Like i wrote it should be possible in the same way like the Bitcoin-network saves
the valid transactions.
So why not just store valid TANs via hashs (encrypted, not plain) in the network too?
(when they are plaintext, everybody just harvest them :-), they must be
encrypted)
There are two problems associated with this approach:
1. Storage space is limited in the block chain as it is mirrored on all clients. If you're allowing random clients save their TAN in the network, it could be easily spammed. So you would have to introduce a fee for saving TAN hashes in the network, similar to the transaction fee.
2. Online banking TANs with their 6 numbers have a very small search space which is only secure because your bank locks your account after 3 or so wrong entries. This is not possible in Bitcoin because you can brute force the public TAN hashes offline. Thus, the TANs must be impractically long like 30 characters or so.