  Decentralized deep learning plays a key role in collaborative model training
due to its attractive properties, including tolerating high network latency and
less prone to single-point failures. Unfortunately, such a training mode is
more vulnerable to data privacy leaks compared to other distributed training
frameworks. Existing efforts exclusively use differential privacy as the
cornerstone to alleviate the data privacy threat. However, it is still not
clear whether differential privacy can provide a satisfactory utility-privacy
trade-off for model training, due to its inherent contradictions. To address
this problem, we propose D-MHE, the first secure and efficient decentralized
training framework with lossless precision. Inspired by the latest developments
in the homomorphic encryption technology, we design a multiparty version of
Brakerski-Fan-Vercauteren (BFV), one of the most advanced cryptosystems, and
use it to implement private gradient updates of users'local models. D-MHE can
reduce the communication complexity of general Secure Multiparty Computation
(MPC) tasks from quadratic to linear in the number of users, making it very
suitable and scalable for large-scale decentralized learning systems. Moreover,
D-MHE provides strict semantic security protection even if the majority of
users are dishonest with collusion. We conduct extensive experiments on MNIST
and CIFAR-10 datasets to demonstrate the superiority of D-MHE in terms of model
accuracy, computation and communication cost compared with existing schemes.
