While reading through "Cryptographic Extraction and Key Derivation: The HKDF Scheme" by Hugo Krawczyk, I found the following text intriguing:
In some cases, well-defined combinatorial assumptions from the hash functions will suffice while in others one has to resort to idealized modeling and “random oracle” abstractions.
I assume it implies that: HKDF can be secure in certain cases even when the hash function is not a "random oracle".
When I recall that "a PRF appears random if it's selected randomly from the family of functions with the same domain", I think this means when the HMAC key is selected appropriately, the output from HMAC function should satisfy the requirements and goals of HKDF.
Is my reasoning true / somewhat plausible / wrong? Can HKDF be securely instantiated with HMAC-SWIFFT and in what situation?