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Manticore: A Framework for Efficient Multiparty Computation Supporting Real Number and Boolean Arithmetic

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Abstract

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).

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Notes

  1. https://github.com/KULeuven-COSIC/SCALE-MAMBA.

  2. http://www.humangenomeprivacy.org/2020/.

  3. A scheme is called t-out-of-n threshold secret sharing scheme if fulfil the requirements: any subset of t or more of the parties can reconstruct the secret, yet no subset of \(t-1\) fewer parties can learn anything about the secret.

  4. \(\mathcal {M}_{M,\ell }\) can be viewed as \(\sum _{i=\ell }^{M-1} m_i2^i \mod 2^{M}, \quad \text {for} \quad m_i \in \{0,1\}\).

  5. The choice of 58 above in order to resemble the plaintext of type \(\texttt {float64}\), whereby the mantissa is 53 bits.

  6. A set of vectors is orthonormal if every vector in the set has norm 1 and the set of vectors are mutually orthogonal.

  7. https://scikit-learn.org.

  8. https://github.com/data61/MP-SPDZ.

  9. This is done in two steps: (1) Player i locally computes \(\pi _i(a_i)\) and updates its share of y to \(\pi _i(a_i)\) minus its share of \(\pi _i(\lambda _i)\); (2) Everyone else updates its share of y to the negative of its share of \(\pi _i( \lambda _i )\).

  10. https://tls.mbed.org.

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Authors and Affiliations

  1. Inpher, Lausanne, Switzerland

    Mariya Georgieva Belorgey, Sergiu Carpov, Kevin Deforth, Dimitar Jetchev, Abson Sae-Tang & Marius Vuille

  2. SandboxAQ, Palo-Alto, USA

    Nicolas Gama

  3. University of Maryland, College Park, USA

    Jon Katz

  4. ZenGo, Tel Aviv, Switzerland

    Iraklis Leontiadis

  5. Microsoft, Redmond, USA

    Mohsen Mohammadi

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  1. Mariya Georgieva Belorgey
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  2. Sergiu Carpov
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Belorgey, M.G., Carpov, S., Deforth, K. et al. Manticore: A Framework for Efficient Multiparty Computation Supporting Real Number and Boolean Arithmetic. J Cryptol 36, 31 (2023). https://doi.org/10.1007/s00145-023-09464-4

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