School of Computer and Electronic Information, Guangxi University, Nanning, China.
PLoS One. 2022 Mar 18;17(3):e0265572. doi: 10.1371/journal.pone.0265572. eCollection 2022.
To solve the problems in the existing fully homomorphic encryption (FHE)-based secure multi-party computation (SMC) protocols such as low efficiency, the FHE scheme that supports multi-bit encryption was modified during the generation of the public key so that the users could generate their public keys independently without the common random string (CRS) matrix. Further, a multi-bit Gentry-Sahai-Waters scheme (MGSW) scheme without CRS was constructed. The modified LinkAlgo algorithm was adopted to expand the single-key ciphertext into the multi-key ciphertext and simplify the way of generating the expanded ciphertext. In this way, a multi-key FHE (MFHE) scheme was achieved based on the MGSW scheme. Finally, a three-round SMC protocol without CRS was constructed using the MFHE scheme and the decisional learning with errors (DLWE) assumption, which was secure in the semi-malicious model. Compared to the existing protocols, the protocol proposed herein can support multi-bit encryption and is found with smaller ciphertext size and lower storage overhead and generate the expanded ciphertext in a simpler way. Overall performance is better than existing protocols.
为了解决现有基于全同态加密（FHE）的安全多方计算（SMC）协议中存在的效率低等问题，在生成公钥时修改了支持多位加密的 FHE 方案，使得用户可以在没有公共随机字符串（CRS）矩阵的情况下独立生成其公钥。此外，构建了一个没有 CRS 的多比特 Gentry-Sahai-Waters 方案（MGSW）。采用修改后的 LinkAlgo 算法将单密钥密文扩展为多密钥密文，并简化了生成扩展密文的方式。这样，基于 MGSW 方案实现了多密钥 FHE（MFHE）方案。最后，使用 MFHE 方案和带误差的判定学习假设（DLWE）构建了一个无需 CRS 的三回合 SMC 协议，该协议在半恶意模型中是安全的。与现有协议相比，本文提出的协议可以支持多位加密，并且发现密文尺寸更小、存储开销更低，生成扩展密文的方式更简单。整体性能优于现有协议。
