LIPIcs - Leibniz International Proceedings in Informatics. 2nd Conference on Information-Theoretic Cryptography (ITC 2021)
Doi
Abstract
Oblivious RAM (ORAM)
is a technique for compiling any RAM program to an oblivious counterpart, i.e.,
one whose access patterns do not leak information about the secret inputs.
Similarly, Oblivious Parallel RAM (OPRAM) compiles a
{\it parallel} RAM program to an oblivious counterpart.
In this paper, we care about ORAM/OPRAM with {\it perfect security}, i.e.,
the access patterns must be {\it identically distributed}
no matter what the program\u27s memory request sequence is.
In the past, two types of perfect ORAMs/OPRAMs
have been considered:
constructions whose performance bounds hold {\it in expectation} (but may occasionally
run more slowly);
and constructions whose performance bounds hold {\it deterministically} (even though
the algorithms themselves are randomized).
In this paper, we revisit the performance metrics for perfect
ORAM/OPRAM, and
show novel constructions that achieve asymptotical improvements
for all performance metrics.
Our first result
is a new perfectly secure OPRAM
scheme with O(log3N/loglogN) {\it expected} overhead.
In comparison, prior literature
has been stuck at O(log3N) for more than a decade.
Next, we show how to construct a perfect ORAM
with O(log3N/loglogN)
{\it deterministic} simulation overhead. We further show how
to make the scheme parallel, resulting in an perfect OPRAM
with O(log4N/loglogN)
{\it deterministic} simulation overhead.
For perfect ORAMs/OPRAMs
with deterministic performance bounds, our results achieve
{\it subexponential} improvement over the state-of-the-art.
Specifically, the best known prior scheme
incurs more than N deterministic simulation overhead
(Raskin and Simkin, Asiacrypt\u2719); moreover, their scheme works
only for the sequential setting and is {\it not} amenable to parallelization.
Finally, we additionally consider perfect ORAMs/OPRAMs
whose performance bounds hold with high probability.
For this new performance metric, we show new constructions
whose simulation overhead is upper bounded by O(log3/loglogN)
except with negligible in N probability, i.e., we prove
high-probability performance bounds that match the expected
bounds mentioned earlier