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Is it fair to say a PBKDF is a specialization of KDF? Sure. A PBKDF is a KDF, just one that uses a password/passphrase as the entropy source. OTOH, a KBKDF (key-based KDF, if you want to call it that) is also a specialization of a KDF. A different specialization, which is why it may not be a good idea to treat them as a single thing. Will ...

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