If "fast" did not matter, we could use generic constructions of most cryptographic primitives and have very strong security claims e.g. "If you can find collisi

If "fast" did not matter, we could use generic constructions of most cryptographic primitives and have very strong security claims e.g. "If you can find collisions for this hash function, you can solve the discrete logarithm problem on elliptic curves." There are a few downsides to such an approach but the primary one, the one that kills it in practice, is speed.