TY - GEN
T1 - Exploring differential obliviousness
AU - Beimel, Amos
AU - Nissim, Kobbi
AU - Zaheri, Mohammad
N1 - Publisher Copyright: © Amos Beimel, Kobbi Nissim, and Mohammad Zaheri.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - In a recent paper, Chan et al. [SODA’19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM’96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.
AB - In a recent paper, Chan et al. [SODA’19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM’96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.
KW - Differential Obliviousness
KW - Differential Privacy
KW - Graph Property Testing
KW - Oblivious RAM
UR - http://www.scopus.com/inward/record.url?scp=85072860486&partnerID=8YFLogxK
U2 - https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.65
DO - https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.65
M3 - Conference contribution
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019
A2 - Achlioptas, Dimitris
A2 - Vegh, Laszlo A.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019
Y2 - 20 September 2019 through 22 September 2019
ER -