Bridging the Gap Between PHE and FHE: A Performance and Trade-off Analysis of The Somewhat Homomorphic BGN Cryptosystem

arXiv:2607.28700 · cs.CR · Submitted 2026-07-30 · Read on arXiv

Sefik Serengil, Alper Ozpinar

cs.CR

Submitted: 2026-07-30

Code: https://github.com/serengil/LightPHE

License: http://creativecommons.org/licenses/by/4.0/

The gist: Homomorphic encryption (HE) enables privacy-preserving data analytics, but practitioners often face a trade-off between lightweight Partially Homomorphic Encryption (PHE) and computationally dominant

Terminology

Homomorphic Encryption — 35× in this paper
Benchmark — 11× in this paper · explained in 2 episodes
Cosine Similarity — 10× in this paper · explained in 3 episodes
Fully Homomorphic Encryption — 8× in this paper
Embeddings — 6× in this paper · explained in 2 episodes
Partially Homomorphic Encryption — 5× in this paper
Communication Overhead — 4× in this paper · explained in 2 episodes
Computational overhead — 4× in this paper · explained in 2 episodes
Discrete Logarithm Problem — 4× in this paper
Aggregation — 3× in this paper · explained in 1 episode
Core — 3× in this paper · explained in 2 episodes
Federated Learning — 3× in this paper · explained in 14 episodes
Fully Homomorphic Encryption (FHE) — 3× in this paper · explained in 5 episodes
Privacy-Preserving Machine Learning — 3× in this paper
Accuracy — 2× in this paper · explained in 1 episode
Benchmarking — 2× in this paper · explained in 3 episodes
Clustering — 2× in this paper · explained in 2 episodes
Elliptic Curve Cryptography — 2× in this paper
Federated Learning (FL) — 2× in this paper · explained in 7 episodes
Fidelity — 2× in this paper · explained in 2 episodes
Large Language Model — 2× in this paper
RAG — 2× in this paper · explained in 3 episodes
Retrieval-Augmented Generation — 2× in this paper
Retrieval-Augmented Generation (RAG) — 2× in this paper · explained in 16 episodes
Verification — 2× in this paper · explained in 2 episodes
Adam — 1× in this paper · explained in 2 episodes
Adaptability — 1× in this paper · explained in 1 episode
Alignment — 1× in this paper · explained in 1 episode
Consistency — 1× in this paper · explained in 3 episodes
Edge Devices — 1× in this paper · explained in 2 episodes
Generalization — 1× in this paper · explained in 13 episodes
Internet of Things — 1× in this paper
Large Language Model (LLM) — 1× in this paper · explained in 3 episodes
Large Language Models (LLMs) — 1× in this paper · explained in 6 episodes
Mobile Edge Computing — 1× in this paper · explained in 2 episodes
Post-Quantum Cryptography — 1× in this paper
Quantization — 1× in this paper · explained in 12 episodes

Abstract

Homomorphic encryption (HE) enables privacy-preserving data analytics, but practitioners often face a trade-off between lightweight Partially Homomorphic Encryption (PHE) and computationally dominant Fully Homomorphic Encryption (FHE). The Boneh-Goh-Nissim (BGN) cryptosystem bridges this gap as a Somewhat Homomorphic Encryption (SWHE) scheme supporting unlimited additions and one ciphertext multiplication. Despite its algebraic elegance, practical BGN adoption has been hindered by a lack of accessible software implementations. This paper presents a comparative analysis of BGN against PHE and FHE paradigms through its integration into the lightphe Python framework, allowing deployment in just a few lines of code. We benchmark encrypted 128-dimensional vector operations under 80-bit, 112-bit and 128-bit security levels against Paillier, Damgard-Jurik, Okamoto-Uchiyama, and the FHE CKKS scheme via TenSEAL. Results reveal a computation-communication trade-off: BGN is computationally slower due to bilinear pairings compared to PHE and SIMD-optimized FHE, but retains a microscopic public key size of 3-6 KB, up to five orders of magnitude smaller than FHE. Crucially, BGN enables boundless homomorphic aggregation after a single multiplication, supporting complex tasks such as linear regression inference, Cosine Similarity, and Squared Euclidean Distance. Furthermore, an optimized precision of 2 digits suffices to match plaintext ranking baselines, overcoming the target-group discrete logarithm decryption bottleneck. By open-sourcing this pipeline in lightphe, this work establishes BGN as a practical engine for bandwidth-constrained, decentralized architectures.

Bridging the Gap Between PHE and FHE: A Performance and Trade-off Analysis of The Somewhat Homomorphic BGN Cryptosystem

Terminology

Abstract

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