From: Niels Möller Date: Sat, 2 Aug 2014 19:41:03 +0000 (+0200) Subject: Fixed equations for Montgomery->Edwards transformation. X-Git-Tag: nettle_3.1rc1~155^2~30 X-Git-Url: http://git.ipfire.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=b6c445639015fb8dbe4058006dac7a7affcc7437;p=thirdparty%2Fnettle.git Fixed equations for Montgomery->Edwards transformation. --- diff --git a/misc/ecc-formulas.tex b/misc/ecc-formulas.tex index 36c15227..46225066 100644 --- a/misc/ecc-formulas.tex +++ b/misc/ecc-formulas.tex @@ -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 isn't a quadratic residue). The correspondence is then given by \begin{align*} - u &= \sqrt{b} \, x / y \\ + u &= \sqrt{b+2} \, x / y \\ v &= (x-1) / (x+1) \end{align*} \end{itemize} @@ -135,7 +135,7 @@ mapping $P = (x,y)$ to $P' = (u, v)$, as follows. The inverse transformation is \begin{align*} x &= (1+v) / (1-v) \\ - y &= \sqrt{b} x / u + y &= \sqrt{b+2} x / u \end{align*} If the Edwards coordinates are represented using homogeneous coordinates, $u = U/W$ and $v = V/W$, then