A point on the elliptic curve secp256k1

Parameters of the secp256k1 elliptic curve.

• p is the order of the prime field we are working over
• a and b are the parameters in the curve equation y^2 = x^3 + a*x + b (but a=0 here)
• G is the generator of the subgroup in the curve
• n is the order of G, equivalently the size of the subgroup
• H is the cofactor (size of the curve divided by the size of the subgroup)

See http://www.secg.org/collateral/sec2_final.pdf

G is the base point, that is the generator; E = { G^i | iin Z } = { G^i | i<-[1..n] }

Addition in the elliptic curve (or multiplication if you prefer to think it as a multiplicative group)

Doubling a point in the elliptic curve (multiplication by the integer 2)

Inverse (negation) in the elliptic curve

Multiplication by a positive integer (or exponentiation, if you think multiplicatively). This is slow, use the projective version instead!