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If you need security against quantum attacks, there aren't that many options. I would go for a lattice-based encryption like NTRU or something based on ring learning with errors. There are no "magic numbers" involved and the assumptions they are based on have been scrutinized by the academic community. NTRU has been around for a decade and has pretty good ...


Supersingular isogenies are a rather recent attempt at post quantum security. You will have a hard time finding an efficient and secure implementation, and even if you write one yourself, the algorithms have not yet seen that much cryptanalysis. (Although that's a subjective judgement call.) If post quantum security wasn't a concern, you could choose from ...


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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