Mechanism used for offline authentication of software

To prevent user from downloading bootleg copies of software , users often have to enter a string of hexadecimal numbers which would be used to authenticate the user.

I think the basic idea would be that that the secret key is embedded in the software and a successful authentication occurs when there is a match between the user entered string and the secret key.

I would like to know the actual mechanism behind this idea

What are some other possible mechanism used when the software does not require internet connection to authenticate ??

Thanks

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