  Secure multi-party computation enables multiple mutually distrusting parties
to perform computations on data without revealing the data itself, and has
become one of the core technologies behind privacy-preserving machine learning.
In this work, we present several improved privacy-preserving protocols for both
linear and non-linear layers in machine learning. For linear layers, we present
an extended beaver triple protocol for bilinear maps that significantly reduces
communication of convolution layer. For non-linear layers, we introduce novel
protocols for computing the sigmoid and softmax function. Both functions are
essential building blocks for machine learning training of classification
tasks. Our protocols are both more scalable and robust than prior
constructions, and improves runtime performance by 3-17x. Finally, we introduce
Morse-STF, an end-to-end privacy-preserving system for machine learning
training that leverages all these improved protocols. Our system achieves a
1.8x speedup on logistic regression and 3.9-4.9x speedup on convolutional
neural networks compared to prior state-of-the-art systems.
