Isn't the password hashing type stored with the hash?
Otherwise how would the system verify the password without knowing the hash type?
Isn't the password hashing type stored with the hash?
Otherwise how would the system verify the password without knowing the hash type?
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Yes, the system must recognize the hash type.
Either there is only one hash type (and the code working with the hashes implicitly assumes the hash type), or else there is a mix of hash types (and the hash type may still be stored in the code, or else stored with the hash in some way).
But the system doesn't need to expose this information to the user. In the case of Facebook, their password storage approach is public enough that Alec Muffett gave a public recorded talk about it. Many other systems do not disclose their password hashing methodology.
Sometimes, the hashing methodology can be deduced, most famously in the case of descrypt (which truncates at eight characters) and bcrypt (which truncates at 72 characters). In both cases, a password longer than the truncation length, but not an exact match, can be used to infer the password hash being used.