Efficient computation on oblivious RAMs

Abstract

A machine is oblivious if the sequence in which it accesses memory locations is equivalent for any two programs with the same running time. For example, an oblivious Turing Machine is one for which the movement of the heads on the tapes is identical for each computation. (Thus, it is independent of the actual input.) What is the slowdown in the running time of any machine, if it is required to be oblivious?