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Where does Ubuntu keep the password salt for each user?

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From the manual page of shadow(5):

Each line of this file contains 9 fields, separated by colons (“:”), in the following order:

[..] encrypted password
Refer to crypt(3) for details on how this string is interpreted.

Alright, let's have a look at man 3 crypt then. From the notes section:

[..] So $5$salt$encrypted is an SHA-256 encoded password and $6$salt$encrypted is an SHA-512 encoded one.

"salt" stands for the up to 16 characters following "$id$" in the salt. The encrypted part of the password string is the actual computed password.

So, the salt is stored in the password field of /etc/shadow itself. For more details, have a look at the manual page of crypt(3).

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