RSA Security 5.2.2 Summary of Elliptic Curve Terminology, Cofactor, 2Elliptic Curve Parameters

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 page xx.

Table 3-2Elliptic Curve Parameters

Notation	Name	Description
Fq	base 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 = x3 + ax +b
		For F2m:y2 + xy = x3 + ax2 +b
P	point of prime order	(xP,yP)
	or	The pair xP, yP satisfies the curve equation.
	base point
n	order of P	The smallest nonzero number such that P added
		to itself n times is the zero point, Ο, on the curve.
		n is prime.
h	cofactor	The order of the curve divided by the order of P:
		#E(Fq)/n

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