Secure Summation via Subset Sums: A New Primitive for Privacy-Preserving Distributed Machine Learning

For population studies or for the training of complex machine learning models, it is often required to gather data from different actors. In these applications, summation is an important primitive: for computing means, counts or mini-batch gradients. In many cases, the data is privacysensitive and therefore cannot be collected on a central server. Hence the summation needs to be performed in a distributed and privacy-preserving way. Existing solutions for distributed summation with computational privacy guarantees make trust or connection assumptions -- e.g., the existence of a trusted server or peer-to-peer connections between clients -- that might not be fulfilled in real world settings. Motivated by these challenges, we propose Secure Summation via Subset Sums (S5), a method for distributed summation that works in the presence of a malicious server and only two honest clients, and without the need for peer-to-peer connections between clients. S5 adds zero-sum noise to clients' messages and shuffles them before sending them to the aggregating server. Our main contribution is a proof that this scheme yields a computational privacy guarantee based on the multidimensional subset sum problem. Our analysis of this problem may be of independent interest for other privacy and cryptography applications.