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Advanced Composition Theorems for Differential Obliviousness

Authors Mingxun Zhou, Mengshi Zhao, T-H. Hubert Chan, Elaine Shi

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Author Details

Mingxun Zhou
  • Carnegie Mellon University, Pittsburgh, PA, USA
Mengshi Zhao
  • The University of Hong Kong, Hong Kong SAR, China
T-H. Hubert Chan
  • The University of Hong Kong, Hong Kong SAR, China
Elaine Shi
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

This work is in part supported by a grant from ONR, a gift from Cisco, NSF awards under grant numbers CIF-1705007, 2128519, 2044679 and 1704788, and a Packard Fellowship. The work is also supported by DARPA SIEVE research program. T-H. Hubert Chan was partially supported by the Hong Kong RGC grants 17201823 and 17203122.

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Mingxun Zhou, Mengshi Zhao, T-H. Hubert Chan, and Elaine Shi. Advanced Composition Theorems for Differential Obliviousness. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 103:1-103:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.103

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 √k loss for k-fold composition by applying the well-known advanced composition theorem given an appropriate parameter range. 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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Differential Privacy
  • Oblivious Algorithms

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