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In this work, we propose an outsourced Secure Multilayer Perceptron (SMLP) scheme where privacy and confidentiality of the data and the model are ensured during its 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; its parameters are homomorphically encrypted giving thus no clues about them to the cloud; and (ii) can also be used for classifying new encrypted data sent by the user while returning him the encrypted classification result. The originality of this scheme is threefold: To the best of our knowledge, it is the first multilayer perceptron (MLP) secured homomorphically in its training phase with no problem of convergence. It does not require extra-communications with the user. And, 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.

Secure Multilayer Perceptron Based on Homomorphic Encryption