Protecting Statistical Databases Against Snoopers

Comparison of two methods

Disclosure vs. Anonymity

Information disclosure necessary for planning and numerical measurements

Anonymity necessary for protection of the individual and the public’s trust in systems

Medical Data

Necessary for: Measuring effectiveness of

current treatments Finding sources of common

medical mistakes Tracking contagious disease Government spending planning Health Insurance Companies

Anonymity: Not as Easy as it Looks

Race

Profession

SexZip code

Birth date

Complete Identification Without Uniquely Identifying Information

Outside Factors Affecting Privacy

Snooper’s supplementary knowledge Public data sources Rarity

Comparing Two Methods of Protection

What are the privacy guarantees?

Can useful information be gained?

Sensitivity-based Noise-adding Algorithm

Proposed by Dwork, McSherry, Nissim and Smith

Adds noise to each answer based on the sensitivity of the series of queries

Amount of privacy based on ε, a coefficient in the noise-generating formula

SensitivityHow much could changing one row

change an answer?

MEAN COUNT HISTOGRAMS

The sensitivity of a series of queries is the sum of the sensitivities of the queries

Coin-flip Algorithm

Proposed by Mishra and Sandler

A way for individuals to publish their own personal data

Amount of privacy based on ε, the bias in the coin-flip

Implementing the Coin-flip Algorithm

Each of the k possible answers to a query are ordered and numbered

If an individual’s answer to the query is the ith answer, the profile would be a string of k bits where the ith is a one and the others are zero

To sanitize, each bit is flipped with probability ½ + ε/2

All sanitized profiles resemble a random string of ones and zeros

Example: HIV status Ordered possible responses:

“POSITIVE, NEGATIVE, UNKNOWN” The original profile of an HIV+

individual: “1, 0, 0” Results of coin-flips: “STAY, FLIP, STAY”

Resulting sanitized profile: “1, 1, 0” What do we know about the

individual from the sanitized profile?

My Research

Compare the total amount of error generated by histogram / frequency queries

Hypothesis: The noise-adding algorithm will generate less error for few queries and the coin-flip algorithm will generate less error for many queries

Research question: Where is the “sweet spot” where the error lines cross on a graph?

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r as

per

cen

t o

f n

Coinflip

Noise Addition

The “sweet spot” first occurs at 101 queries.

With the smallest histograms first, the first “sweet spot” occurs at 32 queries.

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r a

s p

erce

nt

of

n

Coinflip

Noise Addition

With the largest histograms first, the first “sweet spot” occurs at 189 queries.

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r as

per

cen

t o

f n

Coinflip

Noise Addition

A Second Look Range of sensitivity: 2 to 136

Unordered histograms:At first “sweet spot”, sensitivity= 30.

Smallest histograms first:At first “sweet spot”, sensitivity= 32.

Largest histograms first:At first “sweet spot”, sensitivity= 34.

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r as

per

cen

t o

f n

Coinflip

Noise Addition

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r as

per

cen

t o

f n

Coinflip

Noise Addition

Sum of Error

0.00%

500.00%

1000.00%

1500.00%

2000.00%

2500.00%

3000.00%

3500.00%

4000.00%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381

Number of Frequency Queries

sum

of

erro

r as

per

cen

t o

f n

Coinflip

Noise Addition

Difference in Error

-200.00%

0.00%

200.00%

400.00%

600.00%

800.00%

1000.00%

1200.00%

1400.00%

1600.00%

2 12 22 32 42 52 62 72 82 92

Sensitivity

Dif

fere

nce

in p

erc

ent

err

or

Conclusions

For histogram / frequency queries, “sweet spots” occur between sensitivity=30 and sensitivity=40, so for least error: If sensitivity < 30, use NOISE-ADDING algorithm If sensitivity > 40, use COIN-FLIP algorithm

Quick Bibliography

Survey: N R Adam and J C Wortmann. Security-control methods

for statistical databases: a comparative study. ACM Computing Surveys, 25(4), December 1989.

Noise-adding algorithm: C Dwork, F McSherry, K Nissim, A Smith. Calibrating

noise to sensitivity in private data analysis. 3rd Theory of Cryptography Conference, 2006.

Coin-flip algorithm: N Mishra, M Sandler. Symposium on Principles of

Database Systems, 2006.

Professor Alf Weaver, PhD

Professor Nina Mishra, PhD

REU program at UVa, sponsored by the National Science Foundation