MD5 is considered broken and SHA-1 is closely following, but HMACs built around either are still considered relatively secure. It makes me wonder if MD5 and SHA-1 HMACs can be used as secure hashes.

1. Settle on some constant $C$ that will serve the role of $K$.
2. Define a new hash algorithm as $H\_C(x)=HMAC(C, x)$.

Could this work?