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

• URL: http://arxiv.org/abs/2607.28700v1
• Date: Thu, 30 Jul 2026 12:33:25 GMT
• Title: Bridging the Gap Between PHE and FHE: A Performance and Trade-off Analysis of The Somewhat Homomorphic BGN Cryptosystem
• Abstract summary: 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)<n>The Boneh-Goh-Nissim (BGN) cryptosystem bridges this gap as a Somewhat Homomorphic Encryption (SWHE) scheme supporting unlimited additions and one ciphertext multiplication.<n>This paper presents a comparative analysis of BGN against PHE and FHE paradigms through its integration into the lightphe Python framework.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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