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Nettle
nettle
Commits
a3f8c34c
Commit
a3f8c34c
authored
Aug 28, 2014
by
Niels Möller
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Document better twisted Edwards formulas.
parent
2a1ac1dc
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misc/ecc-formulas.tex
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misc/ecc-formulas.tex
View file @
a3f8c34c
...
...
@@ -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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