  A privacy-preserving framework in which a computational resource provider
receives encrypted data from a client and returns prediction results without
decrypting the data, i.e., oblivious neural network or encrypted prediction,
has been studied in machine learning that provides prediction services. In this
work, we present MOBIUS (Model-Oblivious BInary neUral networkS), a new system
that combines Binarized Neural Networks (BNNs) and secure computation based on
secret sharing as tools for scalable and fast privacy-preserving machine
learning. BNNs improve computational performance by binarizing values in
training to $-1$ and $+1$, while secure computation based on secret sharing
provides fast and various computations under encrypted forms via modulo
operations with a short bit length. However, combining these tools is not
trivial because their operations have different algebraic structures and the
use of BNNs downgrades prediction accuracy in general. MOBIUS uses improved
procedures of BNNs and secure computation that have compatible algebraic
structures without downgrading prediction accuracy. We created an
implementation of MOBIUS in C++ using the ABY library (NDSS 2015). We then
conducted experiments using the MNIST dataset, and the results show that MOBIUS
can return a prediction within 0.76 seconds, which is six times faster than
SecureML (IEEE S\&P 2017). MOBIUS allows a client to request for encrypted
prediction and allows a trainer to obliviously publish an encrypted model to a
cloud provided by a computational resource provider, i.e., without revealing
the original model itself to the provider.
