Authenticated Join Processing in Outsourced Databases - PowerPoint Presentation

Slide1

Authenticated Join Processing in Outsourced Databases

Yin Yang, Dimitris Papadias, Stavros PapadopoulosHKUST, Hong KongPanos KalnisKAUST, Saudi Arabia

Providence, USA, 2009Slide2

Database Outsourcing

AdvantagesThe data owner does not need the hardware / software / personnel to run a DBMSThe service provider achieves economy of scaleThe client enjoys better quality of serviceA main challenge

The service provider is not trusted, and may return incorrect query results

2Slide3

Query Authentication

The owner

signs its data with a digital signature scheme

Given a query, the

service provider attaches a VO

(

Verification Object

) to the

results

The client verifies query results with the

VO

and the owner’s signature

soundness

completeness

3Slide4

Example Queries

Range:

σ

quantity>100Purchase

Join:

Purchase

cid

Customer

Range & Join :(

σ

quantity

>100

Purchase)

cid(σ

city=“New York”Customer

)

4Slide5

State of the ArtRange authentication: many solutionsJoin authentication: few proposals

Materializing join results into viewsAINL (presented in detail later)Joins are inherently more complex than rangesA join combines information from multiple tablesOnly individual tables are signed5Slide6

Previous WorkMulti-dimensional range authentication Y. Yang, S. Papadopoulos, D. Papadias, G. Kollios (BU)

ICDE’08, VLDB J.Continuous range authenticationS. Papadopoulos, Y. Yang, D. PapadiasVLDB’07, VLDB J.Novel authentication frameworkS. Papadopoulos, D. Saccharidis, D. PapadiasICDE’096Slide7

Background

Concepts in CryptographyAuthenticated Data Structure (ADS)Merkle Hash TreeMB-TreeAINL7Slide8

Concepts in Cryptography

One-way, collision-resistant hash functionsh = H(

m)

Computationally infeasible to infer m from

h, or to find two

m

1

,

m

2

with the same hash value

h

Example: SHA1, SHA2, …

Public-key encryptionTwo keys: private key

sk, public key pk

Public key to encrypt, private key to decryptExample: RSADigital SignatureHard to forge without the secret key

Signing:

s

=

encrypt

(

H

(

m), sk)

Verifying: check if H(m) = decrypt

(s, pk)

8Slide9

Merkle Hash Tree (Merkle, Crypto’

89)A binary tree with hash values satisfying hn

= H(

hn.lc

| h

n.rc

)

Authenticates 1D range queries

Example: a query

Q

retrieves

d

4

, d

5

VO(Q) = {s

root

,

h

1-2

,

d

3

, d4, d

5, d6, h

7-8} The client re-constructs hRoot bottom-up, and verifies the signature

9Slide10

Merkle B-Tree (Li et al. SIGMOD

’06)Merkle Hash Tree + B-TreeConceptually, a Merkle Hash Tree with a large fanout (>2)10Slide11

AINL

For binary joinsRequires ADS on the join attribute of the inner relationReduces a join query into multiple rangesAlgorithmFor every tuple in the outer relation Perform an authenticated range on the inner relation11Slide12

Example of AINL

12

r

1

r

1

,

h

F

, h

10

, s

11

, s

12

,

h

E

r

2

,

h

1

, s

2

, s

3

, s

4

, h

5

, h

6

,

h

C

,

h

G

…

r

2Slide13

Drawbacks of AINL

Large VO size|R| records from R (outer relation)2|R|+|RS| records from

|S| (inner relation)Numerous hash values

Often larger than the combined size of R and

SHigh computation overhead at the server and the client

13Slide14

NAI: A Naïve solution

The server transmits all the data to the clientThe client performs the join locallyNAI often outperforms AINL14Slide15

Proposed MethodsBinary join authenticationAISM: requires ADS on one relation

AIM: requires ADSs on both relationsASM: requires no ADSComplex join query authenticationMulti-way joinSelect-project-join15Slide16

AISM: Query Processing

Sort the outer relation R on the join attributeTransmit all tuples in R to the client in their verifiable orderTransmit the sort order

R of

R tuples on the join attributeIncrementally traverse the ADS on

S once with the R

records

16Slide17

Example of AI

SM

17



R

[2

]=4

VO

: signature

of

R

, root signature of

T

S

,

r

1

-r

6

in their verifiable order



R

[1],

h1, s

2, s3, s4;



R

[2],

h

5

, h

6

,

h

C

, s

10

, s

11

, s

12

;



R

[3];



R

[4];



R

[5],

h

13

, h

14

, s

15

;



R

[6];



R

[1

]=2



R

[3

]=6



R

[4

]=1



R

[5

]=3



R

[6

]=5

r

2

r

1

r

3

r

4

r

6

r

5Slide18

AISM: Verification

The client checksR recordscorrectness of the sort order R of R

boundary recordswhether the re-constructed root hash of

TS

matches its signature

18Slide19

AIM

Query processingRequire ADSs on both relationsStart with one relation R, traverse its ADS T

R down to the first tuple r

1

Traverse T

S

until reaching the right boundary record

s

of

r

1

Traverse

TR until reaching the right boundary record r

of s

Alternatively traverse TS and TR similarly to the above

Verification: similar to AISM

19Slide20

Example of AIM

20

VO

: root signature of

T

S

, root signature of

T

R

,

r

1

h

s

1

,

s

2

,

s

3

,

s

4

;

r

2

;

h

s

5

,

h

s

6

,

h

C

,

s

10

,

s

11

,

s

12

;

r

3

,

r

4

;

r

5

;

h

s

13

,

h

s

14

,

s

15

;

h

r

6

;Slide21

ASM

IdeaSort-Merge-Join, sort at the server, merge at the clientQuery processingRequire no ADS

Transmit both R and

S in their verifiable order

Sort R and

S

respectively on the join attribute

Transmit the sort orders of

R

and

S

to the client

Transmit bitmaps

BR and B

S to the client, indicating the tuples with join partners

Verificationcorrectness of the base relations / sort-orders / the bitmaps21Slide22

Complex Query Authentication

Multi-way joinsSelection-Projection-Join queries22Slide23

Build a tree of binary join operators

m-ASM / m-AISM / m-AIM optimized for multi-way joinsExample:

A specialized algorithm AST applies when all relations are joined on the same attribute

One single VO

Multi-Way Join

23Slide24

Example of m-AIM and

m-AISM

VO

(

RS

):{root signature of

T

R

and

T

S

,

s

1

,

s2; hA

,

r

4

,

r

5

,

r6; s

3; s4;

s5; hC

}

VO

(

RST

):{root signature of

T

T

,



[1],

t

1

,

t

2

;



[2];



[3];



[4];

h

t3

}

24Slide25

Example of AST

25Slide26

Selection-Projection-Join Query

26

Selection

Use the m-

algorithms for joinsProjectionBuild a Merkle Hash Tree for each recordQuery optimizationSlide27

Experiments

27Three synthetic relations R(

a1

, a

2)

S

(

a

1

,

a

2

,

b

1,

b2)T(

b

1

,

b

2

)

Queries

R a1 S

R a2 S

(R a1 S)

b

1

T

(

R

a

2

S

)

b

2

T

Foreign keys

S.a

1

references

R.a

1

S.b

1

references

T.b

1

Parameters

Tuple size

Cardinality of

|S|Slide28

Repeatability and WorkabilityWe participated in the ACM SIGMOD 2009 Repeatability & Workability Evaluation (cf.,

http://homepages.cwi.nl/~manegold/SIGMOD-2009-RWE/). The reviewers were able to repeat all the experiments presented in our paper,yielding results that match the ones published in our paper, except from insignificant and to be expected variation due to randomness and/or hardware/software differences. The detailed reports will shortly be made publicly available by ACM SIGMOD.

28Slide29

Evaluations of AINL

29Tuple size (bytes)

32

64

128

256

512

C

VO

(

Gbytes

)

8.9

9.0

9.2

9.6

10.3

C

Client

(seconds)

205

207

210

214

219

C

DSP

(seconds)

262

271

429

1728

4603

|R| / |S|

0.1

0.5

1

2

5

C

VO

(

Gbytes

)

7.8

8.9

9.2

9.5

9.7

C

Client

(seconds)

196

205

210

218

223

C

DSP

(seconds)

296

311

429

540

647Slide30

Binary Join: Effect of Tuple Size

30Slide31

Binary Join: Effect of |R| / |S|

31Slide32

Multi-way Join: Effect of Tuple Size

32Slide33

Multi-way Join: Effect of |S| / |R|

33Slide34

Conclusion

Binary join authenticationAISM: authenticated structure on one relationAIM: authenticated structures on both relationsASM: no authenticated structureComplex query authenticationMulti-way join: eliminate unnecessary intermediate VO elementsSelection-projection-join queryFuture WorkAuthenticated Structures specialized to joins

Hash join instead of SMJ34Slide35

Thank you!

Questions?35