The special case of cyclotomic fields in quantum algorithms for unit groups - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2023

The special case of cyclotomic fields in quantum algorithms for unit groups

Résumé

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.
Fichier principal
Vignette du fichier
Hal-submission.pdf (626.47 Ko) Télécharger le fichier
article.pdf (373.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04012986 , version 1 (07-03-2023)

Licence

Paternité

Identifiants

Citer

Razvan Barbulescu, Adrien Poulalion. The special case of cyclotomic fields in quantum algorithms for unit groups. AFRICACRYPT 2023, Ministry of Communication Technologies of Tunisia; in partnership with the International association of cryptologic research (IACR), Jul 2023, Soussa, Tunisia. pp.229. ⟨hal-04012986⟩
106 Consultations
41 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More