I'm reading the whitepaper of zerocash and I don't understand how a mint transaction works. Here are my following questions:
How do you prove that you have enough bitcoins to form a certain amount of zerocoin? How are the bitcoins locked? What makes you not able to mint bitcoins and using both zerocoins and bitcoins (doubling the value of your bitcoins)?
As an example of the last question, let's say I have 10BTC, I create a zerocoin worth 10BTC, I send it anonymously to Alice, then I make a traditionnal bitcoin transaction of my 10BTC to Bob, what makes this impossible?
If you can't spend the 10BTC anymore (before it has been trasnformed into zerocoin), does that mean we can know how much coin you have minted (eventhough we cannot know how you have spent it)?