I want to implement the ATV-FHE scheme as it is described here https://eprint.iacr.org/2014/039.pdf. How to generate the public key?

Should I compute it as indicated in section 2 :

$h(i) = 2g(i)*[ ( f(i) )^{(-1)} ]$

or should I sample the public key as indicated in section 3 Parameter selection in NTRU_FHE :

Recall that for the NTRU-FHE scheme, the public key is of the form $h = 2gf^{(-1)}$ where $g$; $f$ chosen from a Gaussian distribution $D$ where $f$ is kept secret. The DSPR problem is to distinguish polynomials of the form $h = 2gf^{(-1)}$ from samples $h_0$ picked uniformly at random from the ring $Rq$. If the DSPR problem is hard, we can replace $h = 2gf^{(-1)}$ by some uniformly sampled $h_0$.



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