Supervised learning techniques such as classification algorithms learn from training data to predict the correct label for newly presented input data. In many real-world scenarios, training data required by such techniques can contain personal information and data collection can be a significant problem due to privacy concerns. Cryptographic techniques have been used before to do training on encrypted data. However, such techniques are computationally expensive and they are not scalable most of the time. If a dataset in another party will be used for training, differential privacy technology can be used to preserve the privacy of the individuals in the dataset. When there is no such dataset and data needs to be collected from individuals directly for training, local differential privacy can be used. Local differential privacy is a technology to preserve privacy during data sharing with an untrusted data collector. In this work, we propose to use local differential privacy techniques to train a Naive Bayes classifier. Using the proposed solution, an untrusted party collects perturbed data from individuals that keep the relationship between the feature values and class labels. By estimating probabilities needed by the Naive Bayes classifier using the perturbed data, the untrusted party can classify new instances with high accuracy. We develop solutions that work for both discrete and continuous data. We also propose utilizing dimensionality reduction techniques to decrease communication cost and improve accuracy. We show the accuracy of the proposed Naive Bayes classifier achieving local differential privacy via experiments on several datasets. We also show how dimensionality reduction enhances the accuracy.

Continuous authentication for mobile devices using behavioral biometrics is being suggested to complement initial authentication for securing mobile devices, and the cloud services accessed through them. This area has been studied over the past few years, and low error rates were achieved; however, it was based on training and testing using support vector machine (SVM) and other non-privacy-preserving machine learning algorithms. To stress the importance of carefully designed privacy-preserving systems, we investigate the possibility of reconstructing gestures raw data from users' authentication profiles or synthesized samples' testing results. We propose two types of reconstruction attacks based on whether actual user samples are available to the adversary (as in SVM profiles) or not. We also propose two algorithms to reconstruct raw data: a numerical-based algorithm that is specific to one compromised system, and a randomization-based algorithm that can work against almost any compromised system. For our experiments, we selected one compromised and four attacked gesture-based continuous authentication systems from the recent literature. The experiments, performed using a public data set, showed that the attacks were feasible, with a median ranging from 80% to 100% against one attacked system using all types of attacks and algorithms, and a median ranging from 73% to 100% against all attacked systems using the randomization-based algorithm and the negative support vector attack. Finally, we analyze the results, and provide recommendations for building active authentication systems that could resist reconstruction attacks.