Benchmark overview

Performance evaluation of PVAC-HFHE proof of concept against production FHE schemes

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:

Performance advantages

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

Deep circuit performance

At shallow depths (d=1, d=2), PVAC-HFHE maintains its performance advantage. However, the PoC exhibits exponential degradation at deeper circuit depths, while RLWE schemes maintain near-constant performance through modulus switching:

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

PVAC-HFHE ciphertext size exceeds BFV leveled at depth 4.

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

• Review the detailed comparisons for specific operation benchmarks
• Understand the testing methodology and how to reproduce results
• Explore the API reference to start implementing with PVAC-HFHE