Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
7,
No.
6,
December
2017,
pp.
3593
–
3601
ISSN:
2088-8708
3593
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
T
er
nary
T
r
ee
Based
A
ppr
oach
F
or
Accessing
the
Resour
ces
by
Ov
erlapping
Members
in
Cloud
Computing
Amar
Buchade
1
and
Rajesh
Ingle
2
1
Department
of
Computer
Engineering,
Colle
ge
of
Engineering
Pune,
Sa
vitribai
Phule
Pune
Uni
v
ersity
2
Department
of
Computer
Engineering,
Colle
ge
of
Engineering
Pune
and
Pune
Institute
of
Computer
T
echnology
,
Sa
vitribai
Phule
Pune
Uni
v
ersity
Article
Inf
o
Article
history:
Recei
v
ed:
Feb
14,
2017
Re
vised:
Jul
6,
2017
Accepted:
Jul
22,
2017
K
eyw
ord:
K
e
y
Management
T
ernary
T
ree
Cloud
Computing
Ov
erlapping
members
Join
Lea
v
e
ABSTRA
CT
In
cloud
computing,
immediate
access
of
resources
is
important
due
to
cost
incurred
to
customer
by
pay
per
use
model
of
cloud
computing.
Usually
resource
is
protected
by
using
cryptograph
y
technique.
The
resource
may
be
shared
by
multi
ple
members
in
group.
There
can
be
o
v
erlapping
members
to
access
the
multiple
resources.
Group
k
e
y
management
is
important
to
for
m
the
group
k
e
y
to
access
the
resource.
Group
k
e
y
for
-
mation
t
ime
is
crucial
for
immediate
access
of
protected
resource
in
cloud
computing.
Thus
ternary
tree
based
approach
is
proposed
to
form
the
k
e
y
for
o
v
erlapping
mem-
bers
accessi
ng
resources.
Membership
e
v
ent
such
as
join
and
lea
v
e
also
considered.
Through
the
analysis,
it
is
found
that
computational
o
v
erhead
is
reduced
by
23%
if
ternary
k
e
y
trees
are
combined
than
independent
ternary
k
e
y
tree
s.
It
is
also
observ
ed
that
combined
ternary
k
e
y
tree
outperforms
the
c
ombined
binary
k
e
y
tree
approach
for
group
k
e
y
formation
by
considering
o
v
erlapping
members.
Security
requirement
analysis
of
group
membership
for
k
e
y
formation
is
also
pro
vided
in
the
paper
.
Copyright
c
2017
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Amar
Buchade
Research
Scholar
Colle
ge
of
Engineering,
Pune
Sa
vitribai
Phule
Pune
Uni
v
ersity
amar
.b
uchade@gmail.com
1.
INTR
ODUCTION
In
recent
days,
the
use
of
cloud
computing
is
increasing.
Usage
of
cloud
based
social
media
appli-
cations
whatsapp,
twitter
,
f
acebook
and
collaborati
v
e
applications,
P
ay
TV
[1]
systems
are
increasing.
Man
y
go
v
ernments
ha
v
e
initiated
digital
mo
v
e
including
cashles
s
transactions,
m-w
allet
e
tc.
Thus
security
is
major
concern
o
v
er
the
usage
of
man
y
cloud
based
applications.
Ob
viously
there
is
important
role
of
cryptographic
algorithm
to
secure
the
res
o
ur
ce.
Resource
can
be
considered
as
data,
applications,
storage,
CPU,
virtual
machine
etc.
Thus
k
e
y
management
plays
significance
role
to
access
the
resources
from
cloud
computing.
In
cloud
computing,
it
is
important
to
ha
v
e
instant
(on
demand)
access
of
resources.
It
is
im
portant
to
form
the
group
k
e
y
within
a
time
for
immediate
access
of
resources.
F
or
collaborati
v
e
en
vironment,
group
k
e
y
among
the
members
needs
to
be
formed
to
protect
the
access
of
resources
in
cloud
computing.
There
can
be
member
accessing
multiple
resources.
Such
member
in
group/s
is
called
o
v
erlapping
member
.
Thus
in
this
paper
,
the
problem
of
o
v
erlapping
members
accessing
multiple
resources
is
proposed.
Group
k
e
y
can
be
formed
by
TGDH
approach
[2],[3].
Presently
for
group
k
e
y
formation
separate
k
e
y
trees
are
formed
e
v
en
if
member
has
access
to
multiple
resources.
This
approach
leads
to
computational
o
v
erhead
to
form
the
group
k
e
y
.W
e
preferred
ternary
k
e
y
tree
approach
o
v
er
binary
tree
based
approach
for
group
k
e
y
formation
because
as
the
number
of
members
increased
in
ternary
k
e
y
tree,
the
height
is
also
reduced
compared
to
binary
.
Hence
computational
cost
for
forming
group
k
e
y
is
also
reduced.
The
no
v
elty
of
the
approach
is
that
it
is
computational
ef
ficient
that
the
other
approaches.
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
,
DOI:
10.11591/ijece.v7i6.pp3593-3601
Evaluation Warning : The document was created with Spire.PDF for Python.
3594
ISSN:
2088-8708
[4],[5],[6]
proposes
binary
tree
based
approach
for
multiple
members
o
v
erlapped
to
access
the
re-
sources.
[7]
specified
computational
time
analysis
for
group
k
e
y
formation
by
multiple
members
accessing
re-
sources.Binary
tree
based
approach
[8],[9],[10]
proposes
group
k
e
y
management
protocol
in
distrib
uted
group
communication.
Group
members
are
manage
d
in
the
hierarchical
manner
logically
.
Dif
fie-Hellman
k
e
y
agree-
ment
is
applied.
[11]
proposed
suite
of
group
k
e
y
management
protocols
that
allo
ws
a
group
of
users
to
agree
on
a
shared
group
k
e
y
,
which
can
be
used
to
protect
a
shared
file
system
stored
remotely
in
the
cloud.
[12]
pro-
poses
and
applies
k
e
y
management
methods
to
v
arious
cloud
en
vironments.
[13]
proposes
group
leader
,
group
administrator
approach.Data
is
shared
and
accessed
by
group
member
based
on
the
group
k
e
y
.
[14]
describes
group
k
e
y
management
technique.
[14]
sharing
of
files
among
dif
ferent
users
maintained
at
Cloud.
These
users
form
group.
The
tresor
contains
all
the
encrypted
files.
It
is
protected
by
group
k
e
y
.
The
concept
of
K
e
y
Lock
Box
is
proposed.
Ev
ery
directory
has
k
e
y-lock-box
and
contains
the
k
e
ys
of
files
within
directory
.
Thus
our
contrib
ution
to
w
ards
this
paper
is
1.
Combining
ternary
k
e
y
trees
algorithm.
2.
Consideration
of
membership
e
v
ent
such
as
join
and
lea
v
e.
3.
Computational
and
communication
cost
analysis
of
group
k
e
y
formation
by
considering
separate
k
e
y
trees
and
combining
ternary
based
k
e
y
trees.
4.
Security
analysis
of
proposed
scheme.
The
section
2
presents
the
proposed
method,
section
3
presents
research
method
details,
section
4
presents
the
results
and
analysis
section,
section
5
concludes
the
paper
.
2.
PR
OPOSED
METHOD
2.1.
Moti
v
ation
Figure
1.
Resource
R1
and
R2
k
e
y
trees
formations
with
the
members
Figure
2.
Resource
R3
k
e
y
tree
Figure
1
represents
resource
k
e
y
tree
R
1
.
Members
f
m
1
;
m
2
;
m
3
;
m
4
;
m
5
;
m
6
;
m
7
;
m
8
;
m
9
g
are
part
of
resource
R
1
.
Members
f
m
4
;
m
5
;
m
6
;
m
7
;
m
8
;
m
9
g
are
part
of
resource
R
2
.
Members
f
m
7
;
m
8
;
m
9
g
are
part
of
R
3
.
Respecti
v
e
group
k
e
y
can
be
formed
independently
by
three
w
ay
Dif
fie
hellman
k
e
y
e
xchange
protocol
as
e
xplained
in
subsection
2.3..
From
figures
1
and
2,
it
is
observ
ed
that
if
we
calculate
each
re-
source
group
k
e
y
separately
(independently),
it
causes
the
e
xtra
computations
and
e
xtra
partial
k
e
ys
incurred
by
members
f
m
4
;
m
5
;
m
6
;
m
7
;
m
8
;
m
9
g
.
This
is
because
these
members
are
common
to
access
resource
R
2
and
resource
R
1
.
Members
f
m
7
;
m
8
;
m
9
g
are
common
to
access
resource
R
3
.
Thus
k
e
y
formed
at
resource
R
3
can
be
reused
to
form
the
resource
group
k
e
y
at
R
2
while
k
e
y
formed
at
res
o
ur
ce
R
2
can
be
reused
to
compute
resource
group
at
R
1
.
This
approach
causes
less
c
o
m
putational
cost
to
form
the
k
e
y
than
the
independent
group
k
e
y
formation.
Thus
we
use
o
v
erlapping
members
approach
for
accessing
multiple
resources.
IJECE
V
ol.
7,
No.
6,
December
2017:
3593
–
3601
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
3595
2.2.
Ov
erlapping
Members
Let
R
be
the
set
of
resources
i.e.
f
R
1
;
R
2
;
R
3
;
::::;
R
n
g
Members
f
m
1
;
m
2
;
:::;
m
n
g
2
R
1
.
Members
f
n
1
;
n
2
;
:::;
n
n
g
2
R
2
Ov
erlapping
member
can
be
defined
as
f
x
j
(
x
2
R
1
)
^
(
x
2
R
2
)
g
.
From
figure
3,
members
f
m
2
,
m
3
,
n
2
g
are
o
v
erlapping
members
accessing
resources
R
1
and
R
2
.
Figure
3.
Ov
erlapping
members
access
to
resources
In
earlier
approach,
we
proposed
binary
k
e
y
tree
approach
[4],
[7]
for
o
v
erlapping
resource
acc
ess
members.
In
this
approach,
we
can
pro
v
e
ho
w
ternary
tree
data
structure
impro
v
es
the
perf
ormance
o
v
er
earlier
proposed
approach.
2.3.
Gr
oup
k
ey
f
ormation
by
using
ter
nary
k
ey
tr
ee
Figure
4.
T
ernary
based
resource
k
e
y
tree
Group
k
e
y
can
be
formed
by
TGDH
approach
[2],[3].
It
uses
bottom-up
approach.
Basic
TGDH
uses
tw
o
w
ay
Dif
fie
hellman
k
e
y
e
xchange
algori
thm.
In
this
paper
,
we
modified
it
for
three
w
ay
Dif
fie
hellman
k
e
y
e
xchange
algorithm
.
Figure
4
sho
ws
the
ternary
tree.
Root
node
is
called
as
R1
and
leaf
nodes
represents
the
members
m
1
,
m
2
and
m
3
.
Here
we
assume
that
g
is
generator
and
p
is
prime
number
.
Members
m
1
,
m
2
and
m
3
ha
v
e
1
,
2
,
3
pri
v
ate
k
e
ys
respecti
v
ely
.
Each
member
forms
the
k
e
y
ca
lled
as
blinded
k
e
y
.
Thus
group
k
e
y
among
these
members
is
formed
by
the
follo
wing
steps.
1.
Member
m
1
forms
k
e
y
called
as
g
1
mod
p
2.
Member
m
2
forms
k
e
y
called
as
g
2
mod
p
3.
Member
m
3
forms
k
e
y
called
as
g
3
mod
p
4.
Member
m
1
sends
g
1
mod
p
to
member
m
2
5.
Member
m
2
forms
g
1
2
mod
p
6.
Member
m
2
sends
g
1
mod
p
,
g
2
mod
p
and
g
1
2
mod
p
to
member
m
3
7.
Member
m
3
forms
g
3
2
mod
p
,
g
3
1
mod
p
and
g
1
2
3
mod
p
8.
Member
m
3
sends
g
3
2
mod
p
,
g
3
1
mod
p
to
member
m
1
and
m
2
9.
Member
m
1
forms
g
1
2
3
mod
p
10.
Member
m
2
forms
g
1
2
3
mod
p
T
ernary
T
r
ee
Based
Appr
oac
h
F
or
Accessing
the
Resour
ces
by
Overlapping
...
(Amar
Buc
hade)
Evaluation Warning : The document was created with Spire.PDF for Python.
3596
ISSN:
2088-8708
By
steps
1,
2,
3,
5,
7,9
and
10,
total
modular
e
xponential
operations
(MEO)
required
are
nine.
Group
k
e
y
formed
as
g
1
2
3
mod
p
.
T
otal
messages
in
v
olv
ed
are
mainly
tw
o
unicast
messages
namely
at
step
4
and
step
6
and
one
broadcast
message
namely
at
step
8.
Thus
total
three
messages
are
used
to
establish
the
group
k
e
y
.
In
general
formula
for
calculating
total
number
of
e
xponential
operations
is
as
belo
w
.
N
=
9(3
l
og
n
3
1)
=
2
Where
N
=
Number
of
modular
e
xponential
operations,
n
=
number
of
members
e.g
if
n=3,
by
abo
v
e
formula,
N
=
9
3.
RESEARCH
METHOD
3.1.
Member
Resour
ce
Access
Matrix
(MRAM)
An
y
member
for
resource
access,
broadcast
message
containing
resource
membership
details
and
cur
-
rent
resource
request
for
which
resource.
Thus
e
ach
member
mak
es
entry
in
MRAM.
Ro
ws
represents
members
m
1
,m
2
,m
3
,...,m
n
.
Columns
represents
resources
R
1
,
R
2
,
R
3
,...,R
n
2
6
6
4
1
0
1
0
1
1
1
3
7
7
5
m
1
2
R
1
and
m
3
2
R
1
;
R
2
i.e.
m
3
o
v
erlapped
to
access
the
resources
R
1
and
R
2
.
These
are
indicated
by
’1’
in
the
MRAM.
3.2.
Combining
T
er
nary
K
ey
T
r
ees
Algorithm
In
e
xisting
k
e
y
management
algorithm
[8],[9],[10],[11],[13],[15],[16]
separate
k
e
y
tree
is
b
uilt
for
each
resource,
e
v
en
if
members
are
accessing
multiple
resources.
Thus
we
can
combine
multiple
resource
k
e
y
trees.
Algorithm
1
illustrates
combining
ternary
k
e
y
t
rees
algorithm.
Computation
cost
analysis
is
gi
v
en
in
subsection
3.3.
Algorithm
1
Combining
T
ernary
based
Resource
K
e
y
T
rees
Algorithm
1:
Be
gin
2:
The
member
which
w
ants
the
access
of
particular
resource,
broadcast
request
to
access
the
resource.
Each
member
mak
es
the
entry
in
member
resource
access
matrix.
3:
Let
R
1
,
R
2
,
R
3
,
R
4
,
.........R
n
be
the
set
of
resources.
4:
Let
m
1
,m
2
,m
3
,....,m
n
be
set
of
members.
5:
Each
member
k
eep
the
track
of
resource
membership
in
member
resource
access
matrix.
Ro
ws
represents
members
m
1
,m
2
,m
3
,....,m
n
and
Columns
represents
resources
R
1
,
R
2
,
R
3
,....R
n
2
6
6
4
1
0
1
0
1
1
1
3
7
7
5
6:
Identify
the
members
which
are
o
v
erlapped
to
access
multiple
resources.
7:
Build
the
k
e
y
graph
of
o
v
erlapped
members.
Maintain
the
entries
such
as
resources
and
o
v
erlapping
members
in
table
1.
8:
Identify
the
members
which
are
not
o
v
erlapped.
Build
the
k
e
y
tree
of
members
which
are
not
o
v
erlapped.
9:
Combine
the
trees
which
are
formed
during
Step
7
and
Step
8.
10:
End
T
able
1.
Resources
containing
o
v
erlapped
members
Inde
x
Resources
Ov
erlapping
members
1
R
1
,
R
2
m
3
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3.3.
Computational
Cost
f
or
Gr
oup
K
ey
F
ormation
There
can
be
multiple
members
o
v
erlapping
to
an
y
resources.
Modular
e
xponential
operations
(MEO)
after
combining
ternary
k
e
y
trees
=
MEO
for
separate
ternary
k
e
y
trees
-
MEO
due
to
o
v
erlapping
members
MEO
for
separate
ternary
k
e
y
trees
=
K
P
i
=1
(9(3
l
og
N
i
3
1)
=
2)
MEO
due
to
o
v
erlapping
member
=
T
P
index
=1
(
R
count
[
index
])
1)(9(3
l
og
C
[
index
]
3
1)
=
2)
...
from
T
able
1
where
N
=
Number
of
members
per
ternary
k
e
y
tree
K
=
total
number
of
ternary
k
e
y
trees
T
=
Number
of
entries
formed
as
per
table
1
Rcount
=
T
otal
Resource
count
per
entry
as
per
table
1
C
=
Number
of
Members
o
v
erlapped
per
entry
as
per
table
1
It
is
observ
ed
that
computation
cost
in
terms
of
number
of
modular
e
xponential
for
separate
k
e
y
tree
is
O(N)
while
for
ternary
k
e
y
trees
combined
is
O(N
–
RC)
where
N
is
number
of
members
of
resource
k
e
y
trees,
R
is
number
of
resources
considered
and
C
is
o
v
erlapping
members.
Thus
we
can
observ
e
that
number
of
modular
e
xponential
operations
required
in
separate
k
e
y
trees
is
more
i.e
RC
compared
to
the
combined
k
e
y
trees.
T
able
2
describes
comple
xity
in
terms
of
modular
e
xponential
operations.
T
able
2.
Comple
xity
in
terms
of
MEO
Best
Case
W
orst
Case
(
N
)
O(2N)
Best
case
comple
xity
when
all
members
of
resource
groups
are
o
v
erlapped
to
access
the
resourc
es.
W
orst
case
comple
xity
is
when
members
of
resource
groups
are
not
o
v
erlapped
to
access
the
resources.
3.4.
Security
Requir
ement
The
members
which
are
not
part
of
resource
group
must
not
be
able
to
access
the
res
ource.F
ollo
wing
is
the
list
of
security
requirement
for
group
membership
which
should
not
be
violated.
1.
Backw
ard
secrec
y:
The
members
which
joined
to
access
the
resource
recently
should
not
get
access
of
past
k
e
y
.
This
property
is
called
as
backw
ard
secrec
y
.
2.
F
orw
ard
secrec
y:
The
members
which
left
from
resource
group
should
not
get
access
of
future
k
e
y
.
This
property
is
called
as
forw
ard
secrec
y
.
Section
4.1.
illustrates
the
detailed
security
analysis
of
the
proposed
approach.
3.5.
Gr
oup
K
ey
F
ormation
Steps
f
or
Ov
erlapping
Members
Figure
5
describes
o
v
erlapping
members
access
to
resources
R1,
R2
and
R3.
Members
f
m
1
;
m
2
;
m
3
;
m
4
;
m
5
;
m
6
;
m
7
;
m
8
;
m
9
g
ha
v
e
access
to
resource
R1.
Members
f
m
4
;
m
5
;
m
6
;
m
10
;
m
11
;
m
12
;
m
13
;
m
14
;
m
15
g
ha
v
e
access
to
resource
R2.
Members
f
m
7
;
m
8
;
m
9
;
m
10
;
m
11
;
m
12
;
m
13
;
m
14
;
m
15
g
ha
v
e
access
to
resource
R3.
Resource
access
representation
is
sho
wn
in
the
follo
wing.
OG1
!
f
m
4
;
m
5
;
m
6
g
OG2
!
f
m
7
;
m
8
;
m
9
g
T
ernary
T
r
ee
Based
Appr
oac
h
F
or
Accessing
the
Resour
ces
by
Overlapping
...
(Amar
Buc
hade)
Evaluation Warning : The document was created with Spire.PDF for Python.
3598
ISSN:
2088-8708
Figure
5.
Ov
erlapping
members
access
to
resources
R1,
R2
and
R3
OG3
!
f
m
13
;
m
14
;
m
15
g
R1
!
f
m
1
;
m
2
;
m
3
;
O
G
1
;
O
G
2
g
R2
!
f
O
G
1
;
m
10
;
m
11
;
m
12
;
O
G
3
g
R3
!
f
O
G
2
;
O
G
3
;
m
16
;
m
17
;
m
18
g
When
we
form
the
group
k
e
y
using
ternary
k
e
y
tree
approach,
the
group
k
e
y
formation
steps
are
as
follo
ws
1)
Ov
erlapping
group
(OG)
member
forms
its
partial
group
k
e
y
as
per
TGDH
approach.
2)
Each
subgroup
forms
it
partial
group
k
e
y
by
approach
used
in
subsection
2.3..
3)
Group
DH
used
to
calculate
the
group
k
e
y
.
There
are
dif
ferent
e
v
ents
occurred
during
the
k
e
y
tree
formation.
a)
An
y
member
can
join
the
group
or
o
v
erlapping
members
group.
b)
An
y
member
can
lea
v
e
the
group
or
o
v
erlapping
members
at
an
y
instant
of
time.
3.6.
Scenarios
The
follo
wing
section
elaborates
about
membership
join
at
OG,
non
OG
as
well
as
mo
ving
from
one
OG
to
other
OG.
a)
If
the
member
m19
joins
the
group
to
ha
v
e
access
to
R1
as
sho
wn
in
figure
6.
Member
Figure
6.
Member
m19
join
at
non
o
v
erlapping
members
group
of
resource
R1
m19
is
inserted
at
the
rightmost
node
in
the
k
e
y
tree
of
non-o
v
erlapping
group.
Thus
group
k
e
y
can
be
formed
by
partial
group
k
e
y
formed
by
sub
group
of
non-o
v
erlapping
members
and
o
v
erlapping
group
members.
b)
If
member
m19
joins
OG1
with
respect
to
figure
5.
This
is
sho
wn
in
figure
7.
c)
Member
can
mo
v
e
from
one
OG
to
other
group.
This
is
sho
wn
in
figure
8.
Member
m6
can
mo
v
e
to
non-o
v
erlapping
group
members
of
R2
while
member
m12
can
mo
v
e
to
o
v
erlapping
group
1
to
access
the
resource
R1
as
well.
This
is
sho
wn
in
the
figure
8.
4.
RESUL
T
AND
AN
AL
YSIS
Simulation
is
performed.
The
results
are
compared
by
considering
separate
k
e
y
trees,
combined
k
e
y
trees
with
ternary
approach
and
binary
k
e
y
tree
approach.
From
figure
9,
when
we
consider
number
of
Re-
sources
=2,
total
members
200,
the
number
of
o
v
erlapping
members
v
aried,
the
number
of
modular
e
xponenti-
ation
operations
are
less
for
combing
k
e
y
trees
(ternary)
with
o
v
erlapping
than
the
other
approaches.
In
case
of
combining
k
e
y
trees
(binary)
with
o
v
erlapping,
computational
o
v
erhead
(56%)
is
more
than
the
combining
k
e
y
IJECE
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ISSN:
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3599
Figure
7.
Member
m19
join
at
OG1
of
resource
R1
and
resource
R2
Figure
8.
Member
m6
mo
v
e
from
OG1
to
access
resource
R2
only
and
member
m12
to
OG1
trees
(ternary)
with
o
v
erlapping
approach.
If
we
consider
the
independent
(separate)
k
e
y
trees,
the
computa-
tional
o
v
erhead
(23%)
is
more
than
the
combining
k
e
y
trees
(ternary)
with
o
v
erlapping
approach.Computational
o
v
erhead
is
more
in
binary
tree
is
more
due
to
increase
in
height
of
the
binary
when
members
are
increasing.
Figure
10
sho
ws
that
as
we
v
ary
the
total
number
of
members,
modular
e
xponentiation
operat
ions
in
com
b
i
ning
k
e
y
trees
(ternary)
with
o
v
erlapping
members
are
increased
slo
wly
as
compared
with
other
tw
o
approaches.
The
computational
o
v
erhead
is
(73%)
more
in
combining
k
e
y
tree
(binary)
with
o
v
erlapping
members
and
15%
more
in
group
k
e
y
formation
with
separate
k
e
y
trees
com
p
a
red
with
combined
k
e
y
tree
(ternary)
based
approach.
(a)
Analysis
by
v
arying
o
v
erlapping
members
(b)
Analysis
by
v
arying
members
Figure
9.
Computational
cost
T
able
3
depict
comparisons
in
terms
of
computational
and
communication
cost.
Authors[8],[9],[10],[11],[13]
uses
independent
binary
k
e
y
trees
based
approach.
Authors
[6],[7]
use
binary
k
e
y
tree
based
approach
with
the
consideration
of
o
v
erlapping
members.
Our
approach
uses
ternary
based
k
e
y
trees
with
o
v
erlapping
resource
access
members.
’k’
indicates
total
number
of
k
e
y
trees
(resources),
n
i
indicates
total
number
of
members
per
T
ernary
T
r
ee
Based
Appr
oac
h
F
or
Accessing
the
Resour
ces
by
Overlapping
...
(Amar
Buc
hade)
Evaluation Warning : The document was created with Spire.PDF for Python.
3600
ISSN:
2088-8708
resource
k
e
y
tree,
’c’
indicates
number
of
o
v
erlapping
members
among
resource
k
e
y
trees.
From
the
table
3
,
it
is
observ
ed
that
from
our
approach,
as
the
o
v
erlapping
members
increases,
computational
and
communication
cost
decreases.
T
able
3.
Comparisons:
Computational
and
Communication
cost
Approach
Modular
Exponential
Operations
Number
of
messages
Authors[8],[9],[10],[11],[13],[15],[16]
(
k
P
i
=1
n
i
(1
+
log
2
n
i
))
k
P
i
=1
(2
n
i
2)
Gu
Xiaozhuo[6],
Buchade
[4]
(
k
P
i
=1
n
i
(1
+
log
2
n
i
))
c
(1
+
log
2
c
)
k
P
i
=1
(2
n
i
2)
(2
c
2)
T
ernary
trees
without
o
v
erlapping
k
P
i
=1
9(3
l
og
n
i
3
1)
=
2
k
P
i
=1
(3(
n
i
1)
=
2
Our
approach
(
k
P
i
=1
9(3
l
og
n
i
3
1)
=
2)
(9(3
l
og
c
3
1)
=
2)
(
k
P
i
=1
(3(
n
i
1)
=
2)
(3(
c
1)
=
2)
4.1.
Security
Analysis
The
group
k
e
y
format
ion
for
combined
resource
k
e
y
tree
is
similar
to
TGDH.
Thus
attack
er
does
not
form
an
y
partial
group
k
e
y
due
to
its
discrete
log
problem
of
DH
algorithm.
By
gi
ving
g
and
p,
it
is
impossible
to
form
g
1
mod
p
,
g
2
mod
p
,
g
1
2
mod
p
.
It
is
impossible
to
get
the
group
k
e
y
by
the
attack
ers
because
pri
v
ate
k
e
ys
are
k
ept
with
the
use.
Blinded
k
e
ys
are
used
to
form
the
group
k
e
y
.
Backw
ard
secrec
y
is
also
achie
v
ed
when
ne
w
member
joins
the
group.
Thus
group
k
e
y
is
rene
wed
after
joining
the
members.
So
that
member
does
not
kno
w
pre
viously
formed
group
k
e
y
.
F
orw
ard
secrec
y
is
also
achie
v
ed
when
ne
w
member
lea
v
es
the
group.
Thus
group
k
e
y
is
rene
wed
after
lea
ving
the
members.
So
that
lea
ving
member
does
not
kno
w
future
group
k
e
y
.
When
member
mo
v
es
from
one
o
v
erlapping
group
to
other
,
group
secrec
y
is
also
achie
v
ed.
The
members
in
o
v
erlapping
group
updates
the
partial
subgroup
k
e
y
when
member
joins
or
lea
v
e
occurs
thus
backw
ard
and
forw
ard
secrec
y
is
achie
v
ed.
5.
CONCLUSION
In
cloud
computing,
immediate
access
of
protected
resource
is
important.
Resource
can
be
considered
as
data,
applications,
storage,
CPU,
virtual
machine
etc.
Applications
e.g
social
media
that
uses
cloud
com-
puting
also
increasing.
K
e
y
formation
is
important
step
for
members
of
such
applications.
As
soon
as
group
k
e
y
is
formed,
user
should
be
able
to
access
the
resource
in
cloud
computing
and
not
to
violate
the
on
de-
mand
resource
access
property
of
cloud
computing.
W
e
proposed
no
v
el
ternary
k
e
y
based
group
k
e
y
formation
method
for
members
with
access
to
multiple
resources.
W
e
pro
v
ed
that
group
k
e
y
formation
using
ternary
k
e
y
tree
approach
by
considering
o
v
erlapping
members
is
computationally
e
f
ficient
than
the
independent
group
k
e
y
formation
as
well
as
combined
k
e
y
tree
(binary)
approach.
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.-R.
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2088-8708
3601
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BIOGRAPHY
OF
A
UTHORS
Amar
Buchade
is
Research
Scholar
at
Colle
ge
of
Engineering,
Pune
under
Sa
vitribai
Phule
Pune
Uni
v
ersity
.
He
has
recei
v
ed
B.E.
and
M.E.
in
Computer
Engineering
from
W
alchand
Colle
ge
of
Engineering,
Sangli
in
2002
and
2005
respecti
v
ely
.
He
is
a
member
of
IEEE
and
life
member
of
ISTE.
His
research
area
is
Distrib
uted
System,
Cloud
computing
and
Security
.
Rajesh
Ingle
is
adjunct
professor
at
Department
of
Computer
Engineering,
Colle
ge
of
Engineering
Pune,
India.He
is
professor
at
Pune
Insitute
of
Computer
T
echnology
,
Pune.
It
is
af
filiated
to
Sa
vit-
ribai
Phule
Pune
Uni
v
ersity
.
He
has
recei
v
ed
Ph.D.
CSE
from
Department
of
Computer
S
cience
and
Engineering,
Indian
Institute
of
T
echnology
Bombay
,
Po
w
ai.
He
has
recei
v
ed
the
B.E.
and
M.E.
Computer
Engineering
from
Sa
vitribai
Phule
Pune
Uni
v
ersity
.
He
has
also
recei
v
ed
M.S.
Softw
are
Systems
from
BITS,
Pilani,
India.
He
is
a
senior
member
of
the
IEEE,
IEEE
Communications
Society
,
and
IEEE
Computer
Society
.
He
is
serving
as
Re
gion
10
Asia
P
acific
Student
Acti
vities
Chair
2015-18.
His
research
area
is
Dis
trib
uted
system
security
,
Grid
middle
w
a
re,
Cloud
security
,
Multimedia
netw
orks
and
spontaneously
netw
ork
ed
en
vironments.
T
ernary
T
r
ee
Based
Appr
oac
h
F
or
Accessing
the
Resour
ces
by
Overlapping
...
(Amar
Buc
hade)
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