Cryptography Reference
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4
2
4
2
z
0
-4
-2
0
0
2
4
-
2
-2
x
y
-4
-4
Figure 3.1.
Ey x x
Defi ned over
R
(3-D View)
1
:²
=+
³ 2
3
2
Δ
=- +
(4
A
27
B
)
(3.22)
3
2
We assume that
A
+¹
. Therefore the roots must be distinct.
As examples of elliptic curves, Figures 3.1 and 3.2 show
4
27
0
y
²
=+
over real
x
³
2
x
numbers (
R
).
Figures 3.3 and 3.4 show
y
²
=-
over real numbers.
x
³
3
x
5
y
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-2
-3
-4
-5
Figure 3.2.
Ey x x
Defi ned over
R
(2-D Vi ew)
1
:²
³ 2
=+
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