We provide a generic framework that, with the help of a preprocessing phase that is independent of the inputs of the users, allows an arbitrary number of users to securely outsource a computation to two non-colluding external servers. Our approach is shown to be provably secure in an adversarial model where one of the servers may arbitrarily deviate from the protocol specification, as well as employ an arbitrary number of dummy users. We use these techniques to implement a secure recommender system based on collaborative filtering that becomes more secure, and significantly more efficient than previously known implementations of such systems, when the preprocessing efforts are excluded. We suggest different alternatives for preprocessing, and discuss their merits and demerits.

Background: Analysing distributed medical data is challenging because of data sensitivity and various regulations to access and combine data. Some privacy-preserving methods are known for analyzing horizontally-partitioned data, where different organisations have similar data on disjoint sets of people. Technically more challenging is the case of vertically-partitioned data, dealing with data on overlapping sets of people. We use an emerging technology based on cryptographic techniques called secure multi-party computation (MPC), and apply it to perform privacy-preserving survival analysis on vertically-distributed data by means of the Cox proportional hazards (CPH) model. Both MPC and CPH are explained. Methods: We use a Newton-Raphson solver to securely train the CPH model with MPC, jointly with all data holders, without revealing any sensitive data. In order to securely compute the log-partial likelihood in each iteration, we run into several technical challenges to preserve the efficiency and security of our solution. To tackle these technical challenges, we generalize a cryptographic protocol for securely computing the inverse of the Hessian matrix and develop a new method for securely computing exponentiations. A theoretical complexity estimate is given to get insight into the computational and communication effort that is needed. Results: Our secure solution is implemented in a setting with three different machines, each presenting a different data holder, which can communicate through the internet. The MPyC platform is used for implementing this privacy-preserving solution to obtain the CPH model. We test the accuracy and computation time of our methods on three standard benchmark survival datasets. We identify future work to make our solution more efficient. Conclusions: Our secure solution is comparable with the standard, non-secure solver in terms of accuracy and convergence speed. The computation time is considerably larger, although the theoretical complexity is still cubic in the number of covariates and quadratic in the number of subjects. We conclude that this is a promising way of performing parametric survival analysis on vertically-distributed medical data, while realising high level of security and privacy.

Optimizing the workflow of a complex organization such as a hospital is a difficult task. An accurate option is to use a real-time locating system to track locations of both patients and staff. However, privacy regulations forbid hospital management to assess location data of their staff members. In this exploratory work, we propose a secure solution to analyze the joined location data of patients and staff, by means of an innovative cryptographic technique called Secure Multi-Party Computation, in which an additional entity that the staff members can trust, such as a labour union, takes care of the staff data. The hospital, owning location data of patients, and the labour union perform a two-party protocol, in which they securely cluster the staff members by means of the frequency of their patient facing times. We describe the secure solution in detail, and evaluate the performance of our proof-of-concept. This work thus demonstrates the feasibility of secure multi-party clustering in this setting.

We consider secure integer division within a secret-sharing based secure multi-party computation framework, where the dividend is secret-shared, but the divisor is privately known to a single party. We mention various applications where this situation arises. We give a solution within the passive security model, and extend this to the active model, achieving a complexity linear in the input bit length. We benchmark both solutions using the well-known MP-SPDZ framework in a cloud environment. Our integer division protocol with a private divisor clearly outperforms the secret divisor solution, both in runtime and communication complexity.

We solve the millionaires problem in the semi-trusted model with homomorphic encryption without using intermediate decryptions. This leads to the computationally least expensive solution with homomorphic encryption so far, with a low bandwidth and very low storage complexity. The number of modular multiplications needed is less than the number of modular multiplications needed for one Pallier encryption. The output of the protocol can be either publicly known, encrypted, or secret-shared. The private input of the first player is computationally secure towards the second player, and the private input of the second player is even unconditionally secure towards the first player. We also introduce an efficient client-server solution for the millionaires problem with similar security properties.