Associative noncommutative hash function

Question

Is there a hash function with the following properties?

• is associative
• is not commutative
• easily implementable on 32 bit integers: int32 hash(int32, int32)

If I am correct, such a function allows achieving the following goals:

• calculate hash of concatenated string from hashes of substrings
• calculate hash concurrently
• calculate hash of list implemented on binary tree - including order, but excluding how tree is balanced

The best I found so far is multiplication of 4x4 matrix of bits, but that's awkward to implement and reduces space to 16 bits.

I am grateful for any help.

Answer 1

Polynomial rolling hash could help:

• H(A1,...,An) = (H(A1,...,An-1) * Base + An) Mod P

It's easy to concat two results or substract prefix/suffix from result, as long as the length is known.