BVA

- A BIT VECTORS ALGORITHM FOR ACCELERATING

QUERIES IN MULTILEVEL SECURE DATABASES

Ramzi A. Haraty, Arda Zeitunlian

Lebanese American University, P.O. Box 13-5053 Chouran, Beirut, Lebanon 1102 2801

Keywords: Bit vectors, query accelerations, and multilevel security

Abstract: Much research has been done in the area of multilevel database systems, especially in the security area and

accelerating queries. In this paper, we present BVA

, which is based on bit vectors to accelerate queries in

multilevel secure database systems. As its predecessor (BVA), the BVA

algorithm follows the classic Sea

View Model, but it recovers query output from single-level relations in a faster and more space-efficient

manner than the previous works performed on this subject. In addition, the BVA

algorithm does not

produce spurious or extra tuples, which have always been a major problem in the area of multilevel secure

database systems.

1 INTRODUCTION

Much research has been done in the area of

multilevel database systems, especially in the

security area and accelerating queries (Jajodia, 1991;

Sandhu, 1994; Rahal, 2003). One of the earliest

attempts to model multilevel relations was the Sea

View Model (Lunt, 1990), which represented two

algorithms. 1) The decomposition algorithm, which

partitioned multilevel relations into single-level

relations and stored each single-level relation

separately, and 2) The recovery algorithm, which

regenerated a multilevel relation from the set of

single-level relations. Since multilevel queries

would result in applying repeated joins to single-

level relations, in addition to the problem of spurious

tuples, the Sea View model performed inefficiently.

The later works, the DVA algorithm (Perrizo, 1993)

and the BVA algorithm (Haraty, 2003), following

the Sea View Model, propose faster recovery

algorithms and are more space efficient.

In this paper, we follow the widely accepted

odel for enforcing mandatory access control

policies developed by Bell and LaPadula (Bell,

1976) and describe a fast, space efficient, and secure

technique for accelerating queries that take place

among various single-level relations in a multilevel

secure database system. We show that we achieve a

significant performance improvement over already

published work and produce output data that is

consistent.

The rest of this paper is organized as follows:

Sectio

n 2 provides a brief explanation of multilevel

relations and a description of the concept of

polyinstantiation. Section 3, presents related work.

Section 4 presents the BVA

algorithm and its data

structures. Finally, the conclusion is given in section

2 MULTILEVEL RELATIONS

AND POLYINSTATIATION

A multilevel relation (see figure 1) is a relation of

the form R (A1, C1, ..., An, Cn, TC) where Ai is an

attribute and Ci is its classification (or sensitivity

level). TC is the classification of the tuple. Ci

belongs to the domain of classifications for data

items. We denote A1 to be the apparent key of R.

The concept of a key is a little bit different in

multilevel relations because keys can be duplicated;

this is why we refer to them as apparent keys instead

of just keys. The reason behind this duplication of

keys is polyinstantiation.

495

A. Haraty R. and Zeitunlian A. (2004).

BVA+ - A BIT VECTORS ALGORITHM FOR ACCELERATING QUERIES IN MULTILEVEL SECURE DATABASES.

In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 495-499

DOI: 10.5220/0002593504950499

 SciTePress

Figure 1: A multilevel relation.

A polyinstantiated tuple is a tuple that exists

more than once in a relation with the same apparent

key, but with some other attribute values being

changed. This is due to the fact that different

subjects are authorized to update or view different

data. For example, suppose that a subject X with

clearance C (Confidential) is attempting to write a

new value to a data item Y with sensitivity S

(Secret). The old value in item Y is not viewable by

subject X but the new value written into Y by X is

viewable (it has X's clearance level which is C). To

preserve the old value of Y, a new tuple is inserted

into the relation with same apparent key (and same

attribute values except for Y in this case). Now X can

view the new value inserted into Y and Secret and

Top Secret users will view the two values (the old

value with sensitivity S and the new value with

sensitivity C).

3 RELATED WORK

There are many algorithms built for maintaining and

recovering multilevel relations from single-level

relations. Perhaps the most important of which are

the Sea View model, the DVA algorithm, and the

BVA algorithm.

3.1 The Sea View Model

The Sea View model consists of two algorithms: a

decomposition algorithm and a recovery algorithm.

The decomposition algorithm divides a multilevel

relation R into a set of single level relations. For

every query, an output multilevel relation is

reconstructed from the single-level relations using

the recovery algorithm. Unfortunately, the recovery

algorithm of the Sea View model suffers from the

following: a) Creation of spurious tuples in the

output (due to polyinstantiation), b) Space

inefficiency due to temporary tables, and c) Time

inefficiency due to unions and joins, which are two

of the most expensive database operations.

Spaceship

Name Objective (obj)

Destination

(des)

SHU-1 U Explore U Uranus U

APL-9 U Mine U Neptune C

RDA-6 U Scientific C Pluto C

CLB-2 C Explore C Neptune C

CLB-2 C Spy S NULL S

3.2 The DVA Algorithm

DVA is an algorithm motivated by the recovery

algorithm of the Sea View Model based on domain

vector accelerators, DVAs, to accelerate the

recovery of multilevel relations from single-level

relations. DVAs accelerate joins between relations

and thus lead to reducing the response time of

queries requiring many joins. The DVA algorithm

solves the problems of the Sea View Model recovery

algorithm; it does not create spurious tuples in the

output table and is relatively space and time

efficient. It shows improvement especially in

environments where queries involve selections on

some (one or more) attributes of the multilevel

relations. In spite of these facts, this algorithm uses a

lot of temporary data structures, some of which can

be omitted to improve the algorithm’s space

efficiency without negatively affecting its overall

performance or its functionality.

3.3 The BVA Algorithm

The Bit Vector Algorithm (BVA) is an algorithm

also motivated by the recovery algorithm of the Sea

View Model to accelerate the recovery of multilevel

relations from single-level relations. BVA solves the

problems of the Sea View Model recovery algorithm

and space and time requirements of the DVA

algorithm; it does not create spurious tuples in the

output table and is space and time efficient. In spite

of these facts, it takes much calculation in finding

the temporary storage used to create the output table,

and may produce inconsistent data.

4 THE BVA

ALGORITHM

In this algorithm, we assume that a multilevel

relation is decomposed into single level relations

using the decomposition algorithm of the Sea View

model. The BVA

algorithm will be applied to

recover the multilevel relation from those single

level relations. Suppose, we have the multilevel

relation in figure 1. This multilevel relation is based

on single-level relations as shown in figure 2.

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Rname,u Robj,u,u Rdes,u,u

SHU-1

APL-9

RDA-6

SHU-

APL-9

Explore

Mine

SHU-

Uranus

Robj,u,u Rdes,u,c

RDA-

Scientific

APL-9

RDA-

Neptune

Pluto

Rname,c Robj,c,c Rdes,c,c

CLB-2 CLB-

Explore CLB-

Neptune

Robj,c,s

CLB-

Spy

Figure 2: The decomposed single-level relations.

All relations containing only the key - i.e.,

Rname,u (base single level relation containing all

keys at classification level U) and Rname,c - are

referred to as base relations. Suppose we want to

recover the output of the query “Select name, obj,

des from R where des <> Saturn”. The following is

a description of the steps of the BVA+ associated

with examples from the above the relation (Ai

denotes any attribute and A1 denotes the apparent

key).

1. For every relation RAi,x,y (single level relation

containing all entries form multilevel relation

having keys at classification level x and Ai

attribute values at classification level y), excluding

base relations, create a bit vector BV.RAi,x,y

denoting the presence or absence of the keys at

level x. BV.RAi,x,y should have the same number

entries as the number keys at level x (can be found

in relation Rkey,x).

Keys at level u = {SHU-1, APL-9, RDA-6}

Keys at level c = {CLB-2}

BV.Robj,u,u = 110

BV.Robj,u,c = 001

BV.Robj,c,c = 1

BV.Robj,c,s = 1

BV.Rdes,u,u = 100

BV.Rdes,u,c = 011

BV.Rdes,c

,c = 1

2. For every RAi,x,y excluding base relations create a

Mapping Vector Index, MVI.RAi,x,y, mapping the

position of the keys in RAi,x,y to the position of

the keys in RA1,x. The entries in the MVIs are of

the form (pib, pit) where pib, Position In Base

relation, is the position of the key in the base

relation; and pit, Position In This relation, is the

position of the key in this relation.

3. Create an Output Keys Vector OKVx (contains all

keys with classification x that will appear in the

output table) for all x:

a. As having a number of bits equal to the

number of entries in Rkey,x.

b. Read all relations having an attribute

participating in the selection criteria of the

query.

c. Get all entries from those relations satisfying

the selection criteria at each level x (at level u

we have SHU-1, and APL-9; and at level c we

have CLB-2).

d. For every entry that succeeds, set its position

in OKVx to 1. The position of an entry in

OKVx can be found by matching the key of

this entry to the key in Rkey,x and getting its

position in Rkey,x.

i.OKVu = 110 (the first three keys in

Rname,u will appear in output table)

ii.OKVc = 1 (the first and only key in

Rname,u will appear in output table)

4. Create a Polyinstantiated Keys Vector, PKVx,y

that contains all polyinstantiated keys at level x by

subjects at level y, for all x,y such that x<y. For all

attributes Ai requested in the output of the query

(name, obj and des) except for the key (name) do

the following:

a. Create PKVAi,x,y = the ANDing of all

BV.RAi,x,z where x <= z < y for all z

PK obj,u,c = BV.Robj u,u AND BV.Robj,u,c

= 110 AND 001 = 000

PK obj,u,s = BV.Robj u,u AND BV.Robj,u,c

= 110 AND 001 = 000

PK obj,c,s = BV.Robj c,c AND BV.Robj,c,s

= 1 AND 1= 1

PK des,u,c = BV.Rdesu,u AND BV.Rdes,u,c

= 100 AND 011 = 000

PK des,u,s = BV.Rdesu,u AND BV.Rdes,u,c

= 100 AND 011= 000

PK des,c,s = BV.Rdes c,c = 1

b. Get PKVx.y as the ORing of all PKVAi,x.y

PKVu,c = PK obj,u,c OR PKdes,u,c = 000

PKVu,s = PK obj,u,s OR PK des,u,s = 000

PKVc,s = PK obj,c,s OR PK des,c,s = 1

A 1-bit in position n in any vector PKVx

signifies that the nth entry in Rkey,x is

polyinstantiated. Therefore, entry 1 in Rname,c that

is CLB-2 is polyinstantiated.

BVA+ - A BIT VECTORS ALGORITHM FOR ACCELERATING QUERIES IN MULTILEVEL SECURE

DATABASES

497

BVA+ differs, in this step, from its predecessor.

In order to find if there are any polyinstantiated

keys, BVA creates the Polyinstantiated Key Vector

PKV, first by ORing all the Bit Vector BV.RAi’s,

then ANDing the Bit Vectors, again, with the results

of the first AND, and finally ends up by ORing all

the Polyinstantiated Key Vector PKV’s (of the

attributes) having the same classification. While the

BVA+ algorithm simply ANDs the BV.RAi’s of

each attribute and ORs the resulted PKV’s (of all the

attributes). In this way, BVA+ simplifies and

reduces the calculation, thus making it more

efficient both space and time wise.

5. Create POKVx,y (polyinstantiated output keys

vector) as the ANDing of PKVx,y and OKVx

POKVu,c = OKVu AND PKVu,c

= 110 AND 000 = 000

POKVu,s = OKVu AND PKVu,s

= 110 AND 000 = 000

POKVc,s = OKVc AND PKVc,s = 1 AND 1

6. Create an Output table, as shown in figure 4, as

follows:

a. Having a number of columns equal to the

number of fields, Ai, requested in the output

of the query (name, obj and des) → 3

columns.

b. Scan OKVx for 1-bit entries (appears in the

output). If a 1 bit appears in position n do the

following for all Ai attributes requested in the

output:

i.If Ai is the key (i = 1) then get the nth

record from RA1,x and store it under A1

column in output table. This entry has

classification x.

ii.Else, go to the nth entry in BV.RAi,x,z

where z = x initially . If a 1 bit is found in

position n then get the pit value of the

entry in MVI.RAi,x

,z that has pib = n.

Let p = pit, get the p’th entry from

RAi,x,z and store it under Ai column in

output table. This entry has classification

z. Else (if 1 bit is not found in position n

of BV.RAi,x,z then) increment z to the

next higher level and repeats this step.

c. Scan POKVx,y for 1-bit entries (appears in

the output and polyinstantiated). If a 1 bit

appears in position n do the following for all

Ai attributes requested in the output:

i.If Ai is the key (Ai = A1) then get the nth

record from RA1,x and store it under A1

column in output table. This entry has

classification x.

ii.Else, go to the nth entry in BV.RAi,x,z

where z = y initially . If a 1 bit is found in

position n then get the pit value of the

entry in MVI.RAi,x,z that has pib = n. Let

p = pit, get the p’th entry from RAi,x,z

and store it under Ai column in output

table. This entry has classification z. Else

(if 1 bit is not found in position n of

BV.RAi,x,z

then) decrement z to the next

lower level and repeats this step. If the

BV.RAi does not exist then put a null

value under the Ai column in the output

table. This entry has classification z.

Part c, is also different from its predecessor.

Here, BVA+ requires that if the BV.RAi of any

attribute does not exist, (i.e., if it is neither 0 nor 1) a

null value under that attribute’s column is inserted.

In this way, the output given by the recovery

algorithm of BVA+ is proper and consistent with

respect to the real database. Thus, BVA+ takes care

of null values of the database, which its predecessor

– BVA – did not. The null value will have

classification z and the algorithm will be repeated

for the remaining attributes.

The output table of BVA+ algorithm, after the

above stated query, will look like:

Spaceship

Name Objective

(obj)

Destination

(des)

SHU-1 U Explore U Uranus U

APL-9 U Mine U Neptune C

CLB-2 C Explore C Neptune C

CLB-2 C Spy S NULL S

5 CONCLUSION

The BVA

algorithm is an improvement over the

Sea View Security Model, and DVA and BVA

algorithms. Compared to the first, which was one of

the earliest and most important attempts towards

multilevel database security, the BVA

has the

following advantages: 1) No spurious tuples in the

output table, and 2) No time inefficiency because the

BVA

algorithm does not depend on the use of joins

and unions like the Sea View model to create the

output table.

When compared with the DVA algorithm, BVA+

is more space and time efficient as it eliminates the

following data structures: 1) The Domain Vector

Tables (referred to as DVTs in the DVA algorithm)

used to map keys to their positions in the primary

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relations, 2) The Domain Value Indices (referred to

as DVIs in the DVA algorithm) of primary relations,

3) The Domain Vectors (referred to as DVs in the

DVA algorithm) of primary relations, 4) The

participation of primary relations in the creation of

the Polyinstantiated Domain Vectors (referred to as

PDVs in the DVA algorithm), and 5) Select Omit

Tables (referred to as SOTs in the DVA algorithm),

which are used to produce the Output table.

When compared with the BVA algorithm, BVA+

has the advantages: 1) Reduced calculations in

finding one of the temporary storage used to create

the output table, and 2) Proper output table, without

producing inconsistent data.

REFERENCES

Bell, D. and LaPadula, L., 1976. Secure computer

systems: unified exposition and Multics

interpretation. Technical Report. The Mitre

Corporation.

Haraty, R. and Rahhal, I., 2002. A bit vectors algorithm

for accelerating queries in multilevel secure

databases. Proceedings of the CSITeA 2002, Foz du

Iguazo, Brazil.

Jajodia, S. and Sandhu, R., 1991. Toward a multilevel

secure relational data model. Proceedings of the ACM

SIGMOD International Conference on Management

of Data. Denver, Colorado.

Lunt, T., Denning, D., Schell, R., Hechman, M., and

Shockley, W., 1990. The Sea View security model”.

IEEE Transactions on Software Engineering, Volume

16, Number 6.

Perrizo, W. and Panda, B., 1993. Query acceleration in

multilevel secure distributed database systems.

Proceedings of the 16

National Computer Security

Conference. Baltimore, Maryland.

Rahal, I. and Perrizo, W., 2003. Query acceleration in

multi-level secure database systems using the P-Tree

technology. Proceedings of The International

Conference on Computers and Their Applications

(CATA’03). Honolulu, Hawaii.

Sandhu, R., 1994. Design and implementation of

multilevel databases. Proceedings of the 6

RADC

Workshop on Multilevel Database Security.

Southwest Harbor, Maine.

BIOGRAPHIES

Ramzi A. Haraty is the Chairman of the Division of

Computer Science and Mathematics and an Associate

Professor of Computer Science at the Lebanese American

University in Beirut, Lebanon. He received his B.S. and

M.S. degrees in Computer Science from Minnesota State

University - Mankato, Minnesota, and his Ph.D. in

Computer Science from North Dakota State University -

Fargo, North Dakota. His research interests include

database management systems, artificial intelligence, and

multilevel secure systems engineering. He has well over

50 journal and conference paper publications. He is a

member of Association of Computing Machinery, Arab

Computer Society and International Society for Computers

and Their Applications.

Arda Zeitunlian received her B.S. degree in Computer

Science from Haigazian University in Beirut, Lebanon.

She is currently pursuing her M.S. degree in Computer

Science at the Lebanese American University. Her

research interests include database management systems

and software engineering.

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DATABASES

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