It doesn't have to be, in principle. There are hash functions that take fixed size input, and output no smaller (or arbitrarily long) hashes. Look at the hash

It doesn't have to be, in principle. There are hash functions that take fixed size input, and output no smaller (or arbitrarily long) hashes. Look at the hash construction in stream ciphers, for example. The keystream is very long, but the key is short. Or look at a perfect hash function, as used for hash tables.