H33 vs Microsoft SEAL:
12.5× Faster, Full 7-Step Auth, One API Call

The headline number is 2.2× single-thread, 12.5× at production scale. Microsoft SEAL's BFV encrypt + compute + relin + decrypt cycle takes 2.85ms. H33's full 7-step auth pipeline runs in 1.28ms. That's the apples-to-apples single-thread comparison. At production scale with SIMD batching on 96 cores, H33 hits 1,148,018 auth/sec—12.5× the throughput of a SEAL-based pipeline on identical hardware.

H33's full CollectiveAuthority pipeline—which adds threshold decryption, zero-knowledge proofs, and post-quantum signatures on top of those FHE operations—finishes in 1.28ms. 2.2× faster than SEAL does FHE alone, while doing 3-5x more work. And with zero plaintext exposure.

What SEAL Actually Does

Microsoft SEAL is a research library. It implements the BFV and CKKS homomorphic encryption schemes. When you benchmark SEAL's full FHE cycle, here's what you're actually timing:

71% of SEAL's time is spent on multiply + relinearize. That's the entire scope: encrypt a plaintext, run a computation on the ciphertext, relinearize, decrypt the result. No proof that the computation was correct. No quantum-resistant signatures. No threshold decryption. No attestation chain. SEAL is a library. It does what libraries do: one thing, in isolation.

To ship a production authentication system, you need everything SEAL doesn't provide.

What H33 Does in 1.28ms

H33's CollectiveAuthority pipeline is a complete authentication system. Every operation below runs on every authentication. No shortcuts, no optional steps, no "add your own crypto."

Operations with a bronze left border are things SEAL doesn't do. That's three out of five operations—28% of the pipeline—that simply don't exist in SEAL. H33 completes all five in 1.28ms. SEAL takes 2.85ms for FHE alone—and exposes plaintext to the decrypting server.

The Apples-to-Apples FHE Comparison

Before we talk about the extra work H33 does, here's the direct comparison—the same FHE operations, measured on the same hardware:

H33's encrypt is faster (420µs vs 680µs) thanks to its single-modulus Q=56 bit design. Compute is where the gap is largest: SEAL needs 1,530µs for what H33 does in 260µs. That's a 5.9× difference on the most expensive operation.

The Full Pipeline: 3-5x More Work, Still 2.2× Faster

The 2.2× number is the honest single-thread comparison. But H33's full auth pipeline does 3-5x more work than SEAL—and still finishes faster. At production scale with 32-user SIMD batching across 96 cores, the gap becomes 12.5×:

SEAL FHE-only: 2.85ms ÷ H33 full pipeline: 1.28ms = 2.2× faster single-thread. 12.5× faster at production scale.

Why SEAL Can't Close the Gap

SEAL is a C++ library maintained by Microsoft Research. It's well-engineered. But it's designed for generality, not for authentication. Three structural differences explain the performance gap:

1. No Montgomery NTT

H33's BFV implementation uses Montgomery-form Number Theoretic Transforms. Twiddle factors are pre-stored in Montgomery form, eliminating all division from the hot path. The result: 44% faster NTT operations versus standard implementations. SEAL uses conventional modular arithmetic.

2. No Parallel Moduli Processing

H33 processes all RNS moduli concurrently via Rayon. Encryption processes every modulus in parallel. Multiplication gets a 1.8x speedup from parallel moduli. SEAL processes moduli sequentially.

3. No Pipeline Integration

This is the fundamental gap. Even if SEAL matched H33's raw FHE speed, you'd still need to bolt on threshold decryption, ZK proofs, post-quantum signatures, and attestation. Each integration point adds latency, memory copies, and serialization overhead. H33's pipeline is fused—data flows between stages without serialization boundaries.

What's Inside 1.28ms

Here's the full pipeline visualized by time allocation:

Every percentage point is doing real cryptographic work. There's no I/O wait, no network round-trip, no idle time. 1.28ms of pure computation spread across five operations.

The Security Gap

Speed aside, SEAL and H33 provide fundamentally different security guarantees:

SEAL gives you encrypted computation. H33 gives you encrypted computation plus proof it was done correctly, signed with a quantum-resistant signature, attested through a SHA3 chain, and decrypted without any single party ever holding the complete key.

Measured, Not Modeled

Both systems were benchmarked on identical hardware with equivalent security parameters (128-bit, N=2048). SEAL was compiled with all available optimizations. H33 used production configuration with no special tuning.

Throughput at Scale

Single-request latency tells part of the story. For production deployments, throughput matters:

1.2 million full cryptographic authentications per second on a single 96-core single-socket server. Each one doing seven operations. Each one quantum-safe.

The Bottom Line

There are three honest ways to frame this comparison:

The 2.2× single-thread number is the honest apples-to-apples comparison. The 12.5× is the production-scale number with SIMD batching. H33 does the entire 5-step pipeline — encrypt, FHE inner product, threshold decrypt, ZK proof, Dilithium batch attest — in 1.28ms. SEAL does FHE-only in 2.85ms. The 104-468× DIY number is what matters if you're trying to ship.