Privacy-preserving aggregation

A cryptographic system for performing an aggregation of a set of values according to a corresponding set of keys and according to an aggregation operation, wherein the aggregation is performed in a privacy-preserving way as a cryptographic secure multi-party computation between multiple cryptographic devices, wherein a cryptographic device is configured to:

• obtain the respective values as secret values of the multi-party computation, wherein the respective values are ordered such that matching keys are adjacent in the ordering;
• aggregate the set of respective values to compute the respective aggregate values under the multi-party computation, wherein, for a set of multiple matching keys, at least one of the corresponding aggregate values represents an aggregation according to the aggregation operation of the set of values corresponding to the set of matching keys, wherein the aggregating is performed by:
• dividing the set of values into multiple subsets of adjacent values;
• aggregating adjacent first and second subsets;
• combining the aggregated values of the first and second subset by, if the final key of the first subset matches the first key of the second subset, combining aggregate values for the final key and the first key.