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?


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

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  • 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