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Are KDFs such as PKDF2 and HKDF vulnerable to side-channel attacks such as static and dynamic power analysis including the hash type used internally?

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Technically speaking, a side-channel attack by definition doesn't attack a KDF but a specific implementation of it. An example of an implementation would be the way macOS turns a user's password to a disk encryption key with PKDF2. A gZip application may execute the PKDF2 in a slightly different fashion.

The answer to your question is yes, because you can never know if a developer made a mistake, or something like that. If that isn't what you meant please clarify.

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