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Approximate Arithmetic • Encrypted ML

Compute on Encrypted Floats.
ML Without Decryption.

CKKS approximate arithmetic over encrypted floating-point vectors. Dot products, similarity search, bootstrapping — all on data that never leaves ciphertext. N=8192 turbo mode with auto depth management.

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8,192
Poly Degree
4,096
Slots
50+
Scale Bits
128-bit
Security
Capabilities

Full Encrypted Arithmetic

Every operation runs entirely on ciphertext. The server never sees your data — not the inputs, not the intermediates, not the results.

Encrypted Addition
Add ciphertexts element-wise. Constant-time across all input sizes. Level-preserving — no depth consumed.
Level-Preserving
Encrypted Multiplication
Multiply with auto-rescale and relinearization. Consumes one multiplicative level per operation. Scale management is automatic.
Level-Consuming
Dot Product
Encrypted vector dot product — the key operation for ML inference. Multiply + rotate + sum in a single API call.
Level-Consuming
Rotation
Slot rotation for encrypted SIMD operations. Enables sum-reduction patterns, matrix transpositions, and data movement across encrypted slots.
SIMD Operation
Similarity Search
Normalized dot product in the encrypted domain. Cosine similarity without decryption — compare embeddings while they stay encrypted.
Level-Consuming
Bootstrapping
Level refresh via Chebyshev polynomial approximation. Enables unlimited computation depth — reset noise budget and keep computing.
Level Refresh
Architecture

Turbo → Standard Auto-Switch

CKKS turbo mode (N=8192) delivers fast operations for shallow circuits. When depth is exhausted, the bridge transparently transitions to standard parameters (N=16384) for deeper computation — zero application code changes.

Turbo Mode
N = 8,192
4,096 slots
4 mul levels
Scale: 240
Chain: [58, 40, 40, 40, 40]
→
Bridge
Auto-Switch
Transparent
parameter
transition
→
Standard Mode
N = 16,384
8,192 slots
9 mul levels
Scale: 240
Chain: [60, 40×9]
Fast Start
Most workloads fit in 4 multiplicative levels. Turbo mode runs them at maximum speed with smaller polynomials and lower memory overhead.
Seamless Bridge
When turbo levels run out, ckks_bridge.rs handles the parameter transition. Your application code stays identical.
Deep Compute
Standard mode provides 9 multiplicative levels. Bootstrapping available for circuits that need unlimited depth. Precision mode (N=32768) for extreme depth.
API

Three Tiers of Cryptographic Trust

Start with raw CKKS computation. Layer Dilithium signatures for post-quantum attestation. Add H33-3-Key for full triple-layer verification.

CKKS Endpoints

POST/v1/fhe/h33-ckks/keygen
POST/v1/fhe/h33-ckks/encrypt
POST/v1/fhe/h33-ckks/decrypt
POST/v1/fhe/h33-ckks/add
POST/v1/fhe/h33-ckks/multiply
POST/v1/fhe/h33-ckks/rotate
POST/v1/fhe/h33-ckks/inner-product
POST/v1/fhe/h33-ckks/similarity
POST/v1/fhe/h33-ckks/bootstrap
GET/v1/fhe/h33-ckks/health

Example Request

curl -X POST https://api.h33.ai/v1/fhe/h33-ckks/encrypt \
  -H "Authorization: Bearer $H33_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "public_key_id": "pk_ckks_...",
    "values": [0.123, -0.456, 0.789, 1.234],
    "mode": "turbo"
  }'

CKKS + Dilithium Endpoints

POST/v1/fhe/h33-ckks/keygen
POST/v1/fhe/h33-ckks/encrypt
POST/v1/fhe/h33-ckks/decrypt
POST/v1/fhe/h33-ckks/add
POST/v1/fhe/h33-ckks/multiply
POST/v1/fhe/h33-ckks/rotate
POST/v1/fhe/h33-ckks/inner-product
POST/v1/fhe/h33-ckks/similarity
POST/v1/fhe/h33-ckks/bootstrap
POST/v1/fhe/h33-ckks/dilithium/keygen
POST/v1/fhe/h33-ckks/dilithium/sign
POST/v1/fhe/h33-ckks/dilithium/verify
GET/v1/fhe/h33-ckks/health

Example Request

curl -X POST https://api.h33.ai/v1/fhe/h33-ckks/inner-product \
  -H "Authorization: Bearer $H33_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "ciphertext_a": "ct_ckks_...",
    "ciphertext_b": "ct_ckks_...",
    "dilithium_key_id": "dk_...",
    "sign_result": true
  }'
Dilithium tier: All compute endpoints (add, multiply, rotate, inner-product, similarity, bootstrap) include a dilithium_signature field in the response, attesting that the computation was performed correctly.

CKKS + H33-3-Key Endpoints

POST/v1/fhe/h33-ckks/keygen
POST/v1/fhe/h33-ckks/encrypt
POST/v1/fhe/h33-ckks/decrypt
POST/v1/fhe/h33-ckks/add
POST/v1/fhe/h33-ckks/multiply
POST/v1/fhe/h33-ckks/rotate
POST/v1/fhe/h33-ckks/inner-product
POST/v1/fhe/h33-ckks/similarity
POST/v1/fhe/h33-ckks/bootstrap
POST/v1/fhe/h33-ckks/dilithium/keygen
POST/v1/fhe/h33-ckks/dilithium/sign
POST/v1/fhe/h33-ckks/dilithium/verify
POST/v1/fhe/h33-ckks/3key/keygen
POST/v1/fhe/h33-ckks/3key/sign
POST/v1/fhe/h33-ckks/3key/verify
GET/v1/fhe/h33-ckks/health

Example Request

curl -X POST https://api.h33.ai/v1/fhe/h33-ckks/similarity \
  -H "Authorization: Bearer $H33_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "query_ct": "ct_ckks_...",
    "candidates": ["ct_ckks_...", "ct_ckks_..."],
    "three_key_id": "3k_...",
    "full_attestation": true
  }'
H33-3-Key tier: Every response includes a full 3-layer signature bundle — Dilithium (ML-DSA-65) attestation, SHA3-256 computation digest, and the H33 triple-key verification proof. Provides the highest level of cryptographic trust available.
Included with every API call
H33 Noise Pilot

CKKS Noise Management on Autopilot

CKKS is powerful but fragile — precision degrades with every multiplication. Noise Pilot manages rescaling, level tracking, and bootstrap scheduling automatically so your encrypted floats stay accurate.

Auto-Rescale
After every multiplication, Noise Pilot automatically rescales to maintain precision. No manual level management required.
Bootstrap Scheduling
Noise Pilot monitors remaining levels and triggers bootstrapping before depth exhaustion — enabling unlimited computation depth.
Turbo→Standard Switch
Starts with Turbo parameters for speed, seamlessly switches to Standard when deeper circuits are detected. Zero developer config.
Scale Precision Tracking
Tracks floating-point scale across operations. Warns before precision loss exceeds your tolerance threshold.
Use Cases

Built for Real-World Encrypted Computation

From healthcare to finance, CKKS enables computation on the most sensitive floating-point data without ever exposing it.

ML Inference
Run neural network layers on encrypted inputs. Dot products, activations, and weighted sums — all in ciphertext. The model never sees raw user data.
Encrypted Analytics
Aggregate statistics, compute means, variances, and correlations across encrypted datasets. Multi-party analytics without data sharing agreements.
Healthcare
Process patient vitals, lab results, and diagnostic scores without exposing PHI. HIPAA compliance built into the math — data is never decrypted on server.
Recommendations
Compute similarity scores between encrypted user preference vectors. Serve personalized recommendations without ever learning user preferences.
Financial Modeling
Risk scoring, portfolio optimization, and credit modeling on encrypted financial data. Regulatory compliance and trade secret protection in one API call.
Secure Search
Vector similarity search over encrypted embeddings. The search engine computes relevance scores without learning query content or document contents.

Start Building With H33-CKKS

Encrypted float arithmetic. ML inference on ciphertext. Post-quantum attestation. One API.

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🛡 FIPS 203/204 Compliant
🔐 128-bit NIST Level 1
☁ AWS Graviton4
✅ 1,743 Tests Passing
📜 108 Patent Claims
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