Oblivious RAM
Open-knowledge reference entry
An Oblivious RAM (ORAM) simulator is a compiler that transforms an algorithm in such a way that the resulting algorithm preserves the input-output behavior of the original algorithm but the distribution of the memory access patterns of the transformed algorithm is independent of the memory access pattern of the original algorithm.
The use of ORAMs is motivated by the fact that an adversary can obtain nontrivial information about the execution of a program and the data that the program is using just by observing the pattern in which the program accesses various memory locations during its execution. An adversary can get this information even if the data in memory is encrypted.
This definition is suited for settings like protected programs running on unprotected shared memory or clients running programs on their systems by accessing previously stored data on a remote server. The concept was formulated by Oded Goldreich and Rafail Ostrovsky in 1996.
Definition
A Turing machine (TM), a mathematical abstraction of a real computer (program), is said to be oblivious if, for any two inputs of the same length, the motions of the tape heads remain the same. Pippenger and Fischer proved that every TM with running time
T
(
n
)
{\displaystyle T(n)}
can be made oblivious and that the running time of the oblivious TM is
O
(
T
(
n
)
log
T
(
n
)
)
{\displaystyle O(T(n)\log T(n))}
. A more realistic model of computation is the RAM model. In the RAM model of computation, there is a CPU that can execute the basic mathematical, logical, and control instructions. The CPU is also associated with a few registers and a physical random access memory, where it stores the operands of its instructions.
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