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I didn't get this part right! For example, we have an online box with a 16-digit password, and we don't know what the password is! How can a quantum computer find the correct password faster than classical computers knowing that numbers are chosen at random? this makes both computers have 50/50 chance to guess the correct password if you are lucky enough right?

Thanks.

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In the setting you described we cannot use a Quantum Computer to benefit us. But if we are able to somehow perform the password check itself within a quantum computer, then Grover's algorithm gives us a real advantage. For example, if we're trying to find the correct hash for a Blockchain.

In your scenario, the password-checking is being done by a remote server, and indeed we cannot do much; but if we got hold of the hashed passwords + salt on the server and we know the hashing algorithm, then again we can use a quantum computer to speed up finding the actual passwords.

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  • $\begingroup$ so what you trying to say is if we know the algorithm of how the password generates, we have a high chance to generate the right password? $\endgroup$
    – Zakaria Halloumi
    Apr 21, 2022 at 18:52
  • $\begingroup$ @ZakariaHalloumi you also need to know the final hash, in order to test whether the password is correct $\endgroup$
    – Tristan Nemoz
    Apr 22, 2022 at 9:49
  • $\begingroup$ @ZakariaHalloumi, what we need to have is the explicit password-checking algorithm. Usually passwords are not stored directly, but hashed (with additional data called "salt"), so to check a password we need to have this hash value. $\endgroup$
    – Gadi A
    Apr 23, 2022 at 6:43

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