# What is significance of recovering the chaining value of a hash compression function?

What is significance of recovering the chaining value of a compression function, when the message and its output are known? in other words, if a compression function $CF$ takes a chaining value $h_{in}$ and a message $m$ as inputs and outputs $h_{out}$.

$h_{out}=CF(h_{in}, m)$

Is it a bad property if given $m$ and $h_{out}$ to recover $h_{in}$?

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For instance, consider the prefix MAC scheme, which is constructed out of a hash function $H$ as follows: $$MAC_K(M) = H(K||M).$$ The prefix scheme is secure for some hash functions, for example the SHA-3 (Keccak) hash function.
However, if the compression function used by $H$ is not preimage resistant, then an adversary given $MAC_K(M)$ may recover the chaining value $$CV=H(K),$$ and construct a valid MAC for any other $M'$ even though he does not know $K$.