  In this work, we propose an outsourced Secure Multilayer Perceptron (SMLP)
scheme where privacy and confidentiality of both the data and the model are
ensured during the training and the classification phases. More clearly, this
SMLP : i) can be trained by a cloud server based on data previously outsourced
by a user in an homomorphically encrypted form; ii) its parameters are
homomorphically encrypted giving thus no clues to the cloud; and iii) it can
also be used for classifying new encrypted data sent by the user returning him
the encrypted classification result encrypted. The originality of this scheme
is threefold. To the best of our knowledge, it is the first multilayer
perceptron (MLP) secured in its training phase over homomorphically encrypted
data with no problem of convergence. And It does not require
extra-communications between the server and the user. It is based on the
Rectified Linear Unit (ReLU) activation function that we secure with no
approximation contrarily to actual SMLP solutions. To do so, we take advantage
of two semi-honest non-colluding servers. Experimental results carried out on a
binary database encrypted with the Paillier cryptosystem demonstrate the
overall performance of our scheme and its convergence.
