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Dmitry Baryshkov
nettle
Commits
b6c44563
Commit
b6c44563
authored
Aug 02, 2014
by
Niels Möller
Browse files
Fixed equations for Montgomery->Edwards transformation.
parent
131d068d
Changes
1
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misc/ecc-formulas.tex
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b6c44563
...
...
@@ -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
...
...
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