Signal Processing and Data Privacy Literature Review

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:
• 𝑋𝑗 𝜀𝑗 = 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[𝑞 𝑛(𝐷1)∈𝑅]
𝑃[𝑞 𝑛 𝐷2 ∈𝑅]
≤ 𝑒 𝜀
• 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 ≡ 𝐸
1
𝑛
𝑝
𝑛
𝑖=1
𝑋 𝐾 𝑟,𝑖
, 𝑋 𝐾 𝑟,𝑖
≤ 𝐷 + 𝜖
• p . , . is the distortion function
• 𝐸 is the expectation over the joint distribution 𝑋 𝐾 𝑟,𝑖
, 𝑋 𝐾 𝑟,𝑖
• The subscription 𝑖 , is the 𝑖 𝑡ℎ
𝑡ℎ 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
𝑛
𝐻 𝑋 𝐾ℎ
| 𝐽 ≥ 𝐸 − 𝜖
• 𝐻(. |. ) is Shannon’s conditional entropy
• X and Y are two random variables with a joint distribution 𝑝 𝑋𝑌
• The conditional entropy 𝐻 𝑋 𝑌 = −(𝑥,𝑦) 𝑝 𝑋𝑌 𝑥, 𝑦 𝑙𝑜𝑔𝑝 𝑋|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.

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.

Signal Processing and Data Privacy Literature Review

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