Random Oracles in Python

A random oracle is a function $\mathcal{O}: {0,1}^* \to {0,1}^\infty$ where each output bit is independently and uniformly random, but the function is consistent: same input, same output, every time (: $\text{byte}_i = H(\text{seed} | i)[0]$. Same seed gives the same infinite sequence, on any machine, forever. $O(1)$ space, random access to any position. Only as "random" as the seed and hash function.

Note the fixed-width index encoding (to_bytes(8, 'big')). If you used str(index).encode() instead, index 10 and the concatenation of index 1 + index 0 would collide. Real KDFs like (ROM), used throughout cryptography to prove security. The showed there exist schemes provably secure in the ROM that break when instantiated with any hash function. In practice, it usually works. Understanding why starts with understanding what you are approximating.