What exactly is generator G in Bitcoin's elliptical curve algorithm? What exactly is the generator G in elliptical curve math?  It is typically described as a point on the curve.  Is this a tuple of values?  What properties does it have?
For a curve with for instance the equation:  y^2 = x^3 + a * x + b

The generator point G, or a ECDSA public key, is a pair of coordinates x and y, for which the above equation holds.

To reduce the storage size for a curve point, one can also store a sign and the x coordinate, this is what is known as point-compression.

You can then reconstruct the y by calculating  sign * sqrt(x^3+a*x+b).

Note that for calculations in modular fields the square root can only be calculated efficiently when the p != 1 (mod 8)