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In distributed systems it is often bad practice to have "Shared Master Key". If a bad guy breaks in one of your devices he has the most important crypto piece of the system, and you're pretty much done. Rather have one key per device, and these keys are signed by an Authority I would say.


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The algorithm produces a password based on the value of the time that is input as an argument. That value does not have to be the current time. For the purposes for which TOTPs are generally used, there is no value in producing the password for a time other than the current time step - it won't be recognized by the validator.


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Probably because a simple cascade would only be stronger against some attacks, while opening the door to more implementation bugs. While bcrypt and scrypt are (password based) key-derivation functions, much of what is in the answers to this question about combining hash functions applies here. Different constructions give preimage resistance and PRF-ness, ...



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