Anzeige
Erschienen in:
2010 | OriginalPaper | Buchkapitel
Differential Addition in Generalized Edwards Coordinates
verfasst von : Benjamin Justus, Daniel Loebenberger
Erschienen in: Advances in Information and Computer Security
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We use two parametrizations of points on elliptic curves in generalized Edwards form
x
2
+
y
2
=
c
2
(1 +
d
x
2
y
2
) that omit the
x
-coordinate. The first parametrization leads to a differential addition formula that can be computed using 6
M
+ 4
S
, a doubling formula using 1
M
+ 4
S
and a tripling formula using 4
M
+ 7
S
. The second one yields a differential addition formula that can be computed using 5
M
+ 2
S
and a doubling formula using 5
S
. All formulas apply also for the case
c
≠ 1 and arbitrary curve parameter
d
. This generalizes formulas from the literature for the special case
c
= 1 or
d
being a square in the ground field.
For both parametrizations the formula for recovering the missing
X
-coordinate is also provided.