H33 Consolidated Benchmark Reference
Reconciling measurements across Pure FHE, API Stack, and Full PQC contexts
February 14, 2026 | Corrected for NIST Compliance
What this reference measures — and what it does not
Every figure here is a timing of the H33 FHE Platform (and the surrounding PQC stack): the mechanism that computes on encrypted data without decrypting it. This page reconciles those timings across three measurement contexts and pins each to its hardware (see the Hardware column below). The numbers show how fast the encrypted computation runs; they do not by themselves establish a security level — the “128-bit” and “256-bit NIST L5” labels are the scheme parameters chosen, not results of these benchmarks — and a fast benchmark is not by itself a certification of compliance. Performance is not security, and neither is 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) | ~50µs | 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"
1.28ms 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 | ~50µs 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.