What would be the expected time to find all users passwords in UNIX using dicitionary attack?

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I was reading that the designers of UNIX password algorithm used a 12 bit salt to modify the E-table of the unix hashing function (the DES). Supposing i have a system with 2^(24) users?

Is that ever possible to user dictinary attack? and if so how long would it take? years??

I am really new on computer security

sorry editing: I am not sure what unit time i guess i have to assuming bytes per minute depending on my code?

The reason I am asking is for a project where one of the questions states: "Consider a system with 2^24 users. Assume that each user is asssigned a salt from a uniform random distribution and that anyone can read the password hashes and salt for users." WHat is expected time to find all users' passwords using dictionary attack?"

thanks very much

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Sounds like a homework question that is expecting a formula as an answer. Way too many things unspecified. In particular, a dictionary could be precomputed with all possible salts (2^12 = 4096, not that big) for one password. If all 2^24 users used that same one password, then every password would be in the dictionary and the question is what is the expected time to do 2^24 lookups into a table of 4096. On the other hand, if none of the users passwords are in the dictionary, then you will never find the password using a dictionary attack unless you stumble upon a hash collision.

Probably better asked on security.stackexchange.com