2
$\begingroup$

I am working with my project. I use projective coordinates but when I convert to affine coordinates, I can't get it. Can anyone help me?

Projective Coordinates $(X,Y,Z)$ to Affine Coordinates $(X,Y)$:

  • When $Z$ is not $0$ the point represented is the point (X/Z, Y/Z) in the Euclidean plane (Affine Coordinates)
  • When $Z$ is $0$ the point represented is a point at “infinity”

If I am using projective cordinates, I get 3 points $(x_3,y_3,z_3)$, is that correct? So I must convert to affine coordinates $(x_3,y_3)$? Can I convert projective to present affine coordinates?

$\endgroup$

closed as unclear what you're asking by yyyyyyy, fgrieu, e-sushi Jan 19 '16 at 8:15

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ $(x_3,y_3,z_3)$ is not three points, it's a triplet for the coordinates of one point in protective coordinates. $\;$ Then the answer to the question seems to be clearly given in the paragraph with the two bullets. Are you having a problem understanding what is meant by $X/Z$ in the question? That's $X$ times $1/Z$; where $1/Z$ is the inverse of $Z$ in the base group (e.g. $Z^{-1}\bmod p$ as obtained using the extended Euclidian algorithm when working with base group $\mathbb Z_p$), of the same nature as $X$, $Y$ or $Z$ are; and times is multiplication in the base group. $\endgroup$ – fgrieu Jan 19 '16 at 6:43