弥合PHE与FHE之间的差距：半同态BGN密码系统的性能与权衡分析
Bridging the Gap Between PHE and FHE: A Performance and Trade-off Analysis of The Somewhat Homomorphic BGN Cryptosystem
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中文总结 AI 辅助
本文将半同态BGN密码系统集成到lightphe框架，对比PHE与FHE开展基准测试，揭示其计算与通信的权衡特性，确立其为带宽受限去中心化架构的实用隐私保护加密引擎。
中文摘要 AI 辅助
同态加密（HE）支持隐私保护数据分析，但从业者常需在轻量级部分同态加密（PHE）与计算开销较大的全同态加密（FHE）间做权衡。Boneh-Goh-Nissim（BGN）密码系统作为半同态加密（SWHE）方案可弥合这一差距，支持无限次加法和一次密文乘法。尽管其代数结构简洁，BGN的实际应用因缺乏易用软件实现而受阻。本文通过将BGN集成到lightphe Python框架，对其与PHE和FHE范式开展对比分析，仅需几行代码即可部署。我们在80位、112位和128位安全等级下，针对Paillier、Damgard-Jurik、Okamoto-Uchiyama等PHE方案，以及基于TenSEAL的FHE CKKS方案，对加密128维向量运算进行基准测试。结果显示存在计算-通信权衡：BGN因双线性配对，计算速度慢于PHE和SIMD优化的FHE，但公钥尺寸仅3-6 KB，比FHE小五个数量级。关键在于，BGN在一次乘法后可支持无限同态聚合，能实现线性回归推理、余弦相似度、平方欧氏距离等复杂任务。此外，2位优化精度即可匹配明文排名基线，克服目标群离散对数解密瓶颈。通过在lightphe中开源该流程，本研究确立BGN为带宽受限、去中心化架构的实用引擎。
英文摘要
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.
