Computing cardinalities of Q-curve reductions over finite fields
Number Theory
2019-02-20 v3
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.
Cite
@article{arxiv.1605.07749,
title = {Computing cardinalities of Q-curve reductions over finite fields},
author = {François Morain and Charlotte Scribot and Benjamin Smith},
journal= {arXiv preprint arXiv:1605.07749},
year = {2019}
}
Comments
To appear in the proceedings of ANTS-XII. Added acknowledgement of Drew Sutherland