If the expansion phase of key derivation is captured by the abstract formula (per Krawczyk):
KM = PRF* (PRK, CTX, L)
Then what happens to the security proofs if someone were to swap PRK and CTX. For example, they insert random but not secret number as the first argument and use the secret in their CTX formation?
If I literarily use the proof in Appendix A, Definition 14 of Krawczyk's paper "Cryptographic Extraction and Key Derivation: the HKDF Scheme", it seems that the attacker would gain a great advantage by swapping PRK and CTX. If the attacker knows PRK, he can always differentiate the output of PRF from random regardless how secret CTX is. Is this enough to prove that the swap is a bad idea.
Furthermore, are there any known practical attacks on this swap?