To clarify a couple of points - indeed AT stands for
Automated
Transactions (the "Turing complete" blockchain transaction solution created by CIYAM Developers which is detailed here:
http://ciyam.org/at).
As ATs are stored in a blockchain (which is a public ledger) there is simply no way that it can store secrets, however, it can stored "hashes" of secrets which can later be revealed to match (this is the basis of the Atomic Cross-Chain Transfer AT).
Complete anonymity is never going to be possible with ATs but the technology would allow for "mixing" (of same amounts) that would make it impossible to connect inputs to outputs (but development of such an AT will be done after we have implemented and demonstrated ACCT between Qora and Burst).
One key feature of ATs is that they have their
own account (so you can send them funds and messages and they can do the same). The AT machine code cannot be changed once the AT has been created so provided you (or someone that you trust) can
vet that the AT does what it has been purported to do then it can act as a trustless 3rd party.