Secure Incremental Maintenance of Distributed Association Rules

1
Secure Incremental Maintenance of Distributed
Association Rules
2
Agenda

• Introduction
• Secure Technologies
• Problem Definition
• Our algorithm
• Experiments
• Conclusions

3
Introduction

• Association Rules
• A means to identify patterns and trends
• Secure Distributed Association Rules
• Privacy is concerned
• Restricted usage of some information
• Maintenance of environment
• Association rules with more sites
• Use past results to reduce workload

4
Secure Data Mining

• Approach 1 Data Obfuscation
• Association rules from modified data
• Simple algorithms but may get false rules
• Approach 2 Secure Protocols
• Complex communication
• Difficult and costly algorithms but get accurate
  rules
• Balance between cost and privacy

5
Secure Technologies

• Secure Sum
• There are n sites
• Each site holds a private number
• Compute the sum of a group of sites
• Secure Union
• There are n sites
• Each site holds a private set of items
• Compute the union of sets

6
Secure Sum Example
10
Site 1
Upper Bound 40
R 28
17 28 mod 40 29
8
11
38
17
38 11 mod 40 9
Site 2
Site 3
9
7
Secure Technologies

• Secure Comparison
• Two sites
• A site holds a number a, another holds a number b
• Check if a gt b without letting anyone knows the
  value of a and b

8
Problem Definition

• There are n old sites
• Knows the association rules in these sites
• There are r new sites
• Requires update of association rules in new
  environment
• Maintain the privacy as well

9
Privacy? What to protect?

• Different requirements in different situation
• Basic requirements
• Protect individual transaction
• Protect individual site information
• Local large itemsets, counts for itemsets
• Secure Multi-party computation
• The process does not reveal any other useful
  information except the information that can be
  derived from own input and the final result

10
Algorithms

• Secure Incremental Maintenance of Distributed
  Association Rules (SIMDAR)
• Mining association rules with basic privacy level
• More Secure Incremental Maintenance of
  Distributed Association Rules (MSIMDAR)
• Mining association rules under the definition of
  Secure Multiparty computation

11
SIMDAR What we know? (Assumption)

• Original Large Itemset Lk is available
• Total count for each old large Itemset is known
• All sites follow a semi-honest model
• They follow the rules, but may try to guess
  others information based on the received data
  (intermediate messages)
• No collusion among any sites
• Sites do not exchange intermediate information

12
Algorithm - SIMDAR

• To find the large itemsets
• Generate the candidate sets
• Count on the candidates
• Summing counts
• Check for large itemset
• Check if an association rule holds
• Easy with counts available

13
Generate the candidates

• C1 I
• For Ck,
• Each new site generates its own candidate set
  with own (k-1)th locally large and globally large
  itemsets
• Secure Union to find the candidate sets from the
  new sites
• Union with Lk

14
Summing on candidates

• Partition into 2 groups
• Pk in Lk
• Qk not in Lk
• For Pk, we got the original count, just add up
  the count in new sites using secure sum (no scan
  on old sites)

15
Summing Count for Qk

• First summed up in new sites, we get a count
• If the itemset is large in new sites, send to old
  sites for scan
• Otherwise, prune away

16
Information Protected by SIMDAR

• Individual transaction
• We never access to individual transaction of
  others
• Large Itemset of specific site
• They are input to Secure Union
• Count of each Itemset on each site
• They are input to Secure Sum

17
MSIMDAR for Higher privacy level

• Final result global association rules
• Input Site database
• Other information should be protected
• Cannot reveal large itemsets?
• Costly checking
• We treat the large itemsets as part of the result

18
MSIMDAR

• Target Global large itemsets and association
  rules
• Useful information revealed by SIMDAR
• Total Counts of itemsets
• Original results of large itemset to new sites
• New Candidates at new sites to old sites
• Add fake itemset to hide the actual supported
  itemsets

19
MSIMDAR

• Hiding the total count of an itemset
• Do we really need to find out the total count?
• Protect the large itemsets of the original
  results
• Use a more complex protocol

20
MSIMDAR Adding

• Total excess count
• X.excess X.count s DB
• Instead of summing X.counti, we sum the excess
  count X.excessi
• Even revealed, we cannot know the count and
  database size
• Checking for large itemsets after Secure Sum
• Sa (the first site) holds random key Rx
• Sb (the last site) holds (X.count s DB Rx)
• Secure Comparison between Sa and Sb

21
Storage

• We can reuse it in future and we need it in the
  future
• Checking for association rules requires counting
  information
• Prepare for next update

22
Storage

• Commonly used method
• Each site holds their own information
• Count for each itemset
• Database size
• need to calculate the total count each time

23
Storage

• We first sum the total database size DB using
  Secure Sum
• Su (first site) holds the key of secure sum Rt
• Sv (last site) get the sum DB Rt
• For each itemset X, we store also
• The protecting key Rx
• The protected excess count X.excess Rx

24
Reusing the count

• Checking association rules
• A.count c B.count gt 0
• Can be derived by six stored numbers
• N1 (-1)N2 (-c)N3 (c)N4 (c-1)sN5
  (1-c)N6
• N1 A.excess Ra
• N2 Ra
• N3 B.excess Rb
• N4 Rb
• N5 DB Rt
• N6 Rt
• Secure sum and secure comparison

25
Avoiding new sites knowing past results

• Generating the candidates is similar except an
  old site will join to the Secure Union process
• For counting, two old sites will join
• Define
• Pk Lk intersect Ck
• Qk Ck Pk
• Note that the new sites should not be able to
  distinguish Pk and Qk

26
Adding counts in new site
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Adding for Pk
Old sites
Protected excess
New Sites
A
B
Random Key
A
Sum
Secure Compare
28
Adding for Qk
Old sites
0
New Sites
A
B
0
A
Sum
Secure Compare
29
New site pruning

• New sites sends the count to an old site to
  continue
• We got final excess count for Pk
• Comparison means if the itemset is large in all
  sites
• We got excess count in new sites for Qk
• Comparison means if the itemset is large in new
  sites

30
Experiments

• 3 programs
• With privacy but no maintenance (SEC)
• No Privacy but maintenance (MAN)
• With privacy and maintenance (MSIDMAR)
• Environment
• P4 1.7GHz under Linux
• Each site is simulated by an individual computer
• Measure
• CPU time

31
DB size
32
Support
33
Ratio
Total
123
96
69
312
34
Ratio
35
Analysis

• Process time at new sites takes much longer
• About 3 time to 5 times of that of old sites
• Cost overhead due to secure algorithm
• At old sites, average 10 of total cost
• At new sites, average 6 of total cost
• Both decrease in proportion with increase in db
  size

36
Conclusion

• We have proposed algorithms to solve the
  maintenance problem at different privacy level
• All can give a more efficient solution than
  simply ignoring the past results
• As the number of sites are most likely to
  increase
• The load on old sites will be low relatively to
  new sites
• High entrance cost but low maintenance cost

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End