A group is a set of elements
and one binary operator
that satisfies the following axioms:
- Closure: for any, the elementis in.
- Associativity: for any,.
- Identity:, for all.
- Invertibility:, for all.
In addition to the above properties, if a group exhibits the commutative property of
, it is called an abelian group.
A single-generator group contains an element
, called the generator point, such that repeated additions of
with itself can generate every element in
Additionally, our group is cyclic, which means it has an order
, such that
Let us now represent the generator point
in Python, used in Bitcoin.
# Generator point of the abelian group used in Bitcoin
G = Point(
# Order of the group generated by G, such that nG = I
N = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141