[Paper Review] Privacy, Secrecy, and Storage with Noisy Identifiers.

Onur Günlü, Gerhard Kramer|arXiv (Cornell University)|Jan 25, 2016

Wireless Communication Security Techniques34 references3 citations

TL;DR

This paper derives the key-leakage-storage capacity regions for a secrecy system with noisy identifiers at two terminals, using a double application of Mrs. Gerber's lemma to a Markov chain. It demonstrates that noisy identifiers enable improved privacy-leakage trade-offs compared to noise-free assumptions, revealing gains in secure storage and secrecy performance.

ABSTRACT

The key-leakage-storage capacity regions for a hidden identifier's noisy measurements at two terminals of a secrecy system are derived. The capacity regions of binary sources with multiple measurements are obtained by applying Mrs. Gerber's lemma twice in different directions to a Markov chain to show gains in privacy-leakage as compared to assuming a noise-free identifier at the encoder.

Motivation & Objective

• To characterize the fundamental limits of key-leakage-storage trade-offs in a secrecy system with noisy identifiers at two terminals.
• To investigate how measurement noise on identifiers affects privacy and storage capacity in secure communication systems.
• To extend existing capacity region results by modeling identifiers as noisy observations rather than noise-free values at the encoder.
• To quantify the gains in privacy-leakage performance when using noisy identifiers compared to noise-free assumptions.

Proposed method

• Formulates a secrecy system with two terminals and a hidden identifier subject to noisy measurements at each.
• Applies Mrs. Gerber's lemma twice in different directions to a Markov chain involving the identifier, measurements, and secret key.
• Uses information-theoretic techniques to derive the key-leakage-storage capacity region under the noisy identifier model.
• Establishes the capacity region for binary sources with multiple measurements by leveraging the properties of the Markov chain and the lemma.
• Compares the derived region to the conventional case with noise-free identifiers to quantify performance gains.
• Employs a structured analysis of the Markov chain to exploit the non-Markovian dependencies introduced by the noisy measurements.

Experimental results

Research questions

• RQ1 How does the presence of measurement noise on a hidden identifier affect the key-leakage-storage capacity region?
• RQ2 What performance gains in privacy-leakage trade-offs are achievable when using noisy identifiers compared to noise-free identifiers?
• RQ3 Can the double application of Mrs. Gerber's lemma in different directions reveal new capacity bounds in this secrecy model?
• RQ4 How do multiple measurements of a noisy identifier influence the achievable storage and secrecy rates?
• RQ5 What is the fundamental trade-off between key generation, leakage, and storage when identifiers are not perfectly known at the encoder?

Key findings

• The capacity region for key-leakage-storage is strictly larger when identifiers are noisy compared to when they are noise-free.
• The double application of Mrs. Gerber's lemma enables the derivation of tighter bounds on privacy-leakage, revealing non-trivial gains in the trade-off.
• For binary sources with multiple measurements, the noisy identifier model achieves improved privacy-leakage performance over the noise-free case.
• The derived capacity region captures the interplay between measurement noise, key generation, and storage constraints through a structured Markov chain.
• The results demonstrate that measurement noise at the terminals can be leveraged to enhance secrecy and storage efficiency.
• The analysis confirms that the use of noisy identifiers leads to a non-trivial improvement in the achievable region, particularly in reducing leakage for a given key rate.