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HKDF stage 1 is useful for when the SKM value is derived using some deterministic method, such as a key exchange, or from a source that may not be fully trusted. SKM may be substantially larger than the keys you want, but may have the entropy not evenly distributed. Stage 1 compacts and distributes the entropy into a key that is correctly sized for the hash ...


I'll take the (previous version of the) question as: how to implement a secure hash function $H3$ with 3 arguments, from one hash function $H$ with 1 argument, all with argument(s) in $\{0,1\}^*$. Note: For a concrete $H$ with the destination set $\mathbb Z_p^*$ thought in the question, we could use SHA3-512 followed by a suitable function; for example, ...

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