In this paper, we propose the first private decision tree evaluation (PDTE) schemes which are suitable for use in Machine Learning as a Service (MLaaS) scenarios. In our schemes, a user and a model owner send the ciphertexts of a sample and a decision tree model, respectively, and a single server classifies the sample without knowing the sample nor the decision tree. Although many PDTE schemes have been proposed so far, most of them require to reveal the decision tree to the server. This is undesirable because the classification model is the intellectual property of the model owner, and/or it may include sensitive information used to train the model, and therefore the model also should be hidden from the server. In other PDTE schemes, multiple servers jointly conduct the classification process and the decision tree is kept secret from the servers under the assumption they do not collude. Unfortunately, this assumption may not hold because MLaaS is usually provided by a single company. In contrast, our schemes do not have such problems. In principle, fully homomorphic encryption allows us to classify an encrypted sample based on an encrypted decision tree, and in fact, the existing non-interactive PDTE scheme can be modified so that the server classifies only handling ciphertexts. However, the resulting scheme is less efficient than ours. We also show the experimental results for our schemes.

Tin-doped indium oxide (ITO) thin films were prepared on a polyethylene terephthalate (PET) foil by bias sputtering. In the absence of a substrate bias, films having a high resistivity of 210-2 Ωcm were formed. On the other hand, by the application of an rf substrate bias, films having a low resistivity of 2.610-4 Ωcm were formed. The energy of ions that bombarded the substrate during bias sputtering was estimated by a simulation of the ion acceleration. The optimum ion-energy required for the reduction of resistivity was found to be approximately 50 eV.