Information retrieval (IR) plays an essential role in daily life. However, currently deployed IR technologies, e.g., Apache Lucene – open-source search software, are insufficient when the information is protected or deemed to be private. For example, submitting a query to a publicly available search engine (e.g., Bing or Google) requires disclosing potentially delicate facts (e.g., thoughts about abortion), as well as the websites the user considers interesting. Similarly, when a private database contains sensitive information needed by the user, it cannot be searched freely. Over the past decade, various approaches, generally referred to as private information retrieval, have been proposed to obfuscate queries and responses, but they are limited in that the retrieved information is inadequate to compute relevancy. To address such limitations, this article introduces the necessary techniques to build Lucene-P$^2$that allows one party to discover whether a second party harbors any relevant textual information without either party disclosing any information.

Multi-task learning (MTL), improving learning performance by transferring information between related tasks, has drawn more and more attention in the data mining field. To tackle tasks whose data are stored at different locations (or nodes), distributed MTL was proposed. It not only enhances the learning performance but also improves the computing efficiency since it transforms the original centralized computing framework into a distributed computing framework under which computations can be done in parallel. The major drawback of the distributed MTL is a potential violation of confidentiality when the data stored at each node contain sensitive information (e.g., medical records). Some distributed MTL algorithms were designed to protect the original by only transferring aggregate information (e.g., supports or gradients) from each node to a server who combines the received information to produce the desired models. However, since aggregate data may still leak sensitive information, the security guarantee of the existing solutions cannot be formally proved or verified. Thus, the goal of this paper is to develop a provable privacy-preserving multi-task learning (PP-MTL) protocol that incorporates the state of the art cryptographic techniques to achieve the best security guarantee. We also conducted experiments to demonstrate the efficiency of our proposed method.