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OpenFHE backend — design note (EXPERIMENTAL, PARTIAL)

Status: experimental, partially shipping. An OpenFHE-CKKS backend now exists at regaudit_fhe.fhe.openfhe and registers itself with the backend registry (regaudit_fhe.fhe.get_backend("openfhe-ckks")), installed via the separate [openfhe] extra (the [fhe] extra still installs TenSEAL, which remains the verified reference backend). The OpenFHE backend runs five of the six primitives — encrypted concordance is pending because it needs rectangular mm_pt, whereas the current adapter implements only the square (diagonal-method) case. The notes below record the original design rationale and the remaining work.

Why a separate OpenFHE build is on the roadmap

  1. Native rotation primitive. OpenFHE exposes EvalRotate(ct, k) directly, so the rotation-based prefix-sum and slot-shift implementations of the audit primitives stay at depth zero. The TenSEAL backend lacks this primitive at the CKKSVector level and substitutes a depth-1 plaintext-matrix multiply for prefix-sum (see regaudit_fhe.fhe.slot_vec.mm_pt).
  2. Calibrated polynomial libraries. OpenFHE ships minimax-calibrated sign and reciprocal polynomials at higher degrees, supporting tighter precision bounds than the textbook degree-3 polynomials shipped today.
  3. Bootstrapping support. Even though the audit primitives are designed to run inside the d=6 budget without bootstrapping, an OpenFHE build can support depth-7+ extensions if needed.

Integration surface (target)

A future regaudit_fhe.fhe.openfhe_slot_vec.EncryptedSlotVec would mirror the existing TenSEAL slot-vector API:

TenSEAL backend (today) OpenFHE backend (target)
regaudit_fhe.fhe.context.build_d6_context build_d6_openfhe_context(...)
regaudit_fhe.fhe.slot_vec.EncryptedSlotVec OpenFHEEncryptedSlotVec
EncryptedSlotVec.sum_all via tenseal.sum() EvalSum(ct) (native rotation tree)
EncryptedSlotVec.mm_pt (depth +1 substitute) EvalRotate(ct, k) (depth +0)

The audit primitive surface (fairness_encrypted, …) would not change: the SlotVec algebra is identical.

What we will NOT do

  • We will not silently swap backends behind the same import path. If and when this backend ships, it will be loaded explicitly and the parameter_set.backend field of the audit envelope will read openfhe-ckks.
  • We will not add OpenFHE as a hard dependency of the open-source package. It will live behind a separate extra ([openfhe]) so the baseline install footprint stays small.
  • We will not move OpenFHE into the repo without first shipping a full equivalence-test matrix against the existing TenSEAL backend.

How to follow this work

Outside contributions are not accepted — see CONTRIBUTING.md. Track the roadmap by watching the repository or the [fhe] extra contents in the next release.