Homomorphic encryption and secure multi-party computation (HE·MPC): compute on ciphertext without trusting the remote hardware — at a steep speed cost
In one sentence the remote execution environment is not a trust root — security comes from cryptographic assumptions. The cost is being much slower (HE especially), so today they're used in narrow scenarios, and full private LLM inference is still expensive. Volume 1 covers what they guarantee, where the cost is, and how to choose between them and a TEE.