Counting points on hyperelliptic curves in average polynomial time

• Autores: David Harvey
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 179, Nº 2, 2014, págs. 783-803
• Idioma: inglés
• DOI: 10.4007/annals.2014.179.2.7
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• Resumen

  • Let g=1 , and let Q?Z[x] be a monic, squarefree polynomial of degree 2g+1 . For an odd prime p not dividing the discriminant of Q , let Z p (T) denote the zeta function of the hyperelliptic curve of genus g over the finite field F p obtained by reducing the coefficients of the equation y 2 =Q(x) modulo p . We present an explicit deterministic algorithm that given as input Q and a positive integer N , computes Z p (T) simultaneously for all such primes p