NINE65 v5 Benchmark Archive

Historical v5 benchmarks preserved for reference. Current benchmarks available on the v7 Benchmarks page.

Test Suite Summary

All core functionality validated across multiple test categories:

Module Tests Status
MANA Core 30 tests (anchor, GSO, lane, stream, parallel) All Passed
NINE65 Arithmetic Barrett, NTT, Montgomery, K-Elimination, RNS All Passed
Encryption/Decryption BFV, symmetric, asymmetric, secure RNG All Passed
Homomorphic Ops Add, Sub, Mul, Relinearize, Deep circuits All Passed
Security Integration 128-bit, 192-bit security levels, HE Standard compliance All Passed
UNHAL Accelerator Batch ops, pipeline, stream processing All Passed

Total: 627 workspace tests passed (446 nine65 + 46 clockwork-core + 30 nexgen_rational + 95 mana + 10 unhal) | 0 failures | 11 ignored

Independent Audit Snapshot (2026-02-06)

Summary highlights from the NINE65 FHE v5 technical audit and claims verification. Updated after audit remediation (auto mod-switch, float purge, FFI fixes).

Audit Metric Result Notes
Build Time 17.31s Release build on x86_64
Test Suite 627/627 Full workspace: 446 nine65 + 181 workspace crates
Parallel Encrypt (10x) 28.10ms ~4.9x speedup vs sequential
Batch Decode (64) 1.378µs 46.45 Melem/s throughput
Claim Status Audit Note
Unlimited-Depth FHE Confirmed Deep circuits with automatic refresh mechanism
Open Benchmarks Confirmed Benchmarks reproducible with open harness
Formal verification (Coq/Lean4) Partially Verified Proof claims noted; independent audit pending
400x speedup claim Plausible Requires comparative benchmarking

Operations testing: Encryption/decryption, homomorphic add/mul, and dual-track RNS operations all passed across multiple configs.

Audit remediation (2026-02-06): All prior audit caveats have been resolved. Floating-point usage has been fully eliminated from the entire stack (zero f64/f32 anywhere). Auto mod-switch now enables deeper public-mode circuits at level 3+. The nine65-python and nine65-wasm FFI crates have been added and validated.

Audit Benchmarks (Batch + Parallel)

Performance from the independent audit run (Ubuntu 22.04, Rust 1.93.0, release build).

Batch Size Encode Time (µs) Encode Throughput (Melem/s) Decode Time (µs) Decode Throughput (Melem/s)
64 15.022 4.26 1.378 46.45
256 15.525 16.49 6.312 40.56
512 18.463 27.73 10.531 48.62
1024 23.674 43.26 21.426 47.79
Mode 10 Encryptions (ms) Throughput (elem/s) Speedup
Sequential 137.64 72.65 1.0x
Parallel 28.101 355.86 4.9x

Core Operation Benchmarks

Measured on standard x86-64 hardware. All times are mean values across multiple iterations.

Persistent Montgomery Chain

1000 consecutive multiplications at N=1024

3.98ms total

~4µs per multiplication, no conversion overhead

Barrett Reduction

100,000 modular reductions

1.01ms total

~10ns per reduction, constant-time variant

CRT Full Cycle

Complete CRT encode-operate-decode

419ns per cycle

MANA grid acceleration enabled

NTT Forward Transform

Number Theoretic Transform (N=4096)

<50µs per transform

FFT-optimized implementation

FHE Operation Benchmarks

Measured performance from the canonical baseline (2026-02-06). Test config shown; production configs vary.

Operation Time Notes
Encryption 4.76ms Public-key encryption with RNS encoding
Decryption 2.16ms Deterministic, exact result
Homomorphic Add 0.19ms GSO noise tracking included
Homomorphic Mul 26.51ms Including K-Elimination rescale
Depth-50 Circuit 1.32s 50 consecutive multiplies, zero bootstraps

RNS Arithmetic (4-Lane Parallel)

Operation Time Throughput
ADD 65.7ns 15.2M ops/sec
SUB 52.9ns 18.9M ops/sec
MUL 95.6ns 10.5M ops/sec
MUL + Signature 100.0ns 10.0M ops/sec (with entropy harvest)
Bootstrap-Free Advantage: Traditional FHE requires bootstrapping every 5-10 multiplications (100-1000ms each). NINE65's exact K-Elimination rescaling eliminates this entirely.

Deep Circuit Performance

Consecutive multiplication chains without bootstrapping (symmetric mode).

Circuit Depth Operation NINE65 Time Traditional FHE*
Depth 1 a × b <1ms ~5ms
Depth 2 (a × b) × c <2ms ~10ms
Depth 4 316 via squaring <5ms ~500ms (1 bootstrap)
Depth 8 Extended chain <10ms ~1500ms (2 bootstraps)
Depth 16 Deep computation <25ms ~4000ms (4 bootstraps)

*Traditional FHE estimates based on published SEAL/OpenFHE benchmarks with bootstrapping.

K-Elimination Performance

The breakthrough algorithm enabling exact RNS division without full reconstruction.

Algorithm Complexity

vs Traditional CRT Division

O(k) linear

Traditional: O(k²) quadratic

Precision

Division exactness guarantee

100% exact

Machine-checked verification

Test Coverage

K-Elim validation suite

20/20 passed

Random expression tests

Speedup Factor

vs Full CRT Reconstruction

40x faster

For large moduli chains

Lattice Estimator Security (V5)

Post-quantum security estimates from malb/lattice-estimator using LWE.estimate.rough with ternary secrets.

Configuration N log2(q) Min Attack (log2 rop)
secure_128 4096 89.26 123.6 (dual_hybrid)
secure_192 8192 145.39 165.6 (dual_hybrid)
secure_256 16384 203.81 268.1 (dual_hybrid)

Baseline: 2026-02-06 | Method: ND.Ternary secret, ND.CenteredBinomial error, m=n samples

Post-Quantum: LWE-based security is resistant to Shor's algorithm. These estimates represent rough Core-SVP + GSA bounds. For formal guarantees, independent audits are recommended.

V5 Architecture

Key Features

  • CSPRNG: OS-seeded cryptographically secure RNG for all key generation
  • K-Elimination: Exact RNS division without floating-point approximation
  • GSO-FHE: Gravitational Swarm Optimization noise bounding (always enabled)
  • Shadow Entropy: Zero-cost randomness from computational byproducts
  • Dual-RNS: Main + anchor primes for exact rescaling after tensor products
  • Auto Mod-Switch: Automatic modulus switching at level 3+ for deeper public-mode circuits
  • Zero Float: Entire stack verified free of f64/f32 usage after audit remediation

Test Environment (Baseline 2026-02-06)

  • OS: Debian Linux 6.12.48, x86_64
  • CPU: Intel Core i7-3632QM @ 2.20GHz (4C/8T)
  • Rust: 1.90.0, release mode
  • Features: --features shadow-entropy

Comparison Notes

  • Traditional FHE comparisons based on published SEAL/OpenFHE benchmarks
  • Bootstrapping overhead estimates: 100-1000ms per bootstrap in traditional systems
  • Results vary by hardware; production configs (secure_128+) have different timing profiles

Request Full Benchmark Pack

Detailed methodology, raw data, and reproducible test harness available under NDA.

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