Literature Review: The Role of Signal Processing in Meeting Privacy Challenges: An Overview

Signal Processing and Data Privacy

Literature Review

By Kato Mivule

COSC891 Fall 2013

The Role of Signal Processing in Meeting Privacy Challenges: An

Overview • Sankar, L.; Trappe, W.; Ramchandran, K.; Poor, H.V.; Debbah, M., "The Role of Signal Processing in Meeting Privacy Challenges:

An Overview," Signal Processing Magazine, IEEE , vol.30, no.5, pp.95,106, Sept. 2013, doi: 10.1109/MSP.2013.2264541

Bowie State University Department of Computer Science

Introduction: Information Leakage Everywhere

• Growth of information technology has made personal data easily available.

• This overflow of unconstrained personal data raises privacy concerns.

• Yet such data sources have remarkable value (utility) to their users.

• This leads to a tension between data privacy and utility needs.



Introduction: Information Leakage Everywhere

• Users post information to social networks, unaware of the privacy risks.

• Companies use the cloud for data processing unaware of privacy risks.

• The data cloud is a risk to “leakage” of private data.



Privacy is differs from Security

• Data privacy deals with confidentiality control.

• Data security involves the handling of accessibility control.

• Data privacy is the procedure of protection against illegal data disclosure.

• Data security is the control of data from illegal access. [ 1 2]

• To exemplify this fundamental point, a house might be secured with locks to ensure access

control; however, bystanders could still look inside the house from a distance if there are

no curtains in the windows, thus no privacy even while access is denied to the bystanders.



Privacy differs from Cryptography

• Cryptography works as an access control methodology.

• Privacy works as a confidentiality control method.

• After decryption, a plaintext database is a risk to ‘inside knowledge’ attacks.

• After decryption, a plaintext database loses its confidentiality.



Adversaries could be insiders

• Every user is a potential adversary.

• A database might be secure but vulnerable to confidentiality breaches.

• For example a user learning private information by inference.



Inference Vulnerabilities – Image Source: Sankar, Trappe, Ramchandran, Poor, Debbah (2013)

Attribute types in statistical databases

• Authors: Public attributes and Private attributes.

• More on attributes:

• PII – Personally Identifiable Information attributes

• Quasi attributes

• Non-sensitive attributes

• Sensitive attributes



Privacy versus utility – a.k.a. the Utility-Privacy (U-P) tradeoff problem.

• Data utility – how beneficial a privatized dataset is to a user.

• Data utility (usefulness) diminishes during the data privacy process:

• When PII is removed.

• When data is perturbed.

• Equilibrium between data privacy and utility needs is an intractable problem.

• “Perfect privacy can be achieved by publishing nothing at all, but this has no utility;

perfect utility can be obtained by publishing the data exactly as received, but this offers no

privacy” Dwork (2006)



Types of Privacy

• Database privacy

• Consumer privacy

• Competitive privacy



Data Privacy Mechanisms

Author: k-anonymity and Differential privacy

• Non-perturbative methods: original data values are not modified.

• k-anonymity

• l-diversity

• Suppression

• Generalization

• Perturbative methods: original data values are transformed.

• Noise addition

• Multiplicative noise

• Logarithmic noise

• Differential privacy



Data Privacy Mechanisms

• Non-perturbative methods: original data values are not modified.



Data Privacy Mechanisms – Perturbation methods – data values modified

• Noise addition: random values are added to sensitive numerical attribute

values to ensure privacy. The general expression is: • 𝑋 + 𝜀 = 𝑍

• X is the original continuous dataset and ɛ is the set of random values (noise) with a

distribution 𝑒~𝑁 0, 𝜎2 that is added to X, and finally Z is the privatized dataset.

• Multiplicative noise: random values with mean µ= 1 and variance 𝜎2, is

multiplied to the original values. The general expression is: • 𝑋𝑗𝜀𝑗 = 𝑌𝑗

• Logarithmic noise: a logarithmic adjustment of the original values is done: • 𝑙𝑛𝑋𝑗 = 𝑌𝑗

• Random values 𝜀𝑗 are then created and added the logarithmic values, 𝑌𝑗, producing the privatized

values 𝑍𝑗 as shown below:

• 𝑌𝑗 + 𝜀𝑗 = 𝑍𝑗



Data Privacy Mechanisms – Perturbation methods – data values modified

Differential Privacy (DP):

• DP is enforced by adding Laplace noise to query results from the database.

• With DP, the users of the database cannot discern if an item has been changed in that database.

• A DP mechanism satisfies the following criteria:

•𝑃[𝑞𝑛(𝐷1)∈𝑅]

𝑃[𝑞𝑛 𝐷2 ∈𝑅] ≤ 𝑒𝜀

• Laplace noise between (0, b) is generated and added to f(x), the original query response, such that:

• 𝑏 =∆𝑓

𝜀

• The max difference is calculated, ∆𝑓 is the max difference (most influential observation):

• ∆𝑓 = 𝑀𝑎𝑥 𝑓 𝐷1 − 𝑓 𝐷2

• Finally, 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑝𝑟𝑖𝑣𝑎𝑡𝑒 𝑑𝑎𝑡𝑎 = 𝑓 𝑥 + 𝐿𝑎𝑝𝑙𝑎𝑐𝑒(0, 𝑏)



Utility-Privacy(U-P) Trade-off

• Data sanitization is concerned with:

• The statistics of the output that achieve a desired level of utility and privacy

• Deciding which input values to perturb.

• How to probabilistically perturb values.

• The U-P tradeoff framework requires the following three components:

• A (statistical) model for the data

• Measures for privacy and utility

• A method to formalize the mappings from 𝑋 to 𝑋



Utility-Privacy(U-P) Trade-off

• Data sanitization is concerned with:

• The statistics of the output that achieve a desired level of utility and privacy

• Deciding which input values to perturb.

• How to probabilistically perturb values.



Tension between Privacy and utility - Image Source: Sankar, Trappe, Ramchandran, Poor, Debbah (2013)

Data Utility Measure

• Utility captures how close the revealed database is to the original.

• A possible measure for the utility u is the requirement that the average distortion of the public

variables is upper bounded, for each 𝜀 > 0, and all sufficiently large n:

𝑢 ≡ 𝐸1

𝑛 𝑝

𝑛

𝑖=1𝑋𝐾𝑟,𝑖

, 𝑋 𝐾𝑟,𝑖≤ 𝐷 + 𝜖

• p . , . is the distortion function

• 𝐸 is the expectation over the joint distribution 𝑋𝐾𝑟,𝑖 , 𝑋 𝐾𝑟,𝑖

• The subscription 𝑖 , is the 𝑖𝑡ℎ𝑡ℎ entry of the database

• Distance based distortion examples include:

• Euclidean distance

• Hamming distance

• Kullback-Leibler divergence



Privacy Quantification

• Entropy is used as a measure of information or uncertainty.

• Privacy requires that there is randomness or uncertainty of all the private variables

• 𝑒 ≡1

𝑛𝐻 𝑋𝐾ℎ

| 𝐽 ≥ 𝐸 − 𝜖

• 𝐻(. |. ) is Shannon’s conditional entropy

• X and Y are two random variables with a joint distribution 𝑝𝑋𝑌

• The conditional entropy 𝐻 𝑋 𝑌 = −(𝑥,𝑦) 𝑝𝑋𝑌 𝑥, 𝑦 𝑙𝑜𝑔𝑝𝑋|𝑌(𝑥|𝑦)



Signal Processing applications of Data Privacy

Categories of database privacy:

• Statistical Data Privacy: which involves guaranteeing privacy of any individual in a

database that is used for statistical information processing (utility).

• Competitive Privacy: which involves information sharing for a common system good

(utility) between competing agents that comprise the system.

• Consumer Privacy: guaranteeing privacy in smart devices.

• Image Classification Privacy: privacy guarantees in biometric identification.

• The FBI to spend US$1 billion on a face recognition to scan surveillance video system.

• Civil rights groups are raising objections about possible privacy violations.

• Privacy preserving algorithms could be employed to find a balance by focusing on criminals only



Signal Processing applications of Data Privacy

Categories of database privacy:

• Statistical Data Privacy

• Competitive Privacy

• Consumer Privacy

• Image Classification Privacy



Database Privacy Categories – Image Source: Sankar, Trappe, Ramchandran, Poor, Debbah (2013)

Conclusion

• A general overview of the data privacy and utility problem is given.

• Most data privacy implementations center around data perturbation methods.

• Signal processing could be applied to:

• Finding the optimal balance between privacy and utility

• Filtering out unneeded noise during the perturbation process.

• The paper focused much on the data privacy and utility problem.

• The paper offered new quantification approach to the data privacy and utility problem.

• The actual application and implementation of signal processing to data privacy

problems is left to the readers. Bowie State University Department of Computer Science


References • Sankar, L.; Trappe, W.; Ramchandran, K.; Poor, H.V.; Debbah, M., "The Role of Signal Processing in Meeting

Privacy Challenges: An Overview," Signal Processing Magazine, IEEE , vol.30, no.5, pp.95,106, Sept. 2013,

doi: 10.1109/MSP.2013.2264541

• Mivule, Kato; Turner, Claude, “A Comparative Analysis of Data Privacy and Utility Parameter Adjustment,

Using Machine Learning Classification as a Gauge”, Complex Adaptive Systems 2013, Nov 13-15, 2013,

Baltimore, MD, USA, (In Press)

• Mivule, K; Turner, Claude, "A Review of Privacy Essentials for Confidential Mobile Data Transactions",

eprint arXiv:1309.3953, 09/2013, ARXIV, online; http://arxiv.org/pdf/1309.3953v1

• Mivule, Kato, "Utilizing Noise Addition for Data Privacy, an Overview", Proceedings of the International

Conference on Information and Knowledge Engineering (IKE 2012), Pages 65-71, Las Vegas, NV, USA.



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Literature Review: The Role of Signal Processing in Meeting Privacy Challenges: An Overview