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Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes

Authors Yoav Ben Dov, Liron David , Moni Naor , Elad Tzalik

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Author Details

Yoav Ben Dov
  • Weizmann Institute of Science, Rehovot, Israel
Liron David
  • Weizmann Institute of Science, Rehovot, Israel
Moni Naor
  • Weizmann Institute of Science, Rehovot, Israel
Elad Tzalik
  • Weizmann Institute of Science, Rehovot, Israel

Funding

Research supported in part by grants from the Israel Science Foundation (no.2686/20), by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness and by the Israeli Council for Higher Education (CHE) via the Weizmann Data Science Research Center.

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Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik. Resistance to Timing Attacks for Sampling and Privacy Preserving Schemes. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.FORC.2023.11

Abstract

Side channel attacks, and in particular timing attacks, are a fundamental obstacle for secure implementation of algorithms and cryptographic protocols. These attacks and countermeasures have been widely researched for decades. We offer a new perspective on resistance to timing attacks. 
We focus on sampling algorithms and their application to differential privacy. We define sampling algorithms that do not reveal information about the sampled output through their running time. More specifically: (1) We characterize the distributions that can be sampled from in a "time oblivious" way, meaning that the running time does not leak any information about the output. We provide an optimal algorithm in terms of randomness used to sample for these distributions. We give an example of an efficient randomized algorithm 𝒜 such that there is no subexponential algorithm with the same output as 𝒜 that does not reveal information on the output or the input, therefore we show leaking information on either the input or the output is unavoidable. (2) We consider the impact of timing attacks on (pure) differential privacy mechanisms. It turns out that if the range of the mechanism is unbounded, such as counting, then any time oblivious pure DP mechanism must give a useless output with constant probability (the constant is mechanism dependent) and must have infinite expected running time. We show that up to this limitations it is possible to transform any pure DP mechanism into a time oblivious one.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Random number generation
  • Theory of computation → Cryptographic primitives
  • Theory of computation → Generating random combinatorial structures
Keywords
  • Differential Privacy

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