Warning: Noob question incoming, sorry.

I am coming to Monero from Bitcoin, and I love the vision. You guys are truly addressing real weaknesses in the bitcoin architecture, and I really want to understand this in more detail.

I've read the Cryptonote white paper several times, but I am having some difficulty with its descriptions of the transaction signing process. In particular, I am trying to understand how to prevent double-spending, which requires me to understand the key image, and therefore the key.

1. Alice wants to send Bob half of the Monero in her address A.

2. Alice creates a transaction sending that qty to a one-time address based on some random plus part of Bob's address. (This is totally cool btw)

3. Alice signs that transaction using a ring signature algorithm, but based on what secret?

• If the secret is based on Alice's A key, then won't the key image duplicate check prevent her from ever creating another transaction from address A? (Does she need to fully spend all the contents of this address in the transaction, moving her "change" to another address?)

• If the secret is based on a random (possibly suggested in the white paper... its not clear to me), then what prevents another transaction from simply using a different random, which will produce a different key image?

Would love to hear your thoughts, and also any references you have to technical documentation that I should be reviewing in addition to the CryptoNote white paper!

Thank you! Tengu