Welcome to the resource topic for 2023/842
Title:
Advanced Composition Theorems for Differential Obliviousness
Authors: Mingxun Zhou, Mengshi Zhao, T-H. Hubert Chan, Elaine Shi
Abstract:Differential obliviousness (DO) is a privacy notion which mandates that the access patterns of a program satisfy differential privacy. Earlier works have shown that in numerous applications, differential obliviousness allows us to circumvent fundamental barriers pertaining to fully oblivious
algorithms, resulting in asymptotical (and sometimes even polynomial) performance improvements. Although DO has been applied to various contexts, including the design of algorithms, data structures, and protocols, its compositional properties are not explored until the recent work of Zhou et al. (Eurocrypt’23). Specifically, Zhou et al. showed that the original DO notion is not composable. They then proposed a refinement of DO called neighbor-preserving differential obliviousness (NPDO), and proved a basic composition for NPDO.
In Zhou et al.'s basic composition theorem for NPDO, the privacy loss is linear in k for k-fold composition. In comparison, for standard differential privacy, we can enjoy roughly \sqrt{k} loss for k-fold composition by applying the well-known advanced composition theorem. Therefore, a natural question left open by their work is whether we can also prove an analogous advanced composition for NPDO.
In this paper, we answer this question affirmatively. As a key step in proving an advanced composition theorem for NPDO, we define a more operational notion called symmetric NPDO which we prove to be equivalent to NPDO. Using symmetric NPDO as a stepping stone, we also show how to generalize
NPDO to more general notions of divergence, resulting in Rényi-NPDO, zero-concentrated NPDO, Gassian-NPDO, and g-NPDO notions. We also prove composition theorems for these generalized notions of NPDO.
ePrint: https://eprint.iacr.org/2023/842
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