Commit b6c44563 by Niels Möller

Fixed equations for Montgomery->Edwards transformation.

parent 131d068d
 ... @@ -127,7 +127,7 @@ mapping $P = (x,y)$ to $P' = (u, v)$, as follows. ... @@ -127,7 +127,7 @@ mapping $P = (x,y)$ to $P' = (u, v)$, as follows. that $x^2 + bx + 1 = 0$, or $(x + b/2)^2 = (b/2)^2 - 1$, which also that $x^2 + bx + 1 = 0$, or $(x + b/2)^2 = (b/2)^2 - 1$, which also isn't a quadratic residue). The correspondence is then given by isn't a quadratic residue). The correspondence is then given by \begin{align*} \begin{align*} u &= \sqrt{b} \, x / y \\ u &= \sqrt{b+2} \, x / y \\ v &= (x-1) / (x+1) v &= (x-1) / (x+1) \end{align*} \end{align*} \end{itemize} \end{itemize} ... @@ -135,7 +135,7 @@ mapping $P = (x,y)$ to $P' = (u, v)$, as follows. ... @@ -135,7 +135,7 @@ mapping $P = (x,y)$ to $P' = (u, v)$, as follows. The inverse transformation is The inverse transformation is \begin{align*} \begin{align*} x &= (1+v) / (1-v) \\ x &= (1+v) / (1-v) \\ y &= \sqrt{b} x / u y &= \sqrt{b+2} x / u \end{align*} \end{align*} If the Edwards coordinates are represented using homogeneous If the Edwards coordinates are represented using homogeneous coordinates, $u = U/W$ and $v = V/W$, then coordinates, $u = U/W$ and $v = V/W$, then ... ...
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