Bucket Oblivious Sort: An Extremely Simple Oblivious Sort
This provides a simpler and faster solution for secure computation applications where data access patterns must be hidden.
The paper tackles the problem of oblivious sorting with a new algorithm called bucket oblivious sort that achieves 6n log n time complexity with exponentially small error probability, running 5× faster than bitonic sort for 2^30 elements.
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 $3\times$ slower than a non-oblivious merge sort baseline; for $2^{30}$ elements, it is $5\times$ faster than bitonic sort, the de facto oblivious sorting algorithm in practical implementations.