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
=-
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
=-
³ 3
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