Oblivious Sorting and Queues

TL;DR

This paper introduces new deterministic oblivious data structures including various queues and sorting algorithms, enabling operations without data structure modification, with significant improvements in efficiency and practical evaluation.

Contribution

It presents the first oblivious double-ended queues and LIFO queues, along with an optimized oblivious quicksort, advancing the state of secure data processing techniques.

Findings

Oblivious queues enable push/pop without data structure changes.

Oblivious mergesort improves comparison efficiency over prior work by over 1000 times.

Empirical evaluation confirms practical viability of proposed structures.

Abstract

We present a deterministic oblivious LIFO (Stack), FIFO, double-ended and double-ended priority queue as well as an oblivious mergesort and quicksort algorithm. Our techniques and ideas include concatenating queues end-to-end, size balancing of multiple arrays, several multi-level partitionings of an array. Our queues are the first to enable executions of pop and push operations without any change of the data structure (controlled by a parameter). This enables interesting applications in computing on encrypted data such as hiding confidential expressions. Mergesort becomes practical using our LIFO queue, ie. it improves prior work (STOC '14) by a factor of (more than) 1000 in terms of comparisons for all practically relevant queue sizes. We are the first to present double-ended (priority) and LIFO queues as well as oblivious quicksort which is asymptotically optimal. Aside from theortical analysis, we also provide an empirical evaluation of all queues.