This paper presents a comprehensive investigation into encrypted computations using the CKKS (Cheon-Kim-Kim-Song) scheme, with a focus on multi-dimensional vector operations and real-world applications. Through two meticulously designed experiments, the study explores the potential of the CKKS scheme in Super Computing and its implications for data privacy and computational efficiency. The first experiment reveals the promising applicability of CKKS to matrix multiplication, indicating marginal differences in Euclidean distance and near-to-zero mean square error across various matrix sizes. The second experiment, applied to a wildfire dataset, illustrates the feasibility of using encrypted machine learning models without significant loss in accuracy. The insights gleaned from the research set a robust foundation for future innovations, including the potential for GPU acceleration in CKKS computations within TenSEAL. Challenges such as noise budget computation, accuracy loss in multiplication, and the distinct characteristics of arithmetic operations in the context of CKKS are also discussed. The paper serves as a vital step towards understanding the complexities and potentials of encrypted computations, with broad implications for secure data processing and privacy preservation in various scientific domains.

翻译：本文系统研究了基于CKKS（Cheon-Kim-Kim-Song）方案的加密计算，重点关注多维向量运算及其实际应用。通过两项精心设计的实验，本研究探索了CKKS方案在超级计算中的潜力，及其对数据隐私与计算效率的影响。第一项实验揭示了CKKS在矩阵乘法中的良好适用性，表明在不同矩阵规模下欧氏距离差异极小且均方误差趋近于零。第二项实验针对野火数据集，验证了使用加密机器学习模型时精度无明显损失的可行性。研究所得结论为未来创新奠定了坚实基础，包括在TenSEAL中利用GPU加速CKKS计算的潜力。此外，本文还讨论了噪声预算计算、乘法精度损失及CKKS背景下算术运算的独特特性等挑战。该研究是理解加密计算复杂性与潜力的重要一步，对各类科学领域中的安全数据处理与隐私保护具有广泛意义。