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Hanzo DevandGitHub
378b74758c
Adds the canonical noise-flooding threshold-decryption primitives that
upstream consumers (notably luxfi/threshold/protocols/tfhe) need to
implement true M-of-N FHE decryption without any party holding the
master key.
- ShareLWESecretKey: Shamir-splits the LWE secret coefficient-by-
coefficient over Z_q. No party ever sees the master.
- PartialDecryptLWE: party j computes d_j = c_1 · s_j + e_j with
fresh smudging noise from a discrete Gaussian.
- CombineLWE: integer-Lagrange (Bendlin-Damgård denominator clearing)
+ Δ^{-1} mod q to recover the plaintext polynomial.
- SmudgingSigma: tight noise calibration against the worst-case
integer Lagrange numerator, so Λ_max · σ · √t · 6 ≤ Q/16.
Decomplecting note: this LSSS-over-Z_q lives next to the existing
LSSS-over-RFC-3526-prime in pkg/threshold. The two are different
primitives — large-prime LSSS shares high-entropy secrets where the
secret space need not equal the FHE modulus; Z_q LSSS composes
directly with lattice arithmetic. Both stay in this package.
Decryption follows Bendlin-Damgård (TCC 2010, §4.2) and Asharov-Jain-
López-Alt-Tromer-Vaikuntanathan-Wichs (EUROCRYPT 2012, §4). Noise
flooding is the simulation-soundness mechanism.
Verified by round-trip tests at (t, n) ∈ {(2, 3), (5, 9), (11, 21)},
below-threshold negative test, share-doesn't-equal-master regression
guard, dedup guard, cross-parameter guard, and combine-determinism
test. All 8 new threshold tests pass.
Also adds public accessors:
- fhe.Parameters.ParamsLWE/ParamsBR — expose underlying rlwe.Parameters
so out-of-tree threshold callers can drive lattice primitives
against the same parameter set the encryptor uses.
- fhe.BitCiphertext.Bits / NewBitCiphertextFromBits — iterate per-bit
for threshold decryption without round-tripping MarshalBinary.
References:
- Bendlin, Damgård. Threshold Decryption and Zero-Knowledge Proofs
for Lattice-Based Cryptosystems. TCC 2010.
- Asharov, Jain, López-Alt, Tromer, Vaikuntanathan, Wichs. Multiparty
Computation with Low Communication, Computation and Interaction
via Threshold FHE. EUROCRYPT 2012.
- Mouchet, Troncoso-Pastoriza, Bossuat, Hubaux. Multiparty
Homomorphic Encryption from Ring-Learning-with-Errors. PETS 2021.