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Do we need one of the factors of two factor authentication to be one-time use?

TOTP and password are considered two factor authentication, but does smart card and password also count as two-factor authentication?

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No.

The factors are:

  • something you know (for instance a password);
  • something you have (for instance a device containing a key for TOTP generation)
  • something that you are (for instance a fingerprint).

TOTP is not a factor in itself, it is a scheme that can be used to prove that you have the key / device).

There are however other ways of testing that you have something. If you bring a special amulet as "something that you have" then I could simply have a look at it after all. One time use is therefore not required.

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No; a common example where neither factor is one-time is SSH key-based authentication with a passphrase: the key is something you have (unless you have memorised it...) and the passphrase is something you know. Both are required for authentication.

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