[ref] Curve cryptosystem parameters

http://www.johannes-bauer.com/compsci/ecc/ 에서 발췌

4 Doing useful ECC operations

4.1 Curve cryptosystem parameters

In order to turn all these mathematical basics into a cryptosystem, some parameters have to be defined that are sufficient to do meaningful operations. There are 6 distinct values for the F_p case and they comprise the so-called "domain parameters":

1. p: The prime number which defines the field in which the curve operates, F_p. All point operations are taken modulo p.
2. a, b: The two coefficients which define the curve. These are integers.
3. G: The generator or base point. A distinct point of the curve which resembles the "start" of the curve. This is either given in point form G or as two separate integers g_x and g_y
4. n: The order of the curve generator point G. This is, in layman's terms, the number of different points on the curve which can be gained by multiplying a scalar with G. For most operations this value is not needed, but for digital signing using ECDSA the operations are congruent modulo n, not p.
5. h: The cofactor of the curve. It is the quotient of the number of curve-points, or #E(F_p), divided by n.

4.2 Generating a keypair

Generating a keypair for ECC is trivial. To get the private key, choose a random integer d_A, so that

Then getting the accompanying public key Q_A is equally trivial, you just have to use scalar point multiplication of the private key with the generator point G:

Note that the public and private key are not equally exchangeable (like in RSA, where both are integers): the private key d_A is a integer, but the public key Q_A is a point on the curve.