G

The symbol G refers to a distinguished point on the secpt256k1 elliptic curve known as the generator or base point.

Using elliptic curve point addition, one may add G to itself over and over again to form the sequence

G, G + G = 2G, G + G + G = 3G, ...

and eventually every point on the elliptic curve will be generated in this sequence.

In compressed form G is given by:

G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798

and in uncompressed form is:

G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8

This particular choice of G is chosen to be secure against attacks when used in the context of public key cryptography.

The order of G and the cofactor are:

• n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
• h = 01

The order n is the number of times G may be added to itself to get the identity. The cofactor h = 1 tells us that n is the order of the group of elliptic curve points, and therefore G generates the entire group.