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DSAC (Digital Signature Aggregation and Chaining). Digital Signature Aggregation & Chaining An approach to ensure integrity of outsourced databases. Contents. Signature Aggregation Mechanisms Chaining Mechanism Comparison of the results with previous work. ODB.

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dsac digital signature aggregation and chaining

DSAC(Digital Signature Aggregation and Chaining)

Digital Signature Aggregation & Chaining

An approach to ensure integrity of

outsourced databases

  • Signature Aggregation Mechanisms
  • Chaining Mechanism
  • Comparison of the results with previous work
  • Outsourced Data Base(ODB) model : Client stores its data at an external data base service provider.
  • Concern: Ensure the database security & integrity.
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
result set size of a result set
Result set & Size of a result set
  • Result result includes all the tuples matching the query predicates.
  • Size : 0-n, or 2^n subsets,

where, n is total number of tuples in the database.

merkle hash tree
Merkle Hash Tree
  • Use to prove existence of an element in a set. For eg. prove x1 exists in the set y={x2, 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)
auth ds authenticated data structures
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
vb tree approach
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 !
  • 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.
drawbacks contd
  • Query reply set consists of thousands of


  • Sending/ receiving and verifying signature of each tuple.
  • Expensive for the querier.
dsac correctness
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.
dsac completeness
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.
constructing signature chains
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
computing ipr of a tuple
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.
completeness contd
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.
compleness contd
  • Querier on receiving the result set:
  • Verifies the values in boundary tuples are just beyond the query range.
building a result set
Building a result set
  • Compute the tuple set Ts={Ra…Rz}
  • Compute Tn consisting of immediate predecessor and successor nodes

Tn= {R(a-1), R(b+1)}

  • Obtain corresponding signature of each tuple
  • Calculate the aggregate the signature
  • Chain the signature of all tuples along with its corresponding IPR

Now, the result consists of {Ts, Tn, Sign(r), ∑}

analysis of dsac scheme
Analysis of DSAC scheme
  • We compare the DSAC scheme with other prominent correctness/ completeness guarantee schemes such as AuthDS and VB tree.
  • 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.
further scope
Further scope
  • How to reduce the size of the verification object.

{Ts, Tn, Sign(r), ∑}

  • Freshness Issues
  • 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