Documentation Index
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This benchmark suite provides a comprehensive evaluation of PVAC-HFHE’s performance characteristics. The results compare our early proof of concept implementation against production-optimized FHE libraries from OpenFHE.
PVAC-HFHE is currently a research proof of concept without production optimizations. These benchmarks are provided for hypothesis testing, bounty programs, and academic evaluation.
Key findings
Even as an unoptimized proof of concept, PVAC-HFHE demonstrates significant performance advantages for scalar arithmetic operations:
| Metric | Improvement |
|---|
| Scalar multiplication vs BFV (shallow) | 2.9x faster |
| Scalar multiplication vs BFV (leveled) | 7.4x faster |
| Scalar multiplication vs CKKS | 14.3x faster |
| Scalar addition | 10-87x faster |
| Dot product | 7.5-7.8x faster |
| Ciphertext size (fresh) | 6-85x smaller |
Scalar operations
Multiplication (ct × ct):
- PVAC-HFHE: 2.47 ms
- BFV shallow: 7.23 ms (2.9x slower)
- BFV leveled: 18.28 ms (7.4x slower)
- BGV: 17.61 ms (7.1x slower)
- CKKS: 35.23 ms (14.3x slower)
Addition (ct + ct):
- PVAC-HFHE: 0.012 ms
- BFV: 0.124 ms (10x slower)
- BGV: 0.552 ms (46x slower)
- CKKS: 1.050 ms (87x slower)
Ciphertext size
Fresh ciphertext sizes demonstrate PVAC-HFHE’s efficiency:
| Scheme | Mode | Size | vs PVAC |
|---|
| PVAC-HFHE | scalar | 42 KB | 1.0x |
| BFV | shallow | 256 KB | 6x larger |
| BFV | leveled | 1024 KB | 24x larger |
| BGV | leveled | 1792 KB | 43x larger |
| CKKS | leveled | 3584 KB | 85x larger |
PVAC-HFHE works with arbitrary uint64 values, while BFV requires NTT-friendly primes (p-1 divisible by 2×ring_dim).
Proof of concept limitations
These limitations are specific to the current PoC implementation and are primarily due to unoptimized code paths and debugging systems.
| Metric | Limitation |
|---|
| Deep circuits (d ≥ 3) | 2-30x slower |
| Ciphertext growth | Exponential with depth |
| SIMD throughput | 146x slower |
| Key generation | 22x slower |
| Encryption | 8x slower |
| Depth | PVAC-HFHE | BFV | BGV | CKKS | Fastest |
|---|
| d1 | 2.68 ms | 19.54 ms | 17.40 ms | 35.85 ms | PVAC 7.3x |
| d2 | 10.34 ms | 14.38 ms | 15.11 ms | 31.22 ms | PVAC 1.4x |
| d3 | 31.46 ms | 13.98 ms | 14.39 ms | 30.71 ms | BFV 2.3x |
| d4 | 97.11 ms | 13.84 ms | 11.10 ms | 21.83 ms | BGV 8.7x |
| d5 | 285.83 ms | 11.37 ms | 9.50 ms | 18.93 ms | BGV 30x |
Ciphertext growth with depth
| Depth | Time | Size | Growth |
|---|
| d0 | - | 42 KB | 1.0x |
| d1 | 2.68 ms | 34 KB | 0.8x |
| d2 | 10.34 ms | 136 KB | 3.2x |
| d3 | 31.46 ms | 441 KB | 10.5x |
| d4 | 97.11 ms | 1359 KB | 32x |
| d5 | 285.83 ms | 4112 KB | 98x |
Comparison with bit-level FHE
For 64-bit integer operations, PVAC-HFHE demonstrates dramatic speedups compared to bit-level schemes:
TFHE-rs comparison
| Operation | PVAC-HFHE (PoC) | TFHE-rs CPU | TFHE-rs GPU | vs CPU | vs GPU |
|---|
| Addition | 0.012 ms | 109 ms | 8.97 ms | 9083x | 747x |
| Subtraction | 0.012 ms | 109 ms | 8.97 ms | 9083x | 747x |
| Multiplication | 2.47 ms | 402 ms | 31.9 ms | 163x | 13x |
While the comparison with bit-level FHE demonstrates significant performance differences, it’s important to note that these schemes solve different problems. Bit-level schemes excel at arbitrary boolean circuits, while PVAC-HFHE is optimized for scalar arithmetic.
Use case recommendations
Based on these benchmarks, PVAC-HFHE (even as a PoC) is well-suited for:
- Shallow computation circuits (depth 1-2)
- Scalar arithmetic operations on 64-bit integers
- Applications requiring small ciphertext sizes
- Dot products and vector operations
- Polynomial evaluation (degree ≤ 3)
For deep circuits (depth ≥ 3) or SIMD batch processing, production RLWE schemes currently offer better performance.
Next steps