title: How are public and private keys different?
body: <p>I have a follow up question to <a href="https://stackoverflow.com/questions/696472/given-a-private-key-is-it-possible-to-derive-its-public-key">Given a private key, is it possible to derive it’s public key?</a></p>
  
  <p>Are the public and the private keys the 'same' (in the sense that you just choose to make one public) or can you do more with the private key than with the public key?</p>
  
  <p>EDIT - to better state my question:</p>
  
  <p>When the two keys are generated, could I just randomly choose one of them to be the public key?</p>