Counting points on hyperelliptic curves of type y² = x^2g+1 + ax^g+1 + bx | Applied Discrete Mathematics. Supplement. 2018. № 11. DOI: 10.17223/2226308X/11/9

Counting points on hyperelliptic curves of type y² = x^2g+1 + ax^g+1 + bx

In this work, we investigate hyperelliptic curves of type C : y² = x^2g+i + ax⁹⁺ⁱ + bx over the finite field F_q, q = pⁿ, p > 2. For the case of g = 3 or 4, p \ 4g and b is a 4g-root, we provide efficient methods to compute the number of points in the Jacobian of the curve.

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Keywords

point counting, Legendre polynomials, Cartier - Manin matrix, hyperelliptic curves, многочлены Лежандра, матрицы Картье - Манина, гиперэллиптические кривые

Authors

Name	Organization	E-mail
Novoselov S. A.	Baltic Federal University I. Kant	snovoselov@kantiana.ru

Всего: 1

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