user86215: 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?

user7272: 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.

86215: <p>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?</p>
 7272: <p>There often are multiple points which could be generators. In fact, for prime order curves, every point on the curve is a generator.</p>

<p>For practical use, a specific point is picked based on some constraints.</p>

<p>May curves use rules such as lowest <code>abs(x)</code> value or use some deterministic generator with a random seed.</p>

<p>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.</p>
