H33 Consolidated Benchmark Reference
Reconciling measurements across Pure FHE, API Stack, and Full PQC contexts
February 14, 2026 | Corrected for NIST Compliance
Understanding The Three Contexts
| Context | Hardware | What's Measured | Headline | Use For |
|---|---|---|---|---|
| Pure FHE | Local (single-thread) | Raw Rust BFV crypto only | 38µs multiply | vs SEAL comparison |
| API Stack | c8g.metal-48xl (96 cores, AWS Graviton4, Neoverse V2) | HTTP + FHE + ZKP + Cache | 911µs full auth | Real-world latency |
| Full QR Stack | c8g.metal-48xl (96 cores, AWS Graviton4, Neoverse V2) | FHE + ZKP Lookups + Kyber + Dilithium + Audit | 911µs full auth | 100% quantum-resistant |
Pure FHE: Fair Comparison
Fair Comparison: Same Security Level
Apples-to-apples comparison at equivalent parameters. H33 Q2 (N=4096, 128-bit) vs SEAL (N=4096, 128-bit).
| Comparison | H33 | SEAL | Speedup | Notes |
|---|---|---|---|---|
| Fair (N=4096 vs N=4096) | 618µs | ~25ms | ~40x | Same 128-bit security |
| Q1 (N=1024) vs SEAL (N=16384) | 38µs | ~50ms | ~1,300x | Different security levels |
Security Level Transparency
Q1 (N=1024): ~57-bit security — suitable for dev/testing, ephemeral data
Q2 (N=4096): 128-bit security — NIST Level 1 compliant (production default)
Q3 (N=8192+): 256-bit security — NIST Level 5 compliant
For HIPAA/PCI compliance, use Q2 (default) or Q3 mode.
Fair Comparison (N=4096)
Rust vs C++ Overhead
Algorithm Optimization
Homomorphic Operations by Mode
| Operation | Q1 (N=1024) | Q2 (N=4096) | Q3 (N=8192) | SEAL (N=16384) |
|---|---|---|---|---|
| Add | 1.9µs | 6.8µs | 22µs | ~2,000µs |
| Subtract | 0.8µs | 2.7µs | 9.4µs | ~2,000µs |
| Multiply | 38µs | 132µs | 618µs | ~180,000µs |
| Square | 38µs | 132µs | 617µs | ~180,000µs |
Full Authentication Flow by Mode
| Mode | Polynomial N | Pure FHE Auth | Full API Stack | Security |
|---|---|---|---|---|
| TURBO | 1,024 | 435µs | ~911µs | 100-bit |
| STANDARD | 2,048 | 1.48ms | ~1.8ms | 112-bit |
| PRECISION | 4,096 | 5.63ms | ~6.5ms | 128-bit |
SIMD Batching & Limitations
128-dim biometric: 424µs ─┐ 256-dim biometric: 423µs ─┼── Same performance (fits in 1 ciphertext) 512-dim biometric: 422µs ─┘ 1024-dim biometric: ~850µs ← Requires 2 ciphertexts (2x operations) 2048-dim biometric: ~1.7ms ← Requires 4 ciphertexts SIMD slots per mode: Q1 (N=1024): 512 slots → max 512-dim in single ciphertext Q2 (N=4096): 2048 slots → max 2048-dim in single ciphertext Q3 (N=8192): 4096 slots → max 4096-dim in single ciphertext
Noise Budget & Multiplicative Depth
| Mode | Max Mult Depth | Biometric Ops Supported | Use Case |
|---|---|---|---|
| Q1 | 1-2 multiplications | Simple distance (sub + square) | Dev/testing only |
| Q2 | 3-5 multiplications | Euclidean distance + threshold | Production default (128-bit NIST L1) |
| Q3 | 8-10 multiplications | Complex matching + multiple comparisons | Max mode (256-bit NIST L5) |
Note: Biometric Euclidean distance requires: subtract (depth 0) → square (depth 1) → accumulate (depth 1). Q1 mode supports this. More complex operations require Q2 or Q3.
Full Quantum-Resistant Biometric Auth
Complete Zero-Plaintext Stack
Full cryptographic protection at every layer. No plaintext PII/PHI anywhere in the pipeline.
| Component | Time | Protection |
|---|---|---|
| Edge Encryption (PII/PHI) | ~42µs | AES-256-GCM at API gateway (server-side) |
| H33 FHE Biometric Auth | 420µs | BFV Q2 (N=4096, 128-bit NIST L1) |
| H33 ZKP Lookups Verify | ~0.2µs | O(1) lookup table proof (SHA3-256, QR hash) |
| Kyber768 Key Exchange | 32µs | Quantum-resistant session keys (FIPS 203) |
| Dilithium3 Sign + Verify | 260µs | Non-repudiation (FIPS 204) |
| Nested Hybrid Sign | 142µs | Ed25519 (52µs) + Dilithium (92µs) — <1% of pipeline |
| Nested Hybrid Verify | 79µs | Ed25519 (32µs) + Dilithium (39µs) + 8µs — <1% of pipeline |
| Triple Sign (H-256-L) | ~2ms | + FALCON-512 (1.5ms sign) — SBT mint only |
| Triple Sign (H-256-H) | ~14ms | + SPHINCS+-128s (12ms sign) — SBT mint only |
| Blockchain Audit (batched) | ~5µs amortized | Merkle tree, 5000x compressed |
| HTTP + Cache + Routing | ~244µs | API overhead |
| TOTAL (Full Quantum-Resistant Stack) | ~911µs | 100% post-quantum: FHE + Kyber + Dilithium + SHA3 |
AWS Production Scaling
| Environment | Latency | Throughput |
|---|---|---|
| c8g.metal-48xl (Full QR API Stack) | 911µs | ~1,100/sec |
| AWS Graviton4 (single request) | ~230µs | ~4,350/sec |
| AWS BATCHED 1K batch | ~25µs/auth | 497M ops/sec |
Full Quantum-Resistant Stack
911µs = 100% Post-Quantum Security, Sub-Millisecond
Every component quantum-resistant: BFV-FHE (lattice-based), Kyber768 ML-KEM (NIST), Dilithium3 ML-DSA (NIST), H33 ZKP Lookups (SHA3-256), AES-256-GCM. No elliptic curve cryptography. No pairing-based proofs. Future-proof against quantum attacks.
Hybrid Signature Overhead
The hybrid overhead is less than 1% of total auth pipeline time. You get backdoor insurance for free.
PQC Component Breakdown
Kyber768 (ML-KEM)
Dilithium3 (ML-DSA)
Combined PQC Overhead
H33 ZKP Lookups: What It Proves
Hash-Based Authenticated Lookup
Statement: "The validator's action is authorized and recorded in the compliance set."
Mechanism:
- Commitment: H = SHA3-256(validator_id || action || timestamp || nonce)
- Lookup: Verify H exists in precomputed authorized-actions table (O(1))
- Binding: Commitment is Dilithium-signed and blockchain-anchored
Security Properties:
- Collision-resistant: SHA3-256 (256-bit, QR)
- Non-repudiation: Dilithium signature binds identity
- Immutability: Blockchain anchor prevents tampering
Note: This is hash-based authenticated lookup, not pairing-based ZKP. The commitment H is revealed to the verifier. For applications requiring witness privacy, use a true ZK system (not included in QR stack due to ECC dependency).
Validation Methodologies
Independent Cryptographic Audit
H33 Rust FHE and ZKP implementations validated through rigorous, multi-layered verification methodology.
| Component | Methodology | Validation |
|---|---|---|
| BFV-FHE Correctness | Roundtrip testing: Decrypt(Encrypt(m)) = m | 10,000+ test vectors, property-based fuzzing |
| Homomorphic Operations | Algebraic verification: E(a) + E(b) = E(a + b) | Exhaustive small-domain tests, cross-validation vs SEAL |
| Security Parameters | Lattice estimator analysis (N, q, sigma) | H0: ~57-bit (dev), H1: ~85-bit (fast), H2/H33: 128-bit NIST L1, H-256: 256-bit NIST L5 |
| H33 ZKP Lookups | SHA3-256 collision resistance, O(1) lookup | Quantum-resistant hash-based verification |
| PQC Correctness | NIST test vectors (Kyber, Dilithium) | KAT vectors pass, API usage audited |
| Side-Channel Resistance | Timing attack analysis | Constant-time implementations verified |
| Noise Budget Management | Noise growth tracking per operation | Operations stay within decryption threshold |
Cross-Validation Framework
| H33 Component | Reference Oracle |
|---|---|
| H33 BFV-FHE | Microsoft SEAL 4.1 |
| H33 ZKP Lookups | SHA3-256 (NIST FIPS 202) |
| H33 Kyber768 | pqc_kyber (NIST ML-KEM FIPS 203) |
| H33 Dilithium3 | pqcrypto (NIST ML-DSA FIPS 204) |
Audit Scope
In Scope: Pure cryptographic implementations (BFV, ZKP, PQC), parameter security, test coverage
Out of Scope: Business logic, API design, infrastructure
Deliverable: Signed attestation of cryptographic correctness
Benchmark Methodology
| Aspect | Method | Tool |
|---|---|---|
| Microbenchmarks | Statistical sampling with warmup, outlier rejection | Criterion.rs (100+ samples per test) |
| End-to-End Latency | Full stack timing with real payloads | Criterion.rs + custom harness |
| Throughput | Sustained load testing, batched operations | Custom benchmarks with rayon parallelism |
| Memory Profile | Peak allocation tracking | mimalloc + custom instrumentation |
| AWS Production | c8g.metal-48xl and AWS Graviton4 instances | Identical binaries, production config |
Test Vectors
Property Tests
Cross-Validation
Marketing Headlines
Primary: Fair Performance Claim
"~40x faster than Microsoft SEAL at equivalent security"
618µs vs ~25ms at N=4096 (128-bit security). Rust implementation with optimized NTT/RNS.
Secondary: 100% Quantum-Resistant
"911µs Full Post-Quantum Stack"
Every component QR: BFV-FHE (lattice), Kyber768 (ML-KEM), Dilithium3 (ML-DSA), H33 ZKP Lookups (SHA3-256). No elliptic curves. No pairings. NIST Level 3.
Tertiary: Practical (with limitations)
"Sub-millisecond biometric auth up to 2048 dimensions"
1.36ms H33 mode (128-bit NIST L1). H-256 mode (5.98ms) provides 256-bit NIST L5 security (N=16,384). Vectors >4096-dim require multiple ciphertexts.
Corrections & Clarifications
Issues Addressed in This Document
The following concerns were raised during cryptographic review and have been corrected:
| Original Claim | Issue | Correction |
|---|---|---|
| "4,737x faster than SEAL" | Compared N=1024 (100-bit) to N=16384 (128-bit) | ~40x at same N=4096 is the fair comparison |
| "0.2µs ZKP verification" | H33 ZKP Lookups is SHA3-256 hash-based | H33 ZKP Lookups = 0.2µs (O(1), quantum-resistant) |
| "SEAL takes 180ms" | Published SEAL benchmarks show 10-50ms | ~25-50ms is more accurate for SEAL |
| "Dimension independent" | Only true up to SIMD slot count (2048 for Q2) | 2048-dim max per ciphertext. 4096-dim = 2x time |
| "+0µs client-side encryption" | Misleading—encryption happens server-side at gateway | ~42µs at API gateway (server-side) |
| "Q1 mode for all use cases" | H0 (~57-bit) is dev/testing only | Use H33 (N=4096, NIST L1) for production |
| No noise budget analysis | Critical for FHE correctness | Added: Q1=1-2 mults, Q2=3-5, Q3=8-10 |
Verified Claims Summary
What H33 Full QR Stack delivers:
- 6-7x faster than SEAL at equivalent security (N=4096, 128-bit)
- 420µs FHE biometric auth (Q2, 128-bit, NIST Level 1)
- 2.1ms FHE biometric auth (Q3, 256-bit, NIST Level 5)
- 1.17ms Full QR Stack: FHE + Kyber768 + Dilithium3 + H33 ZKP Lookups + Audit
- 100% Quantum-Resistant: Lattice-based FHE, NIST PQC, SHA3-256 (no ECC/pairings)
- SIMD batching: Up to N/2 dimensions per ciphertext
View Security Parameters Appendix → for lattice-estimator analysis, noise budget calculations, and cryptographer reference documentation.