Earlier quoted context omitted.
That's what I understood from the article, and why I suggested the salts and hashes should be handled separately. If you give the attacker the salts, difficulty scales linearly. For two identical plaintexts, all that differs is the salt, but it is given to him. If you store the hashes and salts separately (the technical details of which I know nothing about), then you augment the keyspace exponentially. For N byte sa…
The server must have access to both the salt and the hash to verify a password. Therefore, upon compromise of the server, the attacker automatically has access to both the salt and the hash. There is no way around this problem that isn't simply obfuscation.
Edit: Or one could move just the salts into the device and store an index into them in the password file. Hashing would be carried out by the device but an attacker would only gain access to the indices. Without stealing the device itself it'd be impossible to properly salt the passwords for hashing.