Solutions · Fully Homomorphic Encryption

NTT primes for SEAL, OpenFHE, Zama in a single API call.

FHE schemes need chains of NTT-compatible primes with specific arithmetic form. Ethoryx generates full coefficient modulus chains in milliseconds, with every prime guaranteed to satisfy q ≡ 1 (mod 2n) for any polynomial degree. Drop-in compatible with CoeffModulus::Create and equivalent interfaces across all major FHE libraries.

NTT candidate reduction
75%
q ≡ 1 (mod 2n) form · measured
FHE chain (n=4096)
~9ms
5-prime 55-bit modulus chain
Compatibility
SEAL · OpenFHE
CoeffModulus::Create drop-in
Polynomial degrees
1024–16384
all standard SEAL configurations
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Full coefficient modulus chains

FHE schemes require not one prime but a chain of NTT-compatible primes that define the RNS (Residue Number System) decomposition. Ethoryx generates the full chain in a single API call, with every prime satisfying both the NTT constraint and the scheme's bit-size specification.

Drop-in for SEAL and OpenFHE

The generated chains plug directly into Microsoft SEAL's CoeffModulus::Create() and OpenFHE's equivalent constructors. Zama's Concrete/TFHE-rs toolchain is also compatible through standard NTT parameter interfaces.

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Machine-learning-ready bit sizes

We offer 50-62 bit primes for FHE-friendly NTT configurations; the exact range required for CKKS, BGV, and BFV schemes. Chain depths from 3 to 20 primes, suitable for inference-only through deep-circuit FHE machine learning.

SEAL integration in 3 lines

Fetch an FHE coefficient modulus chain from the Ethoryx API, pass it straight to SEAL. No custom parameter-generation code needed.

# 1. Fetch a 5-prime chain for polynomial degree n=4096, 55 bits each
curl "https://api.ethoryx.io/v1/generate/fhe?n=4096&count=5&bits_each=55" \
     -H "X-API-Key: YOUR_KEY"

# 2. Response (abbreviated)
{
  "poly_degree_n": 4096,
  "primes": [
    "36028797018963791",
    "36028797018963977",
    "36028797018964181",
    "36028797018964397",
    "36028797018964571"
  ],
  "ntt_compatible": true,
  "seal_compatible": true,
  "usage_example": "seal::CoeffModulus::Create(4096, {55, 55, 55, 55, 55})"
}

// 3. Pass directly to SEAL
using namespace seal;
EncryptionParameters parms(scheme_type::ckks);
parms.set_poly_modulus_degree(4096);
parms.set_coeff_modulus(CoeffModulus::Create(4096, {55,55,55,55,55}));
SEALContext context(parms);
// Or build from the exact primes returned above for bit-exact reproducibility

FHE applications

Private machine learning inference

Serve ML predictions over encrypted inputs without seeing the data. Ethoryx FHE chains are suitable for CKKS-based inference on encrypted patient records, encrypted financial data, and encrypted user queries. Used at polynomial degrees n=8192 and n=16384.

Private set intersection

Two parties compute the intersection of their data sets without either revealing their full set. Applicable to contact discovery (WhatsApp-style), fraud detection across banks, and genomic overlap analysis. Uses BFV-style schemes with 3-7 prime chains.

Private database queries

Query a database without revealing the query. CKKS and BGV both support range queries and dot-product queries over encrypted data. Used by Zama, Duality Technologies, and Inpher in production systems.

Secure multiparty computation

FHE primitives underlie many SMPC protocols. Generating the shared public parameters (coefficient moduli) correctly and reproducibly is essential and deterministic-start Ethoryx output makes cross-party verification straightforward.

Scheme compatibility

SEALMicrosoft · C++
OpenFHEDuality · C++
ConcreteZama · Rust/Python
HEAANSeoul Nat'l Univ

Supported FHE parameters

Polynomial degreeStandard schemesTypical chain depthUse case
n = 1024BFV / BGV2–3 primesSimple boolean circuits
n = 2048BFV / BGV / CKKS3–5 primesSmall arithmetic circuits
n = 4096CKKS / BFV / BGV5–8 primesML inference · PSI
n = 8192CKKS8–14 primesDeep ML · large-dim PSI
n = 16384CKKS14–20 primesTraining · deep networks

Build private FHE applications

Start generating FHE chains today. Free tier includes 100 calls per month. Starter ($29/mo) unlocks full FHE chain generation up to 7 primes.