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

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 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

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 nodesRoot of the MHT is digitally signed using

public key signature scheme (RSA/ DSA)

MHT example…

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

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 !

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.

Drawbacks(contd.)

Query reply set consists of thousands of

tuples.

Sending/ receiving and verifying signature of each tuple.

Expensive for the querier.

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

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

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

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

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.

Example of signature chainingConsider tuple R5

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

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

(Contd)

Chain the signature of all tuples along with its corresponding IPR

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

Analysis of DSAC scheme

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

Query Verification Time (Naïve approach vs DSAC)

VO Size (Naïve approach vs DSAC approach)

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.

Further scope

How to reduce the size of the verification object.

{Ts, Tn, Sign(r), ∑}

Freshness Issues

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