Research seriesL3algorithms
Fully homomorphic encryption computes directly on ciphertext, so a model you do not trust can run inference on a prompt it never sees in the clear — at a real, quantifiable performance tax. This series builds FHE from the noise-growth problem and bootstrapping through the scheme families, private neural-network inference, and an honest comparison with trusted hardware and multi-party computation. Grounded in Gentry, BGV, and CKKS.
Fully homomorphic encryption lets you compute on data while it stays encrypted. The obstacle is noise that grows with every operation; the breakthrough is bootstrapping, which refreshes it.
Homomorphic schemes split by the numbers they encrypt: BGV and BFV do exact integer arithmetic; CKKS does approximate real arithmetic. The choice follows the workload.
Bootstrapping makes FHE unbounded, but it is the dominant cost. Its price is set by a three-way tension between security, performance, and how much computation you can do between refreshes.
The linear layers of a network are natural under homomorphic encryption; the non-linear activations are the hard part, and how you approximate them decides what private inference can do.
Three roads lead to inference that hides the prompt: homomorphic encryption, trusted hardware, and multi-party computation. They differ most in where trust lives and what it costs.