eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-02-04
68:1
68:19
10.4230/LIPIcs.ITCS.2021.68
article
Differentially Oblivious Turing Machines
Komargodski, Ilan
1
2
https://orcid.org/0000-0002-1647-2112
Shi, Elaine
3
4
The Hebrew University in Jerusalem, Israel
NTT Research, Palo Alto, CA, USA
Cornell University, Ithaca, NY, USA
Carnegie Mellon University, Pittsburgh, PA, USA
Oblivious RAM (ORAM) is a machinery that protects any RAM from leaking information about its secret input by observing only the access pattern. It is known that every ORAM must incur a logarithmic overhead compared to the non-oblivious RAM. In fact, even the seemingly weaker notion of differential obliviousness, which intuitively "protects" a single access by guaranteeing that the observed access pattern for every two "neighboring" logical access sequences satisfy (ε,δ)-differential privacy, is subject to a logarithmic lower bound.
In this work, we show that any Turing machine computation can be generically compiled into a differentially oblivious one with only doubly logarithmic overhead. More precisely, given a Turing machine that makes N transitions, the compiled Turing machine makes O(N ⋅ log log N) transitions in total and the physical head movements sequence satisfies (ε,δ)-differential privacy (for a constant ε and a negligible δ). We additionally show that Ω(log log N) overhead is necessary in a natural range of parameters (and in the balls and bins model).
As a corollary, we show that there exist natural data structures such as stack and queues (supporting online operations) on N elements for which there is a differentially oblivious implementation on a Turing machine incurring amortized O(log log N) overhead per operation, while it is known that any oblivious implementation must consume Ω(log N) operations unconditionally even on a RAM. Therefore, we obtain the first unconditional separation between obliviousness and differential obliviousness in the most natural setting of parameters where ε is a constant and δ is negligible. Before this work, such a separation was only known in the balls and bins model. Note that the lower bound applies in the RAM model while our upper bound is in the Turing machine model, making our separation stronger.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol185-itcs2021/LIPIcs.ITCS.2021.68/LIPIcs.ITCS.2021.68.pdf
Differential privacy
Turing machines
obliviousness