Details

Autor(en) / Beteiligte

• Gilani, Atefeh
• Kurri, Gowtham R.
• Kosut, Oliver
• Sankar, Lalitha

Titel

Unifying Privacy Measures via Maximal (α, β)-Leakage (MαbeL)

Ist Teil von

• IEEE transactions on information theory, 2024-06, Vol.70 (6), p.4368-4395

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2024

Quelle

IEEE Electronic Library Online

Beschreibungen/Notizen

• We introduce a family of information leakage measures called maximal <inline-formula> <tex-math notation="LaTeX">(\alpha,\beta) </tex-math></inline-formula> -leakage (<inline-formula> <tex-math notation="LaTeX">\text{M}\alpha </tex-math></inline-formula>beL), parameterized by real numbers <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\beta </tex-math></inline-formula> greater than or equal to 1. The measure is formalized via an operational definition involving an adversary guessing an unknown (randomized) function of the data given the released data. We obtain a simplified computable expression for the measure and show that it satisfies several basic properties such as monotonicity in <inline-formula> <tex-math notation="LaTeX">\beta </tex-math></inline-formula> for a fixed <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>, non-negativity, data processing inequalities, and additivity over independent releases. We highlight the relevance of this family by showing that it bridges several known leakage measures, including maximal <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula>-leakage <inline-formula> <tex-math notation="LaTeX">(\beta =1) </tex-math></inline-formula>, maximal leakage <inline-formula> <tex-math notation="LaTeX">(\alpha =\infty,\beta =1) </tex-math></inline-formula>, local differential privacy (LDP) <inline-formula> <tex-math notation="LaTeX">(\alpha =\infty,\beta =\infty) </tex-math></inline-formula>, and local Rényi differential privacy (LRDP) <inline-formula> <tex-math notation="LaTeX">(\alpha =\beta) </tex-math></inline-formula>, thereby giving an operational interpretation to local Rényi differential privacy. We also study a conditional version of <inline-formula> <tex-math notation="LaTeX">\text{M}\alpha </tex-math></inline-formula>beL on leveraging which we recover differential privacy and Rényi differential privacy. A new variant of LRDP, which we call maximal Rényi leakage, appears as a special case of <inline-formula> <tex-math notation="LaTeX">\text{M}\alpha </tex-math></inline-formula>beL for <inline-formula> <tex-math notation="LaTeX">\alpha =\infty </tex-math></inline-formula> that smoothly tunes between maximal leakage (<inline-formula> <tex-math notation="LaTeX">\beta =1 </tex-math></inline-formula>) and LDP (<inline-formula> <tex-math notation="LaTeX">\beta =\infty </tex-math></inline-formula>). Finally, we show that a vector form of the maximal Rényi leakage relaxes differential privacy under Gaussian and Laplacian mechanisms.