In a cryptography book I read that people does not known how to compute the number of points on a Jacobian of a hyperelliptic curve $C$ over a finite field $F_q$? Is this true? It seems easy to compute it knowing the eigenvalues of the Frobenius action on $H^1(C)$, which could be recovered knowing $\sharp C(F_{q^l})$ for all $l$ between $1$ and the genus of $C$.