Homomorphic encryption isn't currently practical, even for small-ish problems. It needs to use constant space, and every operation needs to flip on average hal

Homomorphic encryption isn't currently practical, even for small-ish problems. It needs to use constant space, and every operation needs to flip on average half of the bits. There aren't obvious ways around these restrictions, though off hand I can only come up with a quick hand-wavy "proof" that this must always be so if less than one bit of the unencrypted state is to be lost with every state update. So, in order to perform machine learning on terabytes of data, you need to flip terabits for every update of the homomorphic state machine. That being said, I could imagine someone coming up with a homomorphic encryption algorithm that starts out with a few megabits of excess entropy and leaks entropy at a bounded rate while remaining more efficient at calculation, and where the initial state is set up cleverly such that after a bounded number of steps, the state machine starts making nonsense computations and stops leaking entropy. Though, this just feels very brittle to intentionally leak entropy, and I have no idea how anything remotely like this could be actually constructed.