Computing cardinalities of Q-curve reductions over finite fieldsReportar como inadecuado

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1 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau 2 GRACE - Geometry, arithmetic, algorithms, codes and encryption Inria Saclay - Ile de France 3 Ministère de l-Education Nationale

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.

Keywords : Elliptic curve cryptography Schoof-s algorithm Q-curves Point counting

Autor: François Morain - Charlotte Scribot - Benjamin Smith -



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