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So in ECC GF(next_prime(2^160)) then construct the curve, base point
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I'm not sure how in hyper elliptic curve;
I think 
$ `q = next_prime(2^80)`
$ `K.<x>=GF(q,'x')[]`
$ `f = x^5 + x^3 + 1`
$ `H = HyperellipticCurve(f, 0)`
$ `J = H.jacobian()`
$ `z = Integer(randrange(2, q-2))`
$ `D = J(H.lift_x(F(z)))`               # divisor
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To compare time 
ECC => `%timeit (Integer(randrange(1, 2^160))) * base point`
HECC => %timeit (Integer(randrange(1, 2^80))) * divisor`
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is this correct?
and if this correct, how ECC time = 13.2 millisecond;
                         HECC time = 185 millisecond