I have a point in affine coordinates: $(x,y)$.

What should I do when I want to convert to $(X,Y,Z)$ in Jacobian coordinates? I need it for calculating ECC in a prime field.


When you go from Affine to Jacobian, $X$ and $Y$ stay the same, and $Z$ is equal to $1$

Affine -> Jacobian:

$(X',Y',Z') = (X,Y,1)$

Jacobian -> Affine:

$(X',Y') = (\frac{X}{Z^2}, \frac{Y}{Z^3} )$

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  • 2
    $\begingroup$ Note that the division in the Jacobian -> Affine transformation is based on the Modular multiplicative inverse. You can't just use the integer division operation offered by common programming languages. $\endgroup$ – CodesInChaos Oct 13 '14 at 10:20

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