Bucket Oblivious Sort: An Extremely Simple Oblivious Sort

We propose a conceptually simple oblivious sort and oblivious random permutation algorithms called bucket oblivious sort and bucket oblivious random permutation. Bucket oblivious sort uses 6n log n time (measured by the number of memory accesses) and 2Z client storage with an error probability exponentially small in Z. The above runtime is only 3× slower than a non-oblivious merge sort baseline; for 230 elements, it is 5× faster than bitonic sort, the de facto oblivious sorting algorithm in practical implementations.