I know how to create a paper wallet and send bitcoin to it from Coinbase.  If I want to spend the paper wallet bitcoin do I just give the merchant my public key?  How does the network know I hold the private key from just that private key info?  If I want to send the bitcoin to someone do I have to download the entire bitcoin protocol to do that?  Is there a smaller version I can use to just send bitcoin?  Thanks for your help.