Chapter 3 Cryptography 71
Cryptography Overview
•The order n of P
P is sometimes called the base point.

The Cofactor

We mentioned previously that the prime number n that is the order of P must evenly
divide the order of the elliptic curve. That is, we know that the number h=#E(Fq)/n is
an integer. We call h the cofactor, and set it as our last parameter:
•The cofactor h=#E(Fq)/n
Summary of Elliptic Curve Terminology
Table 3-2 lists the elliptic curve parameters and gives a short description of each
parameter. For a brief description,refer to the previous sections in this chapter; for a
detailed discussion, see [13], [14], and [19] in “Related Documents” on pagexx.
Table 3-2 Elliptic Curve Parameters
Notation Name Description
Fqbase field Either:
Fp : {0,1,...,p–1} with arithmetic mod p
or
F2m : strings of m bits. Addition is bitwise XOR,
multiplication exists, but has no quick description
a, b coefficients of the curve a and b are elements of Fq. They determine an
equation, which depends on the base field:
For Fp:y2=x
3+ax+b
For F2m:y2+ xy= x3+ax
2+b
P point of prime order
or
base point
(xP
,yP)
The pair xP
, yP satisfies the curve equation.
norder of PThe smallest nonzero number such that P added
to itself n times is the zero point, Ο, on the curve.
n is prime.
hcofactor The order of the curve divided by the order o f P:
#E(Fq)/n