Explicit-Formulas Database
Genus-1 curves over large-characteristic fields
Doubling-oriented Doche–Icart–Kohel curves
An elliptic curve in doubling-oriented Doche–Icart–Kohel form
[database entry;
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Sage output]
has parameters
a
and coordinates
x
y
satisfying the following equations:
y^2=x^3+a*x^2+16*a*x
This curve shape was introduced in 2006 Doche–Icart–Kohel.
The parameter a is required to have a(a-64) nonzero.
The neutral element of the curve is the unique point at infinity,
namely (0:1:0) in projective coordinates.
Representations for fast computations
Standard coordinates
[more information]
represent
x
y
as
X
Y
Z
ZZ
satisfying the following equations:
x=X/Z
y=Y/ZZ
ZZ=Z^2