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
Matouv{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.

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