Quantum Security of the Legendre PRF - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematical Cryptology Year : 2022

Quantum Security of the Legendre PRF

Abstract

In this paper, we study the security of the Legendre PRF against quantum attackers, given classical queries only, and without quantum random-access memories. We give two algorithms that recover the key of a shifted Legendre symbol with unknown shift, with a complexity smaller than the exhaustive search of the key. The first one is a quantum variant of the table-based collision algorithm. The second one is an offline variant of Kuperberg's abelian hidden shift algorithm. We note that the latter, although asymptotically promising, is not currently the most efficient against practical parameters.
Fichier principal
Vignette du fichier
legendre.pdf (311.15 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03529834 , version 1 (17-01-2022)

Licence

Identifiers

  • HAL Id : hal-03529834 , version 1

Cite

Paul Frixons, André Schrottenloher. Quantum Security of the Legendre PRF. Mathematical Cryptology, 2022, 1 (2), pp.52--69. ⟨hal-03529834⟩

Collections

INRIA INRIA2
31 View
35 Download

Share

Gmail Mastodon Facebook X LinkedIn More