title: Elliptic curves for ECDSA: choosing "generator"
body: <p><code>G(Gx, Gy)</code> -- which is also called <strong>generator</strong> -- is a point on Elliptic Curve (<em>EC</em>) on Finite field.  Finite field size = <code>p</code> -- prime modulus.<br /></p>
  
  <p>Say we have an <em>EC(Fp)</em>: <code>y**2 = x**3 + ax + b (mod p)</code><br />
  How should the point <code>G</code> be selected on it?<br /></p>
  
  <p>Does every point has to be found on <em>EC(Fp)</em> and then chosen one of those?<br />
  Or <code>Gx</code>\ <code>Gy</code> have to be somehow specific?</p>
  
  <p><br />The only thing i know: <code>G</code>'s order must be a prime number.</p>
  
  <p><em>P.S.</em>
  Sorry for my English and Thank you.</p>