I'm looking for a hashing function that can combine random numbers together in any order yet still find the same value. But it needs to be secure against hackers.
The idea is if I'm hashing together: $A, B, C$, and $D$
Where hash of $x = h(x)$:
I'm looking for a hash function that allows: $$h(A+B+C+D) = h(A)+h(B)+H(C+D) = h(A+B) + h(C) + h(D)$$
The $+$ symbol could be the same hash, could be something different.
I want something that is highly compressed, as in no matter how many additional items you add, the length doesn't grow.
The idea is that I can pop out any item from a long list of hashed items and prove that the items before X plus X plus the items after X can be proved to be part of a set.
I don't want Merkle tree or accumulator because both have relatively long proofs or the total size of the 'key' though that's kind of what I'm looking for. For my application, unfortunately, memory is very important.