Computing cardinalities of Q-curve reductions over finite fields - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles LMS Journal of Computation and Mathematics Year : 2016

Computing cardinalities of Q-curve reductions over finite fields

Abstract

We present a specialized point-counting algorithm for a class of elliptic curves over F_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generally, any elliptic curve over F_{p^2} with a low-degree isogeny to its Galois conjugate curve. These curves have interesting cryptographic applications. Our algorithm is a variant of the Schoof–Elkies–Atkin (SEA) algorithm, but with a new, lower-degree endomorphism in place of Frobenius. While it has the same asymptotic asymptotic complexity as SEA, our algorithm is much faster in practice.
Fichier principal
Vignette du fichier
qcsea.pdf (221.5 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01320388 , version 1 (23-05-2016)
hal-01320388 , version 2 (06-06-2016)
hal-01320388 , version 3 (17-06-2016)

Licence

Copyright

Identifiers

Cite

François Morain, Charlotte Scribot, Benjamin Smith. Computing cardinalities of Q-curve reductions over finite fields. LMS Journal of Computation and Mathematics, 2016, 19 (A), pp.15. ⟨10.1112/S1461157016000267⟩. ⟨hal-01320388v3⟩
396 View
217 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More