# Is there a single point generator G for every elliptic curve?

I understand that G is a point on curve which holds true for y^2 = x^3 + ax + b. But there can be several other points as well which holds true for above equation but how do we choose which one is our G?

## 2 Answers

There often are multiple points which could be generators. In fact, for prime order curves, every point on the curve is a generator.

For practical use, a specific point is picked based on some constraints.

May curves use rules such as lowest `abs(x)` value or use some deterministic generator with a random seed.

I can't seem to find the login behind the G selection for secp256k1, however, but the point itself is defined in the curve specification.

• Thanks for the answer. I am actually trying to understand elliptic curve cryptography, specifically how the signature is verified, shared secret generation and the math behind it. I have gone through lot of information on internet, i am still not able to connect dots to fully understand it. can you help me? – Ishwar Chandra Aug 10 '18 at 12:58

It's defined in the specification of the curve. In Bitcoin, the curve was SECP256k1 is chosen and the curve parameters are defined here: SEC 2: Recommended Elliptic Curve Domain Parameters, Version 1.0