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Abstract-In this paper, we study the problem of constructing private classifiers using decision trees, within the framework of differential privacy. We first construct privacy-preserving ID3 decision trees using differentially private sum queries. Our experiments show that for many data sets a reasonable privacy guarantee can only be obtained via this method at a steep cost of accuracy in predictions.We then present a differentially private decision tree ensemble algorithm using the random decision tree approach. We demonstrate experimentally that our approach yields good prediction accuracy even when the size of the datasets is small. We also present a differentially private algorithm for the situation in which new data is periodically appended to an existing database. Our experiments show that our differentially private random decision tree classifier handles data updates in a way that maintains the same level of privacy guarantee.

In this paper we present two protocols for asynchronous Byzantine Quorum Systems (BQS) built on top of reliable channels-one for self-verifying data and the other for any data. Our protocols tolerate ¢ Byzantine failures with ¢ fewer servers than existing solutions by eliminating nonessential work in the write protocol and by using read and write quorums of different sizes. Since engineering a reliable network layer on an unreliable network is difficult, two other possibilities must be explored. The first is to strengthen the model by allowing synchronous networks that use time-outs to identify failed links or machines. We consider running synchronous and asynchronous Byzantine Quorum protocols over synchronous networks and conclude that, surprisingly, "self-timing" asynchronous Byzantine protocols may offer significant advantages for many synchronous networks when network time-outs are long. We show how to extend an existing Byzantine Quorum protocol to eliminate its dependency on reliable networking and to handle message loss and retransmission explicitly.

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Privacy has become an increasingly important issue in data mining. In this paper, we consider a scenario in which a data miner surveys a large number of customers to learn classification rules on their data, while the sensitive attributes of these customers need to be protected. Solutions have been proposed to address this problem using randomization techniques. Such solutions exhibit a tradeoff of accuracy and privacy: the more each customer's private information is protected, the less accurate result the miner obtains; conversely, the more accurate the result, the less privacy for the customers. In this paper, we propose a simple cryptographic approach that is efficient even in a many-customer setting, provides strong privacy for each customer, and does not lose any accuracy as the cost of privacy. Our key technical contribution is a privacy-preserving method that allows a data miner to compute frequencies of values or tuples of values in the customers' data, without revealing the privacy-sensitive part of the data. Unlike general-purpose cryptographic protocols, this method requires no interaction between customers, and each customer only needs to send a single flow of communication to the data miner. However, we are still able to ensure that nothing about the sensitive data beyond the desired frequencies is revealed to the data miner. To illustrate the power of our approach, we use our frequency mining computation to obtain a privacypreserving naive Bayes classifier learning algorithm. Initial experimental results demonstrate the practical efficiency of our solution. We also suggest some other applications of privacy-preserving frequency mining.