DSAC (Digital Signature Aggregation and Chaining)

1
DSAC(Digital Signature Aggregation and Chaining)

• Digital Signature Aggregation Chaining
• An approach to ensure integrity of
• outsourced databases

2
Contents

• Signature Aggregation Mechanisms
• Chaining Mechanism
• Comparison of the results with previous work

3
ODB

• Outsourced Data Base(ODB) model Client stores
  its data at an external data base service
  provider.
• Concern Ensure the database security integrity.

4

• Authenticity The tuples in the result set have
  not been tampered i.e correctness.
• Integrity No valid tuples have been omitted from
  the result set i.e completeness

5
Result set Size of a result set

• Result result includes all the tuples matching
  the query predicates.
• Size 0-n, or 2n subsets,
• where, n is total number of tuples in the
  database.

6
Merkle Hash Tree

• Use to prove existence of an element in a set.
  For eg. prove x1 exists in the set
  yx2, x6, x1, x9
• Constructed as binary tree where leaves are hash
  value of corresponding element.
• Non leaf Leaf nodes
• Root of the MHT is digitally signed using public
  key signature scheme (RSA/ DSA)

7
MHT example
8
Auth DS (Authenticated Data Structures)

• Approach to prove correctness
• Uses MHT to prove correctness of the result set.
• Limitation Need to pre-compute and store a
  potentially large number of authenticated data
  structures to answer queries.
• Completeness issue not answered

9
VB Tree Approach

• Uses a modified MHT
• Not only root of MHT is signed but all nodes as
  well
• Limitation Consumes large storage space and
  increased verification time.
• Provides proof of correctness
• Completeness issue not answered !

10
Drawbacks

• Overheads associated with building, storing and
  updating data structures in AuthDS and VB tree.
• Signs each individual tuple before storing.
• Server stores tuples along with its corresponding
  signature.
• In response to a query, server sends both tuple
  and its signature.

11
Drawbacks(contd.)

• Query reply set consists of thousands of
• tuples.
• Sending/ receiving and verifying signature of
  each tuple.
• Expensive for the querier.

12
DSAC Correctness

• Combines multiple individual signatures in the
  result set into a unified/ aggregated signature.
• Verifying a unified signature is same as
  verifying signatures of each individual tuple in
  the result set.

13
DSAC Completeness

• Includes the boundary tuples as well to ensure
  all the tuples matching the query is returned.
• Link the tuple level signatures to form a
  signature chain.

14
Constructing signature chains

• If h() is a hash function such as SHA,
• denotes concatenation,
• IPRi denotes immediate predecessor tuple along
  dimension i ,
• l being number of searchable dimensions,
• SK is private signing key of the data owner

15

• then the signature of a tuple r can be computed
  as follows

16
Computing IPR of a tuple

• Sort tuple in increasing order of the attribute
  value for each dimension.
• IPR of a given tuple in a given dimension is a
  tuple with highest value of the attribute that is
  less than the value of that tuple.
• Each tuple has as many IPRs as the number of
  searchable dimensions.

17
Example of signature chaining

• Consider tuple R5

18
Completeness (contd.)

• In this way, server answers range queries by
  releasing all matching tuples, boundary tuples as
  well as aggregated signature.
• Signature chain proves querier that server has
  returned all tuples in the query range proving
  completeness.

19
Compleness(contd.)

• Querier on receiving the result set
• Verifies the values in boundary tuples are just
  beyond the query range.

20
Building a result set

• Compute the tuple set TsRaRz
• Compute Tn consisting of immediate predecessor
  and successor nodes
• Tn R(a-1), R(b1)
• Obtain corresponding signature of each tuple
• Calculate the aggregate the signature

21
(Contd)

• Chain the signature of all tuples along with its
  corresponding IPR
• Now, the result consists of
  Ts, Tn, Sign(r), ?

22
Analysis of DSAC scheme

• We compare the DSAC scheme with other prominent
  correctness/ completeness guarantee schemes such
  as AuthDS and VB tree.

23
Query Verification Time (Naïve approach vs DSAC)
24
VO Size (Naïve approach vs DSAC approach)
25
Freshness

• Freshness The result set in response to a query
  should be the recent snapshot of the database.
• Prevents the server from replaying the old
  signature chains, hence freshness is part of data
  integrity concerns.

26
Further scope

• How to reduce the size of the verification
  object.
• Ts, Tn, Sign(r), ?
• Freshness Issues

27
Reference

• DSAC An approach to ensure integrity of
  outsourced databases using signature aggregation
  and chaining
• Authors Maithili Narasimha Gene Tsudik
• Computer Science Department
• University of California,
  Irvine