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Conference Papers Year : 2023

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

Abstract

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

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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⟩
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