Definition
The generator point, often called the base point and written G, is a single fixed point on the secp256k1 curve that every participant in Bitcoin agrees on. It is one of the curve's published domain parameters, identical for every wallet and node on the network. Your public key is nothing more than G multiplied by your private key scalar.
Why a single base point works
Because secp256k1 has a cofactor of 1, the generator point has prime order n, and repeatedly adding G to itself cycles through all n points of the group before returning to the start. In other words, G generates the entire usable key space, which is what its name refers to. Every valid Bitcoin private key corresponds to a distinct multiple of G, and that multiple is the public key.
From generator to address
Key creation is a single operation: pick a secret scalar k between 1 and n − 1, then compute Q = kG using point multiplication. The result Q is the public key, which is then hashed and encoded into an address. Recovering k from Q and the known G is exactly the discrete logarithm problem, so publishing Q reveals nothing usable about k.
The compressed encoding of secp256k1's generator begins with the bytes 0279BE667E…, a constant worth recognizing as the literal origin of every Bitcoin key. It is a fixed point in the curve's finite field, not a secret.
In Simple Terms
The generator point, often called the base point and written G, is a single fixed point on the secp256k1 curve that every participant in Bitcoin…