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Privacy Preservation of Aggregates in Hidden Databases: Why and How?
Arjun Dasgupta, Nan Zhang,
Gautam Das, Surajit Chaudhuri
Presented by PENG Yu
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Privacy leakage
An airline company’s flight search form lets a user search for a flight by specifying a set of attributes such as departure and destination, date, number of stops, carrier, and cabin preferences.
Privacy of Preservation of Aggregates
Reasons: Legitimate interfaces give chances to attackers to detect the
sensitive aggregates information. Aggregates information can be used by adversaries to master the
whole distribution and other features of the hidden databases behind the interfaces.
To some extent, aggregates information is more useful than individual information.
Challenge: Given a hidden database, develop techniques that make it very
difficult to obtain uniform random samples of the database via its search interface without necessitating human intervention.
Privacy of Preservation of Aggregates
Some AssumptionsData is only accessible through a web-
based interfaceConsider sampling attacks onlyKeep bona fide users unaffectedExternal knowledge is omittedConsider Boolean attribute and extend it to
categorical or numerical one
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Preliminaries
Terms:D: database tablem: number of tuples in DQs: search querySel(Qs): the result set of tuples in D that satisfy Qs
n: number of predicates in QsNotification
If |Sel(Qs)|>k, only the top-k tuples in Sel(Qs) will be returned according to a ranking function.
Preliminaries (Cont.)
A query Qs is called – Underflow; if |Sel(Qs)|=0– Overflow; if |Sel(Qs)|>k– Valid; if 0<|Sel(Qs)|≤k
Universal space Ω : the set of all possible search queries
Active space Θ : a subset of Ω containing only those queries that are candidates for issuing at a subsequent time
Problem Definition
(ε,δ)-privacy For a sensitive aggregate query QA:
(ε,δ,p)-privacy
Problem
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Our Approach
Observation To obtain a uniform random sample tuple t, a sampler must have
discovered at least one valid research query that contains t in its result.
Main idea In order to thwart sampling attacks, we carefully construct and
insert dummy tuples into databases such that most valid and some underflowing queries are converted to overflowing queries.
Single-Sample Attack
Observation
|Ω|=3n
Pr(picking a valid query)≤m•(2/3)n
Three possible outcomes of Q1:– underflow : the size of Θ shrinks to 3n-1 – overflow : the size of Θ shrinks to 3n-1 – valid: the size of Θ shrinks to 1
Single-Sample Attack and Defense
Three possible outcomes of Qc:– underflow : the size of Θ shrinks to (c+1)3n-c – overflow : the size of Θ shrinks to |Θ|/3c – valid: the size of Θ shrinks to 1
Key Observation:− Shrinking Θ significantly reduces sampling
query cost.− Valid queries as well as long overflowing
queries contribute the most to shrinking Θ.
Single-Sample Defense
Techniques: Neighbor Insertion It is difficult to find long overflowing queries,
with Pr ≤ m/2c.Short valid queries are the most dangerous
threat. We insert dummy tuples into the “neighboring zone” of real tuples, such that all valid queries with fewer than b predicates will overflow, b is a parameter.
Multi-Sample Attack and Defense
Similarly, we analyze the shrinkage of ΘE and ΘF , and try to minimize it.
Multi-Sample Attack and Defense
Three possible outcomes of Qc:– underflow : up to (c+1)3n-c queries should be removed
from both ΘE and ΘF.
– overflow : 2c queries removed from ΘE, ΘF can be as small as |ΘE|/3c .
– valid: similar to underflow, (c+1)3n-c queries should be removed from both ΘE.
Key Observations Shrinking ΘE contributes more to the efficiency of
sampling than shrinking ΘF. Short underflowing queries become a major threat to
defense.
Multi-Sample Defense
Techniques: High-Level PackingTo convert short underflowing queries to
overflowing ones, we add dummy tuples such that all underflowing queries with fewer than d predicates will overflow, d is a parameter.
For example:
SELECT * FROM D WHERE a1=1
when k=1, we add <1,0,…,0> and <1,0,…,1>
COUNTER-SAMPLER Algorithm
Extensions
The COUNTER-SAMPLER can be directly applied to both Boolean and categorical databases.
For numerical data, we can use discretization techniques to convert it into categorical data.
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Privacy Guarantee
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Delay of Sampling for Boolean
Delay of Sampling for categorical
Efficiency
Outline
IntroductionProblem DefinitionOur ApproachPrivacy GuaranteeExperimentsConclusion
Conclusion
Main contributionsDevelop a dummy tuple insertion method to
prevent sampling of hidden databases.Extend it to categorical and numerical
databasesFuture Directions
Integration of dummy insertion and query auditing
Take external knowledge in to consideration
Thank you!