We propose a novel framework, \(\texttt{Manticore}\), for multiparty computations, with full threshold and semi-honest security model, supporting a combination of real number arithmetic (arithmetic shares), Boolean arithmetic (Boolean shares) and garbled circuits (Yao shares). In contrast to prior work (Mohassel and Zhang, in 2017 IEEE symposium on security and privacy (SP), 2017; Mohassel and Rindal, in Proceedings of the 2018 ACM SIGSAC conference on computer and communications security, 2018), \(\texttt{Manticore}\) mitigates overflows, which is of paramount importance for machine learning applications, without compromising efficiency or security. Compared to other overflow-free recent techniques such as MP-SPDZ (Escudero et al., in 40th annual international cryptology conference, CRYPTO. Lecture notes in computer science, 2020) that convert arithmetic to Boolean shares, \(\texttt{Manticore}\) uses an efficient modular lifting/truncation method that allows for scalable high numerical precision computations with optimal numerical windows and hence, highly efficient online phases. We adapt basic MPC operations such as real-valued polynomial evaluation, division, logarithms, exponentials, Fourier series evaluations and oblivious comparisons to \(\texttt{Manticore}\) by employing our modular lift in combination with existing efficient conversions between arithmetic, Boolean and Yao shares. We also describe a highly scalable computations of logistic regression models with real-world training data sizes and high numerical precision through PCA and blockwise variants (for memory and runtime optimizations) based on second-order optimization techniques. On a dataset of 50 M samples and 50 features distributed among two players, the online phase completes in 14.5 h with at least 10 decimal digits of precision compared to plaintext training. The setup phase of \(\texttt{Manticore}\) is supported in both the trusted dealer and the interactive models allowing for tradeoffs between efficiency and stronger security. The highly efficient online phase makes the framework particularly suitable for MPC applications where the output of the setup phase is part of the input of the protocol (such as MPC-in-the-head or Prio).

我们提出了一种新颖的多方计算框架\(\texttt{Manticore}\)，具有全阈值和半诚实安全模型，支持实数算术（算术份额）、布尔算术（布尔份额）和乱码的组合电路（耀股份）。与之前的工作相比（Mohassel 和Zhang，2017 年 IEEE 安全与隐私 (SP) 研讨会，2017 年；Mohassel 和 Rindal，2018 年 ACM SIGSAC 计算机和通信安全会议记录，2018 年），\(\texttt { Manticore}\)可以减少溢出，这对于机器学习应用程序至关重要，而且不会影响效率或安全性。与其他无溢出的最新技术（例如MP-SPDZ）相比（Escudero 等人，第 40 届年度国际密码学会议，CRYPTO。计算机科学讲座笔记，2020）将算术转换为布尔共享，\(\texttt{ Manticore}\)使用高效的模块化提升/截断方法，允许具有最佳数值窗口的可扩展高精度计算，因此具有高效的在线阶段。我们采用基本的 MPC 运算，例如实值多项式求值、除法、对数、指数、傅立叶级数求值以及与\(\texttt{Manticore}\) 的不经意比较通过采用我们的模块化提升与算术、布尔和姚份额之间现有的高效转换相结合。我们还通过基于二阶优化技术的 PCA 和块式变体（用于内存和运行时优化）描述了具有真实训练数据大小和高数值精度的逻辑回归模型的高度可扩展计算。在分布在两个玩家之间的 50 M 样本和 50 个特征的数据集上，在线阶段在 14.5 小时内完成，与明文训练相比，精度至少为 10 位小数。\(\texttt{Manticore}\)的设置阶段受信任的经销商和交互式模型的支持，允许在效率和更强的安全性之间进行权衡。高效的在线阶段使该框架特别适合 MPC 应用程序，其中设置阶段的输出是协议输入的一部分（例如MPC-in-the-head或Prio）。