基于NTRU自同构生成元的全同态加密算法设计技术资料及实验代码

自举的低效率是阻碍全同态加密（FHE）实际应用的主要瓶颈。使用硬件加速改进自举性能的主要障碍之一是自举密钥的巨大存储开销。对于128位安全参数，现有技术需要约为70MB（包括60MB用于密钥交换密钥和约10MB用于盲旋转密钥）。项目提出了一种新的密文自举算法，重构了类TFHE自举算法的核心流程，并通过优化密钥交换机制，将密钥交换密钥的存储需求从原来的基于格维度的平方数量级大幅降低至线性数量级；同时创新性地采用单生成元实现自同构计算，将盲旋转密钥规模进一步压缩，实现了密钥大小减少30倍和速度提升1.2倍。该数据集基于国际主流的OpenFHE开源代码库，对项目提出的上述优化算法和优化技术进行了代码实现，实验结果符合理论研究结果，有力支撑了项目任务一研究指标的完成。

The inefficiency of bootstrapping is a major bottleneck hindering the practical application of Fully Homomorphic Encryption (FHE). One of the main obstacles to improving bootstrapping performance using hardware acceleration is the enormous storage overhead of bootstrapping keys. For a 128-bit security parameter, existing technologies require approximately 70MB (including 60MB for key switching keys and about 10MB for blind rotation keys). The project proposes a new ciphertext bootstrapping algorithm, which reconstructs the core process of TFHE-like bootstrapping algorithms and optimizes the key switching mechanism, significantly reducing the storage requirement of key switching keys from the original lattice dimension-based quadratic order of magnitude to linear order of magnitude; meanwhile, it innovatively uses a single generator to implement automorphism computation, further compressing the size of blind rotation keys, resulting in a 30-fold reduction in key size and a 1.2-fold speed improvement. This dataset is based on the internationally mainstream OpenFHE open-source codebase, implements the above-mentioned optimization algorithms and techniques proposed by the project in code, and the experimental results are consistent with theoretical research results, strongly supporting the achievement of the research indicators of Project Task 1.