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The conversion formula from twisted Edwards to Montgomery form is: $$x_{mont} = \frac{X_{mont}}{Z_{mont}}= \frac{1+y_{ed}}{1-y_{ed}} = \frac{1+\frac{Y_{ed}}{Z_{ed}}}{1-\frac{Y_{ed}}{Z_{ed}}} = \frac{Z_{ed}+Y_{ed}}{Z_{ed}-Y_{ed}}$$ If you want the affine $x_{mont}$, you need to compute the inversion. But if you just need $X_{mont}$ and $Z_{mont}$ you can ...



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