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Commit a3f8c34c authored by Niels Möller's avatar Niels Möller
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Document better twisted Edwards formulas.

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misc/ecc-formulas.tex
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...@@ -138,20 +138,20 @@ coordinate $T$, with $Z T = X Y$ (see ...@@ -138,20 +138,20 @@ coordinate $T$, with $Z T = X Y$ (see
According to djb, the formulas in Section 3.1 are the once to use, According to djb, the formulas in Section 3.1 are the once to use,
because they are complete. See because they are complete. See
\url{http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd}, \url{http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-3},
\begin{align*} \begin{align*}
A &= x_1 x_2 \\ A &= (y_1 - x_1)(y_2 - x_2) \\
B &= y_1 y_2 \\ B &= (y_1 + x_1)(y_2 + x_2) \\
C &= t_1 d' t_2 \\ C &= 2 t_1 d' t_2 \\
D &= z_1 z_2 \\ D &= 2 z_1 z_2 \\
E &= (x_1+y_1) (x_2+y_2)-A-B \\ E &= B - A \\
F &= D - C \\ F &= D - C \\
G &= D + C \\ G &= D + C \\
H &= B-a A \\ H &= B + A \\
x_3 &= E*F \\ x_3 &= E F \\
y_3 &= G*H \\ y_3 &= G H \\
t_3 &= E*H \\ t_3 &= E H \\
z_3 &= F*G z_3 &= F G
\end{align*} \end{align*}
In our notation $a = -1$, and the $d'$ above is $-d$. In our notation $a = -1$, and the $d'$ above is $-d$.
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