedings | oui | |
| hal.conference.organizer | Ministry of Communication Technologies of Tunisia | |
| hal.conference.organizer | in partnership with the International association of cryptologic research (IACR) | |
| hal.conference.end | 2023-07-21 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04012986v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.btitle=Progress%20in%20cryptology%20--%20AFRICACRYPT%202023Lecture%20notes%20in%20computer%20science%20(LNCS)&rft.date=2023-07-21&rft.volume=14064&rft.spage=229&rft.epage=229&rft.au=BARBULESCU,%20Razvan&POULALION,%20Adrien&rft.isbn=0302-9743&rft.genre=unknown |
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