# New Approach To Handle Information Leakage English Language Essay

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Abstract- We explore the problem of managing information leakage by connecting two hitherto disconnected topics: entity resolution (ER) and data privacy (DP). As more of our sensitive

## data gets exposed to a variety of merchants, health

## care providers, employers, social sites and so on, there is

## a higher chance that an adversary can "connect the dots"

## and piece together our information, leading to even more

## loss of privacy. For instance, suppose that Alice has a social

## networking profile with her name and photo and a web

## homepage containing her name and address. An adversary

## Eve may be able to link the profile and homepage to connect

## the photo and address of Alice and thus glean more

## personal information. The better Eve is at linking the information, the more vulnerable is Alice's privacy. Thus in

## order to gain DP, one must try to prevent important bits

## of information being resolved by ER. In this paper, we formalize

## information leakage and list several challenges both

## in ER and DP. We also propose using disinformation as a

tool for containing information leakage.

Keywords- data leakage,entity resolution,data privacy,

management,information

Introduction

In this paper we explore the connections between two hither todisconnected topics: entity resolution and data privacy.

In entity resolution (ER), one tries to identify data records

that refer to the same real world entity. Matching records

are often merged into "composite" records that reflect the

aggregate information known about the entity. The goal of

data privacy (DP) is to prevent disclosure to third parties of

sensitive user (entity) data. For instance, sensitive data can

be encrypted to make it hard for a third party to obtain, or

the sensitive data can be "modified" (e.g., changing an age

24 to a range "between 20 and 30").

We will argue that in a sense ER and DP are opposites:

the better one is at ER, them more one learns about real

world entities, including their sensitive information. And to

achieve DP, one must try to prevent the bits of information

that have been published about an entity from being glued

together by ER.

To illustrate, we present a simple motivating example.

Consider an entity (person) Alice with the following information:

her name is Alice, her address is 123 Main, her phone number is 555, her credit card number is 999, her social security number is 000. We represent Alice's information as the record: { (N, Alice), (A, 123 Main), (P, 555), (C, 999),

(S, 000) }. Suppose now that Alice buys something on the

Web and gives the vendor a subset of her information, say

{(N, Alice), (A, 123 Main), (C, 999)}. By doing so, Alice has

already partially compromised her privacy. We can quantify

this "information leakage" in various ways: for instance we

can say that the vendor has 3 out of 5 of Alice's attributes,

hence the recall is 3/5 . We view leakage as a continuum, not

as all-or-nothing. Low leakage (recall in our example metric)

is desirable, since the vendor (or third party) knows less

about Alice, hence we try to minimize leakage. (Note we

can actually weight attributes in our leakage computation

by their sensitivity.)

Next, say Alice gets a job, so she must give her employer

the following data: {(N, Alice), (A, 123 Main), (P, 555), (S,

000)}. In this case the leakage is 4/5. This is where ER

Comes into play: If the employer and vendor somehow pool

Their data, they may be able to figure out that both records

refer to the same entity. In general, in ER there are no

unique identifiers: one must analyze the data and see if there

is enough evidence. In our example, say the common name

and address (and the lack of conflicting information)

imply that the records match and are combined (and say the

attributes are unioned). Then the third party has increased

leakage (recall) to 1.

If Alice wants to prevent this increase in leakage, she may

release disinformation, e.g., a new record that prevents the

resolution that increased leakage. For example, say that

Alice somehow gives the vendor the following additional

record: {(N, Alice), (A, 123 Main), (P, 666), (C, 999)}.

(Note the incorrect phone number.) Now the vendor resolves this third record with its first record, reaching the

conclusion that Alice's phone number is 666. Now, when

the vendor and employer pool their information, the different phone numbers lead them to believe that records correspond to different entities, so they are not merged and

leakage does not increase. The incorrect phone number also

decreases another metric we will consider, precision, since

now not all of the third party's data is correct. Thus, leakage can decrease, not just by knowing less about Alice, but by mixing the correct data about Alice with incorrect data.

Before proceeding with the main body of our paper, we

highlight the key features of our approach, which we believe make it well suited for studying ER and DP:

â€¢ Although not illustrated in our example, our model

Captures data confidences and multiple attribute values,

Both which arise naturally in ER. In particular, we believe

less information has leaked if a third party is uncertain

about Alice's attributes, as opposed to the case where the

third party is certain.

â€¢ In most DP work, privacy is all-or-nothing, while as

Mentioned above, our leakage ranges between 0 (no

informationknown by third party) to 1 (all information, and

only correct information, is known). We believe that our

continuous leakage model is more appropriate in our case:

Alice must give out some sensitive data in order to buy

products, get jobs, and so on. We cannot guarantee full

privacy in this context; we can only quantify (and hopefully

minimize) leakage. Furthermore, we are able to capture

the notion that more leaked attributes is worse than

fewer. For example, if a third party only knows our credit

card number, that by itself is not a great loss. If the third

party also learns our card expiration date, that is a more

serious breach. If in addition they know our name and

address, the information leakage is more serious.

â€¢ So far we have phrased leakage as a bad thing, something

to be minimized. However, our model can also be used

to study the mirror problem, where a good analyst is using

ER to discover information about "bad guys". Here

the goal is to maximize leakage, i.e., to discover how to

perform ER so we can learn the most correct information

about adversaries.

As we will show, our framework can help us answer fundamental questions on information leakage, for instance:

â€¢ Alice needs to give certain information to a store. She

may want to know the impact of this release: Will the

new information allow the store to "connect the dots"

and piece together many previously released records? Or

will the leakage increase be minimal?

â€¢ An analyst may want to understand what ER algorithms

are best to increase information leakage.

â€¢ Alice may want to use disinformation to reduce the impact

of previously leaked information. By adding some bogus

information about herself, it becomes more costly for Eve

to resolve Alice's correct information.

In this short paper we present a relatively brief summary

of our work on the convergence of ER and DP.

In a nutshell, our contributions are two-fold:

(1) We propose a framework for measuring information leakage (summarized in Section 2 of this paper), and

(2) We study how the framework can be used to answer a

variety of questions related to leakage and entity resolution.

Section 3 of this paper briefly describes two of the

questions we have studied (exemplified by the first and

third bullets immediately above).

Models and Algorithms

We assume a database of records R = {r1, r2, . . . , rn}.

The database could be a collection of social networking profiles, homepages, or even tweets. Or we can also think of R

as a list of customer records of a company. Each record r

is a set of attributes, and each attribute consists of a label

and value. (In Section 2.4 we extend the model to values

with confidences.) We do not assume a fixed schema because records can be from various data sources that use different attributes. As an example, the following record may represent

Alice:

r = {(N,Alice), (A, 20), (A, 30), (Z, 94305)}

Each attribute a âˆˆ r is surrounded by angle brackets and consists of one label a.lab and one value a.val. Notice that

there are two ages for Alice. We consider (A, 20) and (A,

30) to be two separate pieces of information, even if they

have the same label. Multiple label-value pairs with identical labels can occur when two records combine and the label-value pairs are simply collected. In our example, Alice may have reported her age to be 20 in some case, but 30 in others. (Equivalently, year of birth can be used instead of age.) Although we cannot express the fact that Alice has only one age (either 20 or 30), the confidences we introduce in Section 2.4 can be used to indicate the likelihood of each value.

A. Record Leakage

We consider the scenario where Eve has one record r of

Alice in her database R. (We consider the case where R

contains multiple records in Section 2.2.) In this scenario,

we only need to measure the information leaked by r in

comparison to the "reference" record p that contains the

complete information of Alice. We define Lr(r, p) as the

record leakage of r against p.

While leakage can be measured in a variety of ways, we

believe that the well known concepts of precision and recall

(and the corresponding F1 metric) are very natural for this

task. We first define the precision Pr of the record r against

the reference p as |râˆ©p|/ |r| . Intuitively, Pr is the fraction of

attributes in r that are also correct according to p. Suppose

that p = {(N, Alice), (A, 20), (P, 123), (Z, 94305)} and

r = {(N, Alice), (A, 20), (P, 111)}. Then the precision

of r against p is 2/3 â‰ˆ 0.67. We next define the recall Re

of r against p as |râˆ©p|/|p| . The recall reflects the fraction of

attributes in p that are also found in r. In our example,

the recall of r against p is 2/4 = 0.5. We can combine the

precision and recall to produce a single metric called

F1 =(2*Pr*re)/Pr+Re.

In our example, the F1 value is 2*0.6*0.5/0.67+0.5 â‰ˆ 0.57.

It is straightforward to extend our definitions of precision

and recall to weighted attributes, where the weight of an

attribute reflects its sensitivity.

B. Query Leakage

We now consider the case where Eve has a database R

containing multiple records. These records can represent

information on different entities, and can be obtained directly from the entities, from public sources, or from other organizations Eve pools information with.

When Eve had a single record (previous section), we implicitly assumed that the one record was about Alice and

we computed the resulting leakage based on what Eve knew about Alice. Now with multiple records, how does Eve know which records are "about Alice" and leak Alice's information?

And what happens if multiple database records are

about Alice?

To address these questions, we now define leakage, not

as an absolute, but relative to a "query". For instance, Eve

Rec

Type

Atrributes

r1

Social

(N, Alice) , (P, 123) , (B, Jan. 10)

r2

Homepage1

(N, Alice) , (C, Google), (A, 30)

r3

Homepage2

(N, Alice), (E, Stanford) , (A, 20)

r4

Homepage3

(N, Alice), (C, Boggle), (A, 50)

Table 1: Records of Alice on the Web

may pose the query "What do I know about {(N, Alice), (A, 123Main)}". In this case, Eve is saying that the attributes

"name: Alice" and "address: 123Main" identify an entity of

interest to her, and would like to know what else is known

about this entity. Note that this pair of attributes is not

necessarily a unique key that identifies entity Alice; the two

attributes are simply how Eve thinks of entity Alice. They

may be insufficient to uniquely identify Alice, they may be

more than is needed. Furthermore, there could be different

attributes that also identify Alice.

Our next step is to compute leakage (relative to this query)

by figuring out what Eve knows related to {(N, Alice), (A,

123Main)}. But which database records are related to this

query? And how are all the related records combined into

what Eve knows about Alice?

To answer these questions, we introduce what we call the

match and the merge functions in ER. A match function M

compares two records r and s and returns true if r and s

refer to the same real-world entity and false otherwise. A

merge function Î¼ takes two matching records r and s and

combines them into a single record Î¼(r, s).

To illustrate how we use these functions to evaluate leakage,

consider the database of Table 1, owned by Eve. Suppose

that Eve identifies Alice by the query q={(N, Alice),

(C, Google)} (i.e., the Alice that works at Google). What

else does Eve know about this Alice? We use a process called

dipping to discover database records that match (defined by

our function) the query record. That is, we first look for

a database record that matches the query. When we find

it, we merge the matching record with the query, using our merge function. In our example, say record r2 matches q,

so we obtain rq = Î¼(q, r2). Then we look for any database record that matches rq, the expanded query, and merge it to

our expanded record. For instance, say M(rq, r1) evaluates

to true, so we replace rq by Î¼(rq, r1). We continue until no

other database record matches. This process is called dipping

because it is analogous to dipping say a pretzel (the

query) into a vat of melted chocolate (the database). Each

time we dip the pretzel, more and more chocolate may adhere

to the pretzel, resulting in a delicious chocolate-covered

pretzel (or an expanded query with all information related

to Alice). Note that dipping is a type of entity resolution,

where records in the database match against one record (the

pretzel), as opposed to any record in the database.

At the end of the dipping process, rq represents what Eve

knows about Alice (q), so we evaluate the leakage by comparing rq to Alice's private information p, as before. Note

that we will get different leakage for different queries. For instance, if Eve thinks of Alice as q={(N, Alice)}, more records

will conglomerate in our example, which may lead to lower

leakage (if r3 and r4 actually refer to different Alices) or

higher leakage (if r3 and r4 are the same Alice as r1 and r2).

In the remainder of this section we define the dipping

process more formally. We start by defining two properties

that match and merge functions generally have (and that

we assume for our work).

We assume two basic properties for M and Î¼ - commutativity

and associativity. Commutativity says that, if r

matches s, then s matches r as well. In addition, the merged

result of r and s should be identical regardless of the merge

order. Associativity says that the merge order is irrelevant.

â€¢ Commutativity: âˆ€r, s,M(r, s) = true if and only if M(s, r)

= true, and if M(r, s) = true, Î¼(r, s) = Î¼(s, r)

â€¢ Associativity: âˆ€r, s, t, Î¼(r, Î¼(s, t)) = Î¼(Î¼(r, s), t)

We believe that most match and merge functions will naturally

satisfy these properties. Even if they do not, they can

easily be modified to satisfy the properties. To illustrate the

second point, suppose that commutativity does not hold because M(r, s) only compares r and s if r has an age smaller

or equal to s and returns false otherwise. In that case, we

can define the new match function Mâ€²(r, s) to invokeM(r, s)

if r's age is smaller or equal to s's age and invoke M(s, r) if

s's age is smaller than r. In the case where the two properties

are not satisfied, we only need to add a few more lines

in our dipping algorithms for correctness.

Before defining the dipping result of a set of records, we

define the "answer sets" for Alice. Throughout the paper, we

use the short-hand notation Î¼(S) for any associative merge

function Î¼ as the merged result of all records in the set of

records S (if S = {r}, Î¼(S) = r).

Definition 2.1. Given a query q, a match function M,

a merge function Î¼, and a set of record R, the collection of

answer sets is A = {S1, . . . , Sm} where each Si âˆˆ A is a set

of records that satisfies the following conditions.

## â€¢

## â€¢

â€¢ The records in Si âˆ’ {q} can be reordered into a sequence

[r1, . . . , rm] such that M(q, r1) = true, M(Î¼(q, r1), r2) =

true, . . . , M(Î¼({q, r1, . . . , rmâˆ’1}), rm) = true

For example, suppose we have a database R = {r1, r2}

where r1 and r2 are clearly not the same person and have

the names Alice and Alicia, respectively. However, say the

query q matches either r1 or r2 because it contains both

names Alice and Alicia and no other information. Then the

answer set is A = {{}, {q, r1}, {q, r2}}. Notice that in this

example the set {q, r1, r2} is not in A because r1, even after

it merges with q, does not match r2.

A dipping result of R is then the merged result of a "maximal"

answer set from Definition 2.1 that has no other matching

record in R.

Definition 2.2. Given the collection of answer sets A, a

match function M, and a merge function Î¼, rq = Î¼(S) is a

dipping result if

Continuing our example from above, the dipping result rq

can be either Î¼(r1, q) or Î¼(r2, q) because once q merges with

r1 (r2), it cannot merge with r2 (r1). Notice that we exclude

the case of merging multiple records with rq at a time. For

example, even if rq matches with the merged record Î¼(r, s),but not with r or s individually, then we still cannot merge

rq with r and s.

While Definition 2.2 assumes that one record is added

to q at a time, it can easily be extended to capture more

sophisticated dipping such as adding multiple records to q

at a time.

We define the query leakage Lq(p, q,M, Î¼,R) of Alice as

the maximum value of Lr(p, rq) for all possible dipping results

rq that can be produced using the match and merge

functions M and Î¼ on the database R. In general, deriving

the query leakage is an NP-hard problem ..

Properties. We identify two desirable properties for M and

Î¼: representativity and negative representativity.

Representativity says that a merged record Î¼(r, s) "represents" r ands and matches with all records that match with either r or

s. Intuitively, there is no "negative evidence" so merging r

and s cannot create evidence that would prevent Î¼(r, s) from

matching with any record that matches with r or s. It can

be shown that representativity guarantees the uniqueness of

a dipping result and is needed for efficient dipping. Negative

representativity says that two records r and s that do

not match will never match even if r or s merges with other

records. That is, there is no "positive evidence" where r and

s will turn out to be the same entity later on. The negative

representativity property also enables efficient dipping.

Note that the two properties above do not assume that r

matches with s. We can show that none of the properties

imply each other.

â€¢ Representativity: If t = Î¼(r, s), then for any u where

M(r, u) = true, we also have M(t, u) = true

â€¢ Negative Representativity: If t = Î¼(r, s), then for any u

where M(r, u) = false, we also have M(t, u) = false

We illustrate a match function called Mc and merge function

called Î¼u that satisfy both representativity and negative

representativity . The Mc function uses

a single "key set" for comparing two records. A key set k is

a minimal set of attribute labels {l1, . . . , lm} that are

sufficient to determine if two records are the same using equality checks.

All records are assumed to have values for the keyset

attributes. The Mc function then matches r and s only

if they have the exact same key-set attributes. For example,

given the key set k = {A,B}, the record r = {(A, a),(B, b)}

matches with s = {(A, a), (B, b), (C, c)}, but not with t =

{(A, a), (A, aâ€²), (B, b)}. As another example, the record r =

{(A, a1), (A, a2), (B, b)} matches with s = {(A, a1), (A, a2),

(B, b)}, but not with t = {(A, a1), (B, b)}. The merge

Function Î¼u unions the attributes of r and s

(i.e., Î¼(r, s) = ).

For instance, if r = {(A, a), (B, b)} and s = {(A, a), (C, c)},

then Î¼(r, s) = {(A, a), (B, b), (C, c)}.

Dipping Algorithms. In our technical report [5], we explore

various dipping algorithms that exploit properties. (Table

2 in Section 2.5 summarizes their complexities.)

C. Database Leakage

What happens if we do not know how Eve identifies Alice,

i.e., if we do not have a specific query q? In such a case, we

may assume that Eve can think of any one of the records

in R as "Alice's record". Thus, for each R record we can

compute a leakage number, and by taking the maximum

value we can obtain a worst case leakage, representing what

Eve can potentially know about Alice.

More formally, we define the database leakage Ld(p,M, Î¼,R)

as That is, for each record

we compute the dipping of q on R âˆ’ {q} (i.e., the

database without q) and choose the worst-case query leakage

of Alice as the entire database leakage. In our technical

report [5], we explore various algorithms that compute the

database leakage of R (Table 2 in Section 2.5 summarizes

their complexities) as well as techniques to further scale the algorithms.

D. Uncertain data

As we argued in the introduction, data confidence plays

an important role in leakage. For instance, Eve "knows more

about Alice" if she is absolutely sure Alice is 50 years old

(correct value), as opposed to thinking she might be 50 years

old with say 30% confidence, or thinking Alice is either 30

or 50 years old. To capture this intuition, we extend our

model to include uncertain data values. Note that there are

many ways to model data uncertainty, and our goal here is

not to use the most sophisticated model possible. Rather,

our goal is to pick a simple uncertainty model that is

sufficient for us to study the interaction between uncertainty

and information leakage.

Thus, in our extended model, each record r in R consists

of a set of attributes, and each attribute contains a

label, a value, and a confidence (from 0 to 1) that captures

the uncertainty of the attribute (from Eve's point of view).

Any attribute that does not exist in r is assumed to have a

confidence of 0. As an example, the following record may

represent Alice:

r = {(N,Alice, 1), (A, 20, 0.5), (A, 30, 0.4), (Z, 94305, 0.3)}

That is, Eve is certain about Alice's name and age, but

is only 50% confident about Alice being 30 years old, 40%

confident in Alice being 30 years old, and 30% confident

about Alice's zip code 94305. For each attribute we

can access a's label a.lab, a single value a.val, and confidence

a.cnf. In Table 1, the outdated record r3 of Alice can be

viewed to have a lower confidence than the up-to-date record

r2. We assume that attributes in the reference p always have

a confidence of 1. We require that no two attributes in the

same record can have the same label and value pair.

The confidences within the same record are independent

of each other and reflect "alternate worlds" for Eve's belief

of the correct Alice information. For example, if we have

r = {(name, Alice, 1), (age, 20, 0.5), (phone, 123, 0.5)},

then there are four possible alternate worlds for r with equal

probability: {(name, Alice)}, {(name, Alice), (age, 20)},

{(name, Alice), (phone, 123)}, and {(name, Alice), (age,

20), (phone, 123).

We show one example on how our record leakage metrics in Section2.1 can be extended to use confidences. We

first define the notation IN(r, s) for two records r and s as That is

IN(r, s) denotes the attributes of r whose label-value pairs

exist in s. The precision Pr or a record r against the reference

p is defined as

Compared to the previous

definition in Section 2.1, we now sum the confidences

of the attributes in r whose label-value pairs are also in p

and divide the result by the total confidence of r. The recall

Re of r against p is defined as

Confidence

Properties

Query

Database

No

(none)

NP-hard

NP-hard

No

Representativity

O(N2)

O(N3)

No

Neg. RepresentativityRepresentativity

O(N)

O(N2)

Yes

(none)

NP-hard

NP-hard

Yes

Representativity

Monotonicity

Increasing

O(N2)

O(N3)

Yes

Neg. Representativity

Representativity

Monotonicity

Increasing

O(N)

O(N2)

Table 2: Summary of Leakage Measurements

This time, we divide the sum of confidences of the attributes in r whose label-value pairs are also in p by the total confidence of p.

We define the record leakage Lr as the F1 metric .

we elaborate on how to extend our leakage algorithms to take into account confidences. In addition, we discuss two properties (called monotonicity and increasing) for the extended match and merge functions that can be exploited to compute leakage efficiently.

E. Summary of Contributions

As mentioned earlier, Table 2 summarizes the scenarios

we have considered in our work. The first column shows

whether or not the adversary (which we call Eve) uses

confidences in the leakage model. The second column shows

properties that are satisfied by the match and merge

functions.

For each scenario (row) we have developed an algorithm

that computes either query or database leakage (given

a reference record p for Alice, and a database R held by

Eve), and columns 3 and 4 show the complexity of these

algorithms. As one can see in the table, the more properties

that hold, the more efficiently we can compute leakage.

The properties depend on the data semantics, and different

applications (e.g., commercial products, publications,

personal information) will have different properties. To

show that the properties are achievable in practice, for each

scenario in Table 2 we have developed simple match and

mergefunctions that satisfy the corresponding properties.

III. Using our framework

Our framework can be used to answer a variety of questions,

and here we illustrate two questions. As we use our

framework, it is important to keep in mind "who knows

what". In particular, if Alice is studying leakage of her

information (as in the two examples we present here), she

needs to make assumptions as to what her adversary Eve

knows (database R) and how she operates (the match and

merge functions, and dipping algorithm Eve uses). These

types of assumptions are common in privacy work, where

one must guess the sophistication and compute power of an

adversary. On the other hand, if Eve is studying leakage she

will not have Alice's reference information p. However, she

may use a "training data set" for known individuals in order

to tune her dipping algorithms, or say estimate how much

she really knows about Alice.

A. Releasing Critical Information

Suppose that Alice wants to purchase a cellphone app

from one of two stores S1 and S2, and is wondering which

purchase will lead to a more significant loss of privacy. Both

stores require Alice to submit her name, credit card number,

and phone number for the app. However, due to Alice's

previous purchases, each store has different information

about Alice.

In particular:

â€¢ Alice's reference information is p = {(N, n1, 1), (C, c1,

1), (C, c2, 1), (P, p1, 1), (A, a1, 1)} where N stands for

name, C for credit card number, P for phone, and A for

address.

â€¢ Store S1 has one previous record R1 = {r = {(N, n1, 1),

(C, c1, 1), (A, a1, 1)}}. That is, Alice bought an item

using her credit card number and shipping address. (We

omit the item information in any record for brevity.)

â€¢ Store S2 has two previous records R2 = {s = {(N, n1, 1),

(C, c1, 1), (P, p1, 1)}, t = {(N, n1, 1), (C, c2, 1), (A, a1,

1)}}. Here, Alice has bought items using different credit

cards. The item of s could be a ringtone that required a

phone number for purchasing, but not a shipping address.

â€¢ Both S1 and S2 require the information u = {(N, n1, 1),

(C, c2, 1), (P, p1, 1)} for the cellphone app purchase. Since

Alice is purchasing an app, again no shipping address is

required.

To compute leakages, say Alice is only concerned with

the previously released information, so she assumes that

the database at store S1 only contains record r, while the

database at store S2 only contains s and t. (The stores are

not colluding in this example.) Alice also assumes that two

records match if their names and credit card numbers are the

same or their names and phone numbers are the same, and

that merging records simply performs a union of attributes.

Under these assumptions, before Alice's app purchase, the

database leakage for both stores is 3/4 .

For the first store, R1 only contains one record r, so the database leakage is

Lr(p, r)= (2Ã-1Ã-3/5)/(1+3/5) =3/4

For the second store, R2 contains two records s and t, so we need to take the maximum of the query leakages of s and t. Since s and t do not match with each other (i.e., they do not have the same name and credit card or name and phone combination), the dipping result of s is s while the dipping result of t is t. Hence, the database leakage is

max{Lr(p, s),Lr(p, t)} =

.If Alice buys her app from S1, then its database will contain

two records, r and u. In this case, the database leakage

at S1 is still 3/4 because r and u do not match and thus

have the same query leakage 3/4 (the maximum query leakage

is thus 3/4 ). On the other hand, if Alice buys from S2, the

database at S2 will contain s, t, and u. Since u matches with

both s and t, the dipping result of u is Î¼({s, t, u}), which is

identical to p. Hence, the database leakage becomes 1.

To compare Alice's two choices, it is useful to think of the

incremental leakage, that is, the change in leakage due to

the app purchase. In our example, the incremental leakage

at S1 is 3/4 - 3/4 = 0 while the incremental leakage at S2 is

1âˆ’ 3/4 = 1/4 . Thus, in this case Alice should buy her app from

S1 because it preserves more of her privacy.

B. Releasing Disinformation

Given previously released information R, a match function

M, and a merge function Î¼, Alice may want to release

either a single record or multiple records that can decrease

the query or database leakage. We call records that are used

to decrease the database leakage disinformation 1 records.

Of course, Alice can reduce the query or database leakage

by releasing arbitrarily large disinformation. However, disinformation itself has a cost. For instance, adding a new

social network profile would require the cost for registering

information. As another example, longer records could require

more cost and effort to construct. We use C(r) to

denote the entire cost of creating r.

We define the problem of minimizing the database leakage

using one or more disinformation records. Given a set of

disinformation records S and a maximum budget of Cmax,

the optimal disinformation problem can be stated as the

minimization function presented below:

The problem of minimizing the query leakage can also be

stated by replacing Ld by Lq in the above formula. The set

of records S that minimizes the database leakage within our

cost budget Cmax is called "optimal" disinformation.

A disinformation record rd can reduce the database leakage

in two ways. First, rd can perform self disinformation

by directly adding the irrelevant information it contains to

the dipping result rq that yields the maximum query leakage.

For example, given the database R = {r, s, t} and a

reference p, suppose the database leakage is Lr(p, Î¼(r, s)).

Then rq can be created to match with Î¼(r, s) and to contain

bogus data not found in p, thus decreasing database

leakage to Lr(p, Î¼({r, s, rd})). Second, rd can perform linkage

disinformation by linking irrelevant records in R to rq.

For example, say that t contains totally irrelevant information

of the target p. If rd can be made to match with both

Î¼(r, s) and t, then the database leakage could decrease to

Lr(p, Î¼({r, s, t, rd})) because of rd. Of course, rd can also

use both self and linkage disinformation.

When creating a record, we use a user-defined function

called Create(S, L) that creates a new minimal record that

has a size less or equal to L and is guaranteed to match all

the records in the set S. If there is no record r such that

|r| â‰¤ L and all records in S match with r, the Create function

returns the empty record {}. A reasonable assumption

is that the size of the record produced by Create is

proportional to |S| when L > |S|. We also assume a function

called Add(r) that appends a new attribute to r. The new

attribute should be "incorrect but believable" (i.e., bogus)

information. We assume that if two records r and s match,

they will still match even if Add appends bogus attributes to

either r or s. (Notice that this property is similar to the

representativity property for match and merge functions.)

The Create function is assumed to have a time complexity

of O(|S|) while the Add function O(|r|).

We release a single disinformation record (S is size 1) and the case where we release multiple records.

In addition, we consider scenarios where different properties hold.If both representativity and negative representativity hold, one can show that a new record can only use self-disinformation to lower the database leakage, which enables efficient algorithms that return the optimal disinformation.

If the properties do not hold, a new record can

also use linkage disinformation, and we might have to

consider all possible combinations of irrelevant records in

the worst case (which makes the disinformation problem

NPhard). Thus, we also propose a heuristic algorithm that

searches a smaller space, where we either combine two

irrelevant records and use self disinformation or use self

disinformation only. As more properties are satisfied by the

match and merge functions, the more efficient the

disinformation algorithms become. Similar results can be

obtained when using confidences and the monotonicity and

increasing properties for the extended match and merge

functions.

IV. Related Work

Many works have proposed privacy schemes for data

publishing in the context of linkage attacks. Various models

including k-anonymity [3] and l-diversity [1] guarantee that

linkage attacks on certain attributes cannot succeed. In

contrast, we assume that the data is already published and

that we want to manage the leakage of sensitive information.

Several closely related products manage information

leakage. A service called ReputationDefender [2] manages

the reputation of individuals, e.g., making sure a person's

correct information appears on top search results.

TrackMeNot [4] is a browser extension that helps protect web searchers from surveillance and data-profiling by search engines using noise and obfuscation. In comparison, our work complements the above works by formalizing information leakage and proposing disinformation as a general tool for containing leakage.

V. Conclusion

We have proposed a framework for managing information

leakage and studied how the framework can be used to

answer a variety of questions related to ER and DP. The algorithms for computing leakage become more efficient as the match and merge functions satisfy more properties. We have

studied the problems of measuring the incremental leakage

of critical information and using disinformation as a tool for

containing information leakage. We believe our techniques

are preliminary steps to the final goal of truly managing

public data, and that many interesting problems remain to

be solved.