Privacy Preserving Approaches for Global Cycle Detections for

Cyclic Association Rules in Distributed Databases

Nirali R. Nanavati and Devesh C. Jinwala

Computer Engineering Department, Sardar Vallabhbhai National Institute of Technology, Surat, India

Keywords: Privacy, Cyclic Association Rules, Distributed Setup.

Abstract: The current massive proliferation of data has led to collaborative data mining that requires preservation of

individual privacy of the participants. A number of algorithms proposed till date in this scenario are limited

to mining association rules and do not consider their cyclic nature that finds associations with respect to the

time segment. Hence catering to this challenge, we propose techniques for privacy preservation while

finding global cycles when mining cyclic association rules in a distributed setup. The proposed techniques

are based on homomorphic encryption and Shamir’s secret sharing that can help us decipher partial and total

global cycles along with maintaining privacy in a distributed setup. Additionally security, efficiency and

correctness analysis of the proposed algorithms are also given.

1 INTRODUCTION

The concept of coopetation (Pedersen and Saygn,

2007) which symbolizes a blend of competition and

cooperation has become an important practice for

various organizations to sustain and succeed in this

competitive world. The approach of coopetation has

its application in Distributed Data Mining in which

privacy needs of the participating parties are to be

guaranteed. That is, the data mining results of each

of the sites that satisfy a certain function only, must

be known in the cumulative data. The identities of

the participants and the remaining data that does not

satisfy the cumulative function must be kept secret.

The solution for efficient implementation of

privacy preserving techniques for distributed data

mining is one of the most researched and

challenging fields of study today.(Venkatadri and

Reddy, 2011)

A major limitation of the existing distributed

privacy preserving algorithms in this area (Kargupta

et al., 2007); (Kantarcioglu and Clifton, 2004);

(Kantarcioglu, 2008); (Vaidya, 2008); (Ge et al.,

2010); (Aggarwal and Yu, 2008); (Sang et al.,

2009); (Shi et al., 2011) is that none of them deal

with cyclic data or data that is segmented and

temporal.

The paper (Sang et al., 2009) does mention

privacy preserving tuple attribute matching in a

distributed setup; but again, it does not deal with

cyclic association rules. In addition, the recent work

by Shi et al. (Shi et al., 2011) does explain

approaches for aggregation of time series based data

using a third party aggregator with its main

application in wireless sensor networks; but then it

does not cater to cyclic association rules.

In a number of real life applications, data is time

based. So it is important to decipher the rules that

are frequent and repeat at regular time intervals.In

this context, we propose a construction comprising

of techniques to find global cycles among cyclic

association rules (Ozden et al., 1998); (Ben and

Gouider, 2010) (which is a subset of temporal rules)

while maintaining the privacy in a co-opetative

model. Our construction is restricted to a

horizontally partitioned homogeneous model. Any

scenario, where there are coopetative parties

involved and the data to be mined is segmented on

the basis of time, can use the approaches we propose

to exchange their information and preserve their

privacy as well.

The two proposed techniques for the multi-party

scenario are based on Efficient Private Matching

(EPM) (Freedman et al., 2004) and Shamir’s secret

sharing technique (Shamir and Adi, 1979)

respectively to find global cycles privately. These

methods have their pros and cons which have been

discussed in this paper.

368

R. Nanavati N. and C. Jinwala D..

Privacy Preserving Approaches for Global Cycle Detections for Cyclic Association Rules in Distributed Databases.

DOI: 10.5220/0004018803680371

In Proceedings of the International Conference on Security and Cryptography (SECRYPT-2012), pages 368-371

ISBN: 978-989-8565-24-2

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

An important example of such a scenario where

privacy preservation is required while mining global

cycles would be a group of television channels who

plan to share their data like their Television Rating

Points (TRPs), timings of the various programmes

being watched and various advertisements being

shown, by maintaining their privacy as well, so as to

figure out which TV program is being watched at

what time periodically by relatively more number of

viewers. The important thing to note here is that the

competing channels do not want to disclose their

identity and still be able to find out global cycles

(i.e. trends that repeat at regular intervals of time)

amongst every channel’s data.

2 THE PROPOSED ALGORITHM

We propose an algorithm that finds cyclic

association rules (Ozden et al., 1998) using the

interleaved algorithm that are supported at all the

participating parties privately. The problem

considers a co-opetative scenario of homogenous

databases where there are ‘p’ semi honest parties

collaborating to find the global cycles (cyclic and

frequent association rules in a particular time

segment at all the participating parties). Let there be

a set of ‘t

’ transactions and maximum N items at

each of the partitions (where 0 < i ≤ p) and each

transaction has a subset of ‘N’ items.

Let the schema at each of the sites be of the form

<tid, items, timestamp>. All the parties decide on

the local minimum Support ‘minSupp’, minimum

Confidence ‘minConf’ and the length of cycle which

is less than or equal to the set of transactions at each

of the parties. They also decide on one of the privacy

preserving protocols (explained below) that they

would follow.

In the first protocol i.e. Efficient Private

Matching algorithm (Freedman, Nissim and Pinkas,

2004), for the multiparty scenario, we consider p

parties, P

…P

, with corresponding lists of inputs

…X

which are the cyclic rules at each party. We

assume each list contains k

(0<i≤p) inputs. The

parties would be able to compute the intersection of

all p lists privately using homomorphic encryption

as explained in (Freedman, Nissim and Pinkas,

2004).

The second protocol is based on Shamir’s secret

sharing (Shamir and Adi, 1979); (Ge et al., 2010).

The algorithm finds the sum of the secret

information (which will help us decipher the global

cycles in our scenario privately) in the cumulative

data.

Figure 1: Secret sharing approach applicable to our

scenario.

There are 2 possible variations that can also be

applied to our approach:

1. If the co–opetative setup decides on finding

global association rules instead of global cycles; if

the association rule is cyclic; only then the count of

the item is exchanged privately (we could use Secret

Sharing or Secure Sum algorithm (Kantarcioglu,

2008) for this) by which we can calculate the global

support and hence find global association rules.

2. If partial cycles (cyclic association rules

supported at some of the parties) above a certain

threshold need to be determined; then the Secret

sharing approach could be used to determine

privately the count of the parties that support a

certain cyclic rule.

3 ANALYSIS

We begin by doing the correctness analysis of our

proposed protocols followed by the complexity and

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369

security analysis. To find the globally cyclic

association rules; assume that the party P

has a

private vector V

for a particular cyclic association

rule C

(j is the total number of rules possible). This

vector V

has bits for whether a particular rule is

cyclic or not in a time segment ‘k’ such that 1<k≤ t(t

is the total no. of time segments). Hence for a

particular rule C

; we try and find the

∑





for a

particular cyclic association rule in a particular time

segment across different parties.

Figure 2: Algorithm to find global cycles privately in a

distributed setup.

Let us consider the protocol 1 based on efficient

private matching. Since this scenario has (p-1)

partitions and one leader S; and for ∀ y ∈ S;the

leader prepares p-1 shares that XOR to y. Now each

party formulates a polynomial equation whose roots

are their respective inputs. The coefficients of these

polynomials are encrypted and sent to the leader.

The leader takes Enc( r

· P(y

′) + y

′ ) and sends

the users the Enc(yi′) where yi′ is one of the shares

that XOR to y ( y ∈ S). Hence all the p – 1 parties

will learn their share of Enc(yi′). The parties decrypt

their share and XOR it with the other parties. They

will learn y only if y ∈ P

∩ P

∩ P

∩ ….S. Hence

we will be able to find the cyclic association rule

that is supported by all the parties privately.

On the other hand, considering the protocol 2

using the secret sharing, we need to solve the linear

equations formulated which have p unknown

coefficients and n equations. Since the polynomials

would have a unique solution; each party P

can

solve the equation and find the value of

∑





for

a particular cyclic association rule. However it

cannot determine the secret values of the other

parties as the polynomial coefficients of each party

are hidden from the other.

If the

∑





= p; it implies that a global cycle

does exist among all parties for C

in the time

segment k. If on the other hand

∑





= z (z < p) ;

it implies that a partial cycle exists at z parties.

Similarly other global cycles can be deciphered

privately with respect to time with the condition that

all parties follow the protocol honestly.

For the complexity analysis, consider first the

complexity of the cyclic association rules

generation. If we have n items, x time segments and

transactions (0 < i ≤ p) such that p is the no. of

partitions; then the number of possible association

rules with respect to time is O(x*n*2

n-1

). So the

computation complexity of the cyclic association

rule generation would be O(n*max(t

)*2

*x).

For the efficient private matching algorithm; the

communication overhead is O (pk) where there are

p-1 parties and one leader and k coefficients sent

using homomorphic encryption to the leader. As far

as the computation cost is concerned it involves

encryption and decryption of k values at each

partition site and for the leader to compute p-1

shares that XOR to y and Enc ( r

·P(y

′) + y

′ ) using

k exponentiations and hence total O(k

). Thus, this

protocol has a much lesser communication cost

compared to the Protocol 2 that uses Shamir’s secret

sharing technique.

Secondly, for the secret sharing algorithm with

‘p’ parties; each party sends its shares to ‘p-1’ other

parties and if we consider ‘k’ such bits based on the

no. of transactions and the no. of time segments; the

complexity would be O (kp

Along with the communication cost there would

also be the computation cost of generating the

random polynomial, p

computations, p(p-1)

additions, and solving the equations with unknowns

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to find the sum

∑





Regarding the security analysis, our protocol that

finds global cycles based on efficient private

matching is semantically secure from attackers and

also preserves privacy. The data of all the clients is

private as the leader only sees the encrypted

coefficients. The leader’s privacy is also protected as

he only sends across encrypted shares that XOR to y

and hence the actual value of y is not known to the

different participants.

Our protocol based on secret sharing, is also

semantically secure from the network attackers. i.e.

network attackers cannot learn any valuable

information except for the shares of each of the

parties which would be of no use. This algorithm

can also effectively prevent collusive behaviour if

the number of collusive parties c < p-1.

4 CONCLUSIONS

In this paper we define a new problem of detecting

partial and total global cycles in a co-opetative setup

while maintaining the privacy of the individual

parties.

We extend the interleaved algorithm to find

global cycles in cyclic association rules privately.

Our first algorithm has higher computation cost and

lesser communication cost compared to the second

one based on Shamir’s Secret sharing.

However there are a few open research

challenges that which include applying these privacy

preserving theories to other temporal rule mining

methods like calendric association rules, temporal

predicate association rules, OLAP cubes and

sequential association rules. The algorithm could

also be extended to a heterogeneous setup and to

malicious models. Since our approach considers the

threshold count at each of the parties individually for

a particular item and gives equal importance to all

the participants; an extension to this could be to

privately decipher global cyclic association rules

considering the global count of the respective item

and hence giving importance to the parties with

respect to their transaction data size.

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