Takeaway

FHE lets you compute on encrypted data without decrypting; the result decrypts to the same output as computing on plaintext, enabling private cloud computation.

The problem (before → after)

  • Before: You must reveal data to compute on it, risking privacy and leakage.
  • After: Encrypt once; untrusted servers evaluate circuits homomorphically; only the data owner decrypts the result.

Mental model first

Think of a locked glovebox: you insert inputs and gloves let the operator manipulate objects without opening the box. Computation happens inside; the key never leaves your pocket.

Just-in-time concepts

  • Homomorphism: Enc(E(x) ⊕ Enc(E(y))) decrypts to x ⊕ y for supported ops.
  • Bootstrapping: Refresh noisy ciphertexts by homomorphically evaluating the decryption circuit.
  • Lattice schemes (LWE/RLWE): Hardness underpins security and efficiency.

First-pass solution

Use leveled HE for bounded-depth circuits; add bootstrapping to support arbitrary depth → fully homomorphic.

Iterative refinement

  1. CKKS supports approximate arithmetic; BFV/BGV support exact modular arithmetic.
  2. Packing/SIMD encodes vectors to amortize costs.
  3. Hybrid MPC+HE and trusted hardware combine strengths.

Principles, not prescriptions

  • Trade accuracy, depth, and performance; choose schemes per workload.
  • Keep secret keys off-server; minimize bootstrapping calls.

Common pitfalls

  • Underestimating latency and memory overheads.
  • Ignoring noise growth and parameter selection.

Connections and contrasts

  • See also: [/blog/secure-multiparty-computation], [/blog/zero-knowledge-proofs], [/blog/differential-privacy].

Quick checks

  1. Why bootstrapping? — To reset noise and allow unbounded depth.
  2. Why lattices? — Post-quantum hardness assumptions enabling practical schemes.
  3. When use CKKS vs BFV? — Approximate real arithmetic vs exact integer arithmetic.

Further reading

  • Gentry’s thesis (source above); SEAL/HElib docs