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DSAC (Digital Signature Aggregation and Chaining)

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VB Tree Approach. Uses a modified MHT. Not only root of MHT is signed but all nodes as well ... Constructing signature chains. If h() is a hash function such as ... – PowerPoint PPT presentation

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Title: 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
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