  Privacy-preserving machine learning (PPML) aims at enabling machine learning
(ML) algorithms to be used on sensitive data. We contribute to this line of
research by proposing a framework that allows efficient and secure evaluation
of full-fledged state-of-the-art ML algorithms via secure multi-party
computation (MPC). This is in contrast to most prior works, which substitute ML
algorithms with approximated "MPC-friendly" variants. A drawback of the latter
approach is that fine-tuning of the combined ML and MPC algorithms is required,
which might lead to less efficient algorithms or inferior quality ML. This is
an issue for secure deep neural networks (DNN) training in particular, as this
involves arithmetic algorithms thought to be "MPC-unfriendly", namely, integer
division, exponentiation, inversion, and square root. In this work, we propose
secure and efficient protocols for the above seemingly MPC-unfriendly
computations. Our protocols are three-party protocols in the honest-majority
setting, and we propose both passively secure and actively secure with abort
variants. A notable feature of our protocols is that they simultaneously
provide high accuracy and efficiency. This framework enables us to efficiently
and securely compute modern ML algorithms such as Adam and the softmax function
"as is", without resorting to approximations. As a result, we obtain secure DNN
training that outperforms state-of-the-art three-party systems; our full
training is up to 6.7 times faster than just the online phase of the recently
proposed FALCON@PETS'21 on a standard benchmark network. We further perform
measurements on real-world DNNs, AlexNet and VGG16. The performance of our
framework is up to a factor of about 12-14 faster for AlexNet and 46-48 faster
for VGG16 to achieve an accuracy of 70% and 75%, respectively, when compared to
FALCON.
