Paper 2023/1912

Dishonest Majority Multiparty Computation over Matrix Rings

Abstract

The privacy-preserving machine learning (PPML) has gained growing importance over the last few years. One of the biggest challenges is to improve the efficiency of PPML so that the communication and computation costs of PPML are affordable for large machine learning models such as deep learning. As we know, linear algebra such as matrix multiplication occupies a significant part of the computation in the deep learning such as deep convolutional neural networks (CNN). Thus, it is desirable to propose the MPC protocol specialized for the matrix operations. In this work, we propose a dishonest majority MPC protocol over matrix rings which supports matrix multiplication and addition. Our MPC protocol can be seen as a variant of SPDZ protocol, i.e., the MAC and global key of our protocol are vectors of length $m$ and the secret of our protocol is an $m\times m$ matrix. Compared to the classic SPDZ protocol, our MPC protocol reduces the communication complexity by at least $m$ times. We also show that our MPC protocol is as efficient as [11] which also presented a dishonest majority MPC protocol specialized for matrix operations. The MPC protocol [11] resorts to the homomorphic encryption scheme (BFV scheme) to produce the matrix triples in the preprocessing phase. This implies that their protocol only supports the matrix operations over integer rings or prime fields of large size. On the contrary, we resort to vector oblivious linear evaluations and random vector oblivious linear evaluations to generate correlated randomness in the preprocessing phase. Thus, the matrices of our MPC protocol can be defined over any finite field or integer ring. Due to the small size of our MAC, the communication complexity of our MPC protocol remains almost the same regardless of the size of the field or the ring.