Privacy-Preserving Distributed Machine Learning Made Faster

Abstract

With the development of machine learning, it is difficult for a single server to process all the data. So machine learning tasks need to be spread across multiple servers, turning the centralized machine learning into a distributed one. Multi-key homomorphic encryption is one of the suitable candidates to solve the problem. However, the most recent result of the Multi-key homomorphic encryption scheme (MKTFHE) only supports the NAND gate. Although it is Turing complete, it requires efficient encapsulation of the NAND gate to further support mathematical calculation. This paper designs and implements a series of operations on positive and negative integers accurately. First, we design basic bootstrapped gates, the efficiency of which is times that the number of using NAND to build. Second, we construct practical k-bit complement mathematical operators based on our basic binary bootstrapped gates. The constructed created can perform addition, subtraction, multiplication, and division on both positive and negative integers. Finally, we demonstrated the generality of the designed operators by achieving a distributed privacy-preserving machine learning algorithm, i.e. linear regression with two different solutions. Experiments show that the consumption time of the operators built with our gate is about 50 ∼ 70% shorter than built directly with NAND gate and the iteration time of linear regression with our gates is 66.7% shorter than with NAND gate directly.