You want every single bit error to avalanche to the whole key. You also don't want bit errors at some offsets modulo X to cancel each other out. Cryptographic h

You want every single bit error to avalanche to the whole key. You also don't want bit errors at some offsets modulo X to cancel each other out. Cryptographic hashes provide these properties. For any custom solution you would first have to prove that it has the security properties needed. The asymmetric crypto of a connection setup takes the lion's share of CPU cycles. I don't think it's worth the risk just to beat the cheap (relatively speaking) symmetric algorithms.