Allele Frequency with Variance

# Security notes — `allele_frequency_with_variance`Scoped to this bundle. The platform-wide threat model lives in`docs/manifesto.md`, `docs/requirements.md`, and `docs/simulation_mode.md` §5.Kerckhoffs applied to a product: **no guarantee rests on the secrecy — or thehonesty — of the server.** Don't trust, verify.This is the multiplication-supporting sibling of the flagship: same inputs, butthe server SQUARES an encrypted value. The trust boundary is unchanged — theserver still holds no secret key and still returns only ciphertext.## Trust classes (what may cross the wire)| class | example artifact | may leave the owner's machine? ||-------|------------------|-------------------------------|| RAW | `raw.json` genotypes | **no** || ENCODED | `encoded.json` dosage vector | **no** || PRIVATE | `secret_context.tenseal` (secret key), `plain.json` | **no, ever** || ENCRYPTED | `cipher.bin`, `result.bin` (one BMCT1 container packing sum_g + sum_g2) | yes || PUBLIC | `public_context.tenseal` (secret key stripped; relin keys retained) | yes |Only ENCRYPTED and PUBLIC are ever uploaded. `00_keygen.py` writes the secret keyto `secret_context.tenseal`, which is used **only** by `40_decrypt.py` on theresearcher's machine. There is no `/api/v1` endpoint that accepts a secret key.## The public context carries relin keys — and that is safeUnlike the additive flagship, the published public context includes**relinearization keys**. Relin keys are a public evaluation key: they let theserver relinearize a degree-3 product ciphertext (the result of ct × ct) back todegree 2. They reveal **nothing** about any plaintext and cannot decrypt — onlythe secret key can. The server needs them purely to perform the square. **NoGalois (rotation) keys are generated**: the square is element-wise per slot, sothere is never a cross-slot rotation. Withholding Galois keys keeps the server'scapability minimal — it can add and element-wise square, nothing else.## Server holds no secret key`30_compute_encrypted.py` — the only server-side stage, a kit shim that runs`server.py`'s `compute` — loads the **public**context plus ciphertexts, homomorphically adds, and homomorphically squares(relin). It defensively refuses a context that carries a secret key(`context.is_private()` → error). The server therefore never sees a singleplaintext genotype; it operates on ciphertext and returns ciphertext (two blobs:`sum_g` and the server-derived `sum_g2`). Decryption happens only where thesecret key lives: locally.## Server-derived second moment — integrity, not blind trust`sum_g2` is computed **by the server, under encryption**, from the same `g`ciphertexts. The researcher never has to trust the server got the square right:the released `sum_g2` is bit-exact-verifiable against the cleartext oracle insimulation (`docs/simulation_mode.md`), and the compute is deterministic, sore-execution reproduces a bit-identical result digest. Squaring server-side (vsthe client sending `g²`) means the contributor payload stays minimal and thesecond moment can never be a client-fabricated value inconsistent with `g`.## The append-1 sentinel is NOT a MACBoth result vectors' trailing sentinel slot decrypts to the exact contributorcount N (sum path `Σ 1 = N`; square path `Σ 1² = N`), and `50_decode.py`cross-checks that the two agree. Dropping one upload yields N−1 in both (test:`test_sentinel_tracks_dropped_upload`). It catches **mechanical corruption /miscounting** — it gives **no** guarantee that contributions are distinct,genuine, or non-Sybil. Call it what it is: an integrity check, not authenticity.## What FHE here does and does not hide- **Hides:** individual genotype vectors from the server (inputs are ciphertext),  and the individual second moments (the server never decrypts `g²` per person).- **Does not hide:** the released aggregates themselves (`sum_g`, `sum_g2`, and  the derived mean/variance), and metadata (researcher identity, participant  count/timing, ciphertext sizes, protocol choice).- **Differencing (K vs K+1):** the *statistics* leak an individual if you can  compute `A_{K+1} − A_K` — and because BOTH moments are released, an attacker who  can difference recovers both `g` and `g²` for the marginal contributor.  `aggregate_only` + `min_contributors ≥ 30` (higher than the flagship's 20) +  `allowed_runs_per_project: 1` (cohort freeze + min-N + run cap) **mitigate**  this; they are not a complete defense. Overlapping/Sybil differencing across  separately frozen cohorts needs DP + cross-job query budgets (v2). Documented,  not hand-waved — see `docs/simulation_mode.md` §5.- **Verify-by-re-execution is determinism, not zero-knowledge.** Re-running  `30_compute_encrypted.py` on the same ciphertexts reproduces bit-identical  result digests; it proves the computation, it is not a ZK proof.## Exactness / parameter safetyBFV is exact in `Z_t`. The plaintext modulus must satisfy `t > max coordinatevalue`. Here the second moment dominates: `max sum_g2 = 4·N` (each `g² ≤ 4`). Thedefault `t = 786433` (a 20-bit batching prime, `≡ 1 (mod 32768)` as required atn=16384) stays exact for N up to ~196k; a real run at larger N must raise `t` (orthe simulation feasibility sweep will report `infeasible-at-these-params` onoverflow). Per-contributor `g² ≤ 4` and the sentinel sum N are both `≪ t`.**Noise budget:** the coeff-modulus chain `[60, 40, 40, 60]` gives twomultiplicative levels; the single depth-1 square consumes one, leaving headroom.A depth-2 circuit would need a longer chain (and a larger ring for the samesecurity), which is precisely the cost the benchmark matrix quantifies.