3 research outputs found
Oblivious Median Slope Selection
We study the median slope selection problem in the oblivious RAM model. In
this model memory accesses have to be independent of the data processed, i.e.,
an adversary cannot use observed access patterns to derive additional
information about the input. We show how to modify the randomized algorithm of
Matou\v{s}ek (1991) to obtain an oblivious version with O(n log^2 n) expected
time for n points in R^2. This complexity matches a theoretical upper bound
that can be obtained through general oblivious transformation. In addition,
results from a proof-of-concept implementation show that our algorithm is also
practically efficient.Comment: 14 pages, to appear in Proceedings of CCCG 202
Path Oblivious Heap: Optimal and Practical Oblivious Priority Queue
We propose Path Oblivious Heap, an extremely simple, practical, and optimal oblivious
priority queue. Our construction also implies a practical and optimal oblivious sorting algorithm
which we call Path Oblivious Sort. Not only are our algorithms asymptotically optimal, we show
that their practical performance is only a small constant factor worse than insecure baselines.
More specificially, assuming roughly logarithmic client private storage, Path Oblivious Heap
consumes 2× to 7× more bandwidth than the ordinary insecure binary heap; and Path Oblivious
Sort consumes 4.5× to 6× more bandwidth than the insecure Merge Sort. We show that these
performance results improve existing works by 1-2 orders of magnitude. Finally, we evaluate our
algorithm for a multi-party computation scenario and show 7× to 8× reduction in the number
of symmetric encryptions relative to the state of the art