Abstract. We present a novel method for constructing linear secret sharing schemes (LSSS) from linear error correcting codes and linear universal hash functions in a blackbox way. The main advantage of this new construction is that the privacy property of the resulting secret sharing scheme essentially becomes independent of the code we use, only depending on its rate. This allows us to fully harness the algorithmic properties of recent code constructions such as efficient encoding and decoding or efficient list-decoding. Choosing the error correcting codes and universal hash functions involved carefully, we obtain solutions to the following open problems:-A linear near-threshold secret sharing scheme with both linear time sharing and reconstruction algorithms and large secrets (i.e. secrets of size Ω(n)). Thus, the computational overhead per shared bit in this scheme is constant. -An efficiently reconstructible robust secret sharing scheme for n/3 ≤ t < (1 − ) · n/2 corrupted players (for any constant > 0) with shares of optimal size O(1 + λ/n) and secrets of size Ω(n + λ), where λ is the security parameter.

Background Recent developments in machine learning have shown its potential impact for clinical use such as risk prediction, prognosis, and treatment selection. However, relevant data are often scattered across different stakeholders and their use is regulated, e.g. by GDPR or HIPAA. As a concrete use-case, hospital Erasmus MC and health insurance company Achmea have data on individuals in the city of Rotterdam, which would in theory enable them to train a regression model in order to identify high-impact lifestyle factors for heart failure. However, privacy and confidentiality concerns make it unfeasible to exchange these data. Methods This article describes a solution where vertically-partitioned synthetic data of Achmea and of Erasmus MC are combined using Secure Multi-Party Computation. First, a secure inner join protocol takes place to securely determine the identifiers of the patients that are represented in both datasets. Then, a secure Lasso Regression model is trained on the securely combined data. The involved parties thus obtain the prediction model but no further information on the input data of the other parties. Results We implement our secure solution and describe its performance and scalability: we can train a prediction model on two datasets with 5000 records each and a total of 30 features in less than one hour, with a minimal difference from the results of standard (non-secure) methods. Conclusions This article shows that it is possible to combine datasets and train a Lasso regression model on this combination in a secure way. Such a solution thus further expands the potential of privacy-preserving data analysis in the medical domain.