Appendix

This appendix contains supplementary material, including detailed performance benchmarks and instructions for citing the HEonGPU library in academic work.

Performance Benchmarks

All benchmarks listed below were performed on an NVIDIA RTX 4090 GPU and are sourced from the project’s main repository. Performance is highly dependent on the chosen parameters and hardware configuration.

TFHE Unsigned Integer Arithmetic

This table compares the latency (in milliseconds) of homomorphic unsigned integer addition between HEonGPU, TFHE-rs, and results from recent academic literature.

TFHE Unsigned Integer Arithmetic Latency (ms)

Library	uint8	uint16	uint32	uint64	uint128	uint256
TFHE-rs	31.53	31.54	31.55	32.03	33.74	58.32
Literature	18.63	18.61	18.87	24.23	29.97	58.30
HEonGPU	12.72	12.75	13.60	15.88	23.10	38.24

CKKS Bootstrapping

This table details the execution times for various CKKS bootstrapping operations implemented in HEonGPU.

• LKM (Less Key Mode): An optimization that reduces the number of required Galois keys by 30% at the cost of a 15-20% performance decrease. This is useful when GPU memory is a constraint.

• Amortized Time: The total execution time divided by the number of slots, providing a per-slot performance metric.

CKKS Bootstrapping Performance

Bootstrapping Type	\(N\)	Slot Count	LKM	Remaining Level	Total Time	Amortized Time
Slim	\(2^{16}\)	\(2^{15}\)	ON	4	164.20 ms	5.01 µs
Bit	\(2^{15}\)	\(2^{14}\)	OFF	6	55.66 ms	3.40 µs
Bit	\(2^{16}\)	\(2^{15}\)	OFF	4	115.88 ms	3.53 µs
Gate*	\(2^{15}\)	\(2^{14}\)	OFF	0	27.03 ms	1.64 µs
Gate*	\(2^{16}\)	\(2^{15}\)	OFF	0	70.73 ms	2.16 µs

*For all logic gates.

How to Cite HEonGPU

Please use the following BibTeX entries to cite HEonGPU and its associated research in academic papers.

Main Library Paper

@misc{cryptoeprint:2024/1543,
      author = {Ali Şah Özcan and Erkay Savaş},
      title = {{HEonGPU}: a {GPU}-based Fully Homomorphic Encryption Library 1.0},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1543},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1543}
}

Key-Switching Optimizations Paper

@misc{cryptoeprint:2025/124,
      author = {Ali Şah Özcan and Erkay Savaş},
      title = {{GPU} Implementations of Three Different Key-Switching Methods for Homomorphic Encryption Schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/124},
      year = {2025},
      url = {https://eprint.iacr.org/2025/124}
}