Let $L = [b_1, \dots, b_k]$ be a list of blocks of a file.
I want to compute the function $f = h(g(b_1), \dots, g(b_k))$ on $N$ untrusted nodes such that:
Anyone can be reasonable convinced (with high probability) of the correctness of the result.
The algorithm is practical (no homomorphic encryption nonsense or similar).
No node has seen the entire list L or can gather it by knowing where the rest of the blocks are.
I'm willing to replicate computation up to a multiplicative constant (not too big).
Is there any protocol you know of that can solve this problem?