How does one claim ownership of an NXT address? Apparently, NTX uses very short addresses and a very small alphabet. There is a system designed to claim ownership of a given address, but I couldn't find much information on it. How is it handled in the NXT system?
The first out-going transaction for an address claims the address. To make such a transaction, you need to know a private key for the address. The first transaction causes the corresponding public key to be stored against the address in the block-chain, and then subsequent transactions are only accepted if they have the same public (and hence private) key.

The addresses are 64-bit, which would probably take a few years to crack by brute force. The public and private keys are 256-bit.