Commit a3f8c34c authored by Niels Möller's avatar Niels Möller

Document better twisted Edwards formulas.

parent 2a1ac1dc
......@@ -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,
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*}
A &= x_1 x_2 \\
B &= y_1 y_2 \\
C &= t_1 d' t_2 \\
D &= z_1 z_2 \\
E &= (x_1+y_1) (x_2+y_2)-A-B \\
F &= D-C \\
G &= D+C \\
H &= B-a A \\
x_3 &= E*F \\
y_3 &= G*H \\
t_3 &= E*H \\
z_3 &= F*G
A &= (y_1 - x_1)(y_2 - x_2) \\
B &= (y_1 + x_1)(y_2 + x_2) \\
C &= 2 t_1 d' t_2 \\
D &= 2 z_1 z_2 \\
E &= B - A \\
F &= D - C \\
G &= D + C \\
H &= B + A \\
x_3 &= E F \\
y_3 &= G H \\
t_3 &= E H \\
z_3 &= F G
\end{align*}
In our notation $a = -1$, and the $d'$ above is $-d$.
......
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