University of Illinois Urbana-Champaign

Bounds on the Privacy Amplification of Arbitrary Channels via the Contraction of fα-Divergence

Grosse, Leonhard; Saeidian, Sara; Oechtering, Tobias J.; Skoglund, Mikael

Permalink

https://hdl.handle.net/2142/130261

Description

Title
Bounds on the Privacy Amplification of Arbitrary Channels via the Contraction of fα-Divergence
Author(s)
  • Grosse, Leonhard
  • Saeidian, Sara
  • Oechtering, Tobias J.
  • Skoglund, Mikael
Issue Date
2025-09-17
Keyword(s)
  • Privacy amplification
  • Local differential privacy
  • Strong data processing inequalities
  • Rényi-divergence
  • F-divergence inequalities
Abstract
We examine the privacy amplification of channels that do not necessarily satisfy any LDP guarantee by analyzing their contraction behavior in terms of fα-divergence, an f-divergence related to Rényi-divergence via a monotonic transformation. We present bounds on contraction for restricted sets of prior distributions via f-divergence inequalities and present an improved Pinsker’s inequality for fα-divergence based on the joint range technique by Harremoës and Vajda [1]. The presented bound is tight whenever the value of the total variation distance is larger than 1/α. By applying these inequalities in a cross-channel setting, we arrive at strong data processing inequalities for fα-divergence that can be adapted to use-case specific restrictions of input distributions and channel. The application of these results to privacy amplification shows that even very sparse channels can lead to significant privacy amplification when used as a postprocessing step after local differentially private mechanisms.
Publisher
Allerton Conference on Communication, Control, and Computing
Series/Report Name or Number
2025 61st Allerton Conference on Communication, Control, and Computing Proceedings
ISSN
2836-4503
Type of Resource
Text
Genre of Resource
Conference Paper/Presentation
Language
eng
Handle URL
https://hdl.handle.net/2142/130261&&
Copyright and License Information
Copyright 2025 owned by the authors.

Owning Collections

61st Allerton Conference - 2025 PRIMARY
Allerton Conference on Communication, Control, and Computing, 1977-present