Optimal Re-encryption Strategy for Joins in Encrypted Databases

In order to perform a join in a deterministically, adjustably encrypted database one has to re-encrypt at least one column. The problem is to select that column that will result in the minimum number of re-encryptions even under an unknown schedule of joins. Naive strategies may perform too many or even infinitely many re-encryptions. We provide two strategies that allow for a much better performance. In particular the asymptotic behavior is O(n 3/2) resp. O(n logn) re-encryptions for n columns. We show that there can be no algorithm better than O(n logn). We further extend our result to element-wise re-encryptions and show experimentally that our algorithm results in the optimal cost in 41% of the cases.