Cryptography Reference
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4
2
4
z
2
0
-4
0
-2
0
-
2
-
4
2
4
-2
x
y
-4
Figure 3.3.
Ey x x
Defi ned over
R
(3-D View)
2
:²
=-
³ 3
3.5.3 Prime Curves
Prime curves are defined over
Z
p
(integer group from 0 to
p
- 1), where
p
is a large prime.
Hence, limiting the variables and coefficients of the Weierstrass equation to a finite field
Z
p
, we have
(
)
2
3
y
mod
p
=++
x
Ax
B
mod
p
(3.23)
For example, Figure 3.5 shows the equation
y
²
=+
over finite field
Z
p
, where
x
³
2
x
p
= 23.
5
y
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
x
-1
-2
-3
-4
-5
Figure 3.4.
Ey x x
Defi ned over
R
(2-D View)
2
:²
=-
³ 3
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