With the advent of cloud computing, traditional machine learning (ML) are migrating into cloud-based ML day by day following the concept of machine learning as a cloud service, which enables multiple entities to contribute to and benefit from shared datasets and models. As well as training the linear classification model, training the nonlinear classification model is also an essential task in cloud-based ML. However, this task commonly involves learning knowledge from different datasets provided by various entities, which often contain sensitive information like patients' physiological indices. Therefore, it gives rise a natural question how to allow multiple users collaboratively participating in a nonlinear classification task while preserving these datas' privacy. As a promising cryptographic tool, the concept of unbounded multiinput functional encryption can be developed to answer such a question, such as google search engines are running over this concept-based ML approaches. However, most of existing approaches are derived from this concept with inner product functionality, specifying for a linear classification model and thus fails to cope with a non-linear classification one. In this paper, we introduce an advanced cryptographic concept called unbounded multi-input quadratic functional encryption, and give a concrete construction which allows arbitrary number of users participating in the classifying tasks with a nonlinear classification model but without divulging their private data. Moreover, we provide a strict mathematical security proof under a well-defined security model as well as some security attacks are analyzed, followed by an experimental analysis and comparison on a real dateset as well as a practical use case to demonstrate our scheme's performance.

As a common metric, maximum similarity between two objects is widely employed by web platforms to provide matching services. However, the calculation of maximum similarity involves numerous sensitive or confidential users’ data, and the web platform server is often not trusted who might peep these data out of curiosity, or even worse sell them to unauthorized entities to make profits. Therefore, many research lines on functional encryption have been suggested and studied on how to calculate the maximum similarity while ensure the privacy of users’ data. Unfortunately, all of them will divulge some intermediate results to the web platform server when processing this issue. In this paper we present a new functional encryption scheme supporting privacy-preserving maximum similarity, which enables the web service platforms to figure out the maximum similarity without learning anything else about their data. Moreover, we provide a formal analysis to prove the security of the proposed scheme, followed by some experimental evaluations and comprehensive comparisons with the related works. It shows that, our scheme is the first functional encryption realization on maximum similarity without divulging the intermediate result and meanwhile achieve a higher security-function privacy, as well as a traditional data privacy.