Journal of Information Security, 2010, 1, 29-40
doi:10.4236/jis.2010.11004 Published Online July 2010 (
Copyright © 2010 SciRes. JIS
Design and Implementation of Multilevel Access Control
in Synchronized Audio to Audio Steganography Using
Symmetric Polynomial Scheme
Jeddy Nafeesa Begum1, Krishnan Kumar1, Vembu Sumathy2
1Department of Computer Science and Engineering, Government College of Engineering, Bargur, India
2Department of Electronics and Communications Engineering, Government College of Technology, Coimbatore, India
E-mail: {nafeesa_jeddy, pkk_kumar} ,
Received March 5, 2010; revised July 15, 2010; accepted July 19, 2010
Steganography techniques are used in Multimedia data transfer to prevent adversaries from eaves dropping.
Synchronized audio to audio steganography deals with recording the secret audio, hiding it in another audio
file and subsequently sending to multiple receivers. This paper proposes a Multilevel Access control in Syn-
chronized audio steganography, so that Audio files which are meant for the users of low level class can be
listened by higher level users, whereas the vice-versa is not allowed. To provide multilevel access control,
symmetric polynomial based scheme is used. The steganography scheme makes it possible to hide the audio
in different bit locations of host media without inviting suspicion. The Secret file is embedded in a cover
media with a key. At the receiving end the key can be derived by all the classes which are higher in the hier-
archy using symmetric polynomial and the audio file is played. The system is implemented and found to be
secure, fast and scalable. Simulation results show that the system is dynamic in nature and allows any type of
hierarchy. The proposed approach is better even during frequent member joins and leaves. The computation
cost is reduced as the same algorithm is used for key computation and descendant key derivation. Steg-
anography technique used in this paper does not use the conventional LSB’s and uses two bit positions and
the hidden data occurs only from a frame which is dictated by the key that is used. Hence the quality of stego
data is improved.
Keywords: Steganography, Multilevel Access Control, Synchronized Audio, Symmetric Polynomial,
Dynamic, Scalable
1. Introduction
Transmission of audio files is very important for many
applications and it is found that this transmission takes
place through an insecure medium. For a live session
where on the go audio transmission takes place, efficient
techniques should be used. One way of preventing the
dissemination of secret audio is through digital audio
stenography. This protects valuable information from
unauthorized persons. For real time audio transmissions
the secret data is recorded and send subsequently to the
receivers. For hiding the message there is a need for a
secret key that is available with all receivers. This key
has to be changed to preserve forward and backward
secrecy. There is an additional very important require-
ment called the multilevel access control. There are
many scenarios in which situation arises, that only some
users should be able to hear the data or all higher level
users should also be able to hear the message that are
relayed to the descendant users. To implement such a
multilevel access control in steganography symmetric
polynomial approach is used. In most existing schemes,
key derivation is different from key computation. Key
derivation needs iterative computation of keys for nodes
along the path from a node to its descendant, which is
inefficient if the path is long. In this scheme, both opera-
tions are same by substituting (different) parameters in
the same polynomial function assigned to node v. Thus,
the key derivation efficiency can be improved. Our
scheme also supports full dynamics at both node and user
levels and permits any random access hierarchies. More
importantly, removing nodes and/or users is an operation
Copyright © 2010 SciRes. JIS
as simple as adding nodes and/or users in the hierarchy.
A trusted Central Authority (CA) can assign secrets (i.e.,
polynomials) to corresponding nodes so that nodes can
compute their keys. Also, nodes can derive their descen-
dants’ keys without involvement of the CA once poly-
nomial functions were distributed to them. In addition,
the storage requirement and computation complexity at
the CA are almost same as that at individual nodes, thus,
the CA would not be a performance bottleneck and can
deal with dynamic operations efficiently.
The rest of the paper is as follows, Section 2 deals
with related work Section 3 gives an insight into multi-
level access control problem. Section 4 gives the system
Overview, Section 5 describes the audio steganography
method Section 6 deals about the symmetric polynomial
approach Section 7 shows the simulation results and Sec-
tion 8 gives the performance analysis and Section 8 con-
cludes the paper.
2. Related Work
2.1. Related Work in Steganography
Information hiding using steganography [1] relates to
protection of text, image, audio and digital content on a
cover medium [2-5]. The cover media in many cases has
been an image [1]. Aoki presented a method in which
information that is useful for widening the base band is
hidden into the speech data [6]. Sub band Phase shifting
was also proposed for acoustic data hiding [3]. All these
schemes focus on data that is stored in a hard disk or any
other hardware whereas there are many applications like
military warfare where the audio data is to be given in
real time as in live broadcast system. Techniques for
hiding the audio in real time came into existence [7] and
systems for synchronized audio steganography has been
developed and evaluated [8]. In our scheme secret speech
data is recorded and at the same time it is sent to the re-
ceiver and a trusted receiver extracts the speech from the
stego data using the key which is shared between the
server and the receiver.
2.2. Related Work in Multilevel Access Control
The first multi level access solution was proposed by Akl
et al. [9,10] in 1983 and followed by many others [11-
21]. These schemes basically rely on a one-way function
so that a node v can easily compute v’s descendants’
keys whereas v’s key is computationally difficult to
compute by v’s descendant nodes. In this paper, we pro-
pose a new scheme based on symmetric polynomials for
synchronized audio data. Unlike many existing schemes
based on one-way functions, our scheme is based on a
secret sharing method which makes the scheme uncondi-
tionally secure [21,22]. Also, this multilevel access con-
trol requires two types of key operations: (1) key com-
putation. A node v computes its own key and (2) key
derivation. A node v computes its descendants’ keys.
3. Multi Level Access Control Problem
In practice, many group applications contain multiple
related data streams and have the members with various
access privileges. These applications prevail in various
1) Multimedia applications distributing data in multi-
layer coding format. For example, in a video broadcast,
users with a normal TV receiver can receive the normal
format, while others with HDTV receivers can receive
both the normal format and the extra information needed
to achieve HDTV resolution.
2) Communications in hierarchically managed organi-
zations, such as military group communications where
participants have different access authorizations.
3) Multilevel access control can be effectively used in
Audio library and patient monitoring system.
4) E-newspaper subscription service may have multi-
ple data streams. The service provider classifies the users
into membership groups and provides data streams ac-
cording to the subscription.
5) Video multicasting service in which users can sub-
scribe to services with different video quality.
Defense messaging systems where the server sends mes-
sages and one or more can see the message according to
the access rights.
In these applications, group members subscribe to dif-
ferent data streams, or possibly multiple of them. Thus, it
is necessary to develop group access control mechanism
that supports the multi-level access privilege, which is
referred to as the Multilevel Access Control.
4. System Overview
Multilevel Access Control applied to real time audio to
audio steganography is useful for organizations which
have a hierarchical structure. e.g., in the Indian Military
system the following hierarchy exists in “Figure 1”.
Figure 1. Military hierarchy.
Copyright © 2010 SciRes. JIS
In such a type of system, audio messages sent to a
lower class should be heard by the active members of
lower class and also by all active members of the higher
class. It is not only essential to maintain the access con-
trol but the data should be hidden as well. The sequence
of events is as follows.
At the server:
1) Generate a general polynomial.
2) Give a symmetric polynomial to each of the classes.
3) Record the real time audio on a microphone.
4) Use Steganography technique to hide the audio into
another audio.
5) A text can also be hidden in an audio file.
6) The file is encrypted by the class key for whom the
Message is to be relayed.
7) The symmetric polynomial generates a key in this
case. The server takes care to include class dynamics so
the hierarchy can be changed at any time.
8) Users can join or leave a class at all instances. Keys
are recalculated so that Forward and Backward secrecy is
9) If the users within the group need to transfer mes-
sage among themselves. The private key of the users is
The above steps are given pictorially in “Figure 2”.
Secret data
Play cover file as
it is upto frame x
The Stego
Take 2 bits from secret data and
perform an operation involving
secret data and key.
replace 2 bits in each
channel starting from
frame x + 1 by the
Generate Key for User Class
Operation on key to
find frame no x
Use the key to hide
the secret audio
Figure 2. At the server.
At the receiver:
1) All the active receivers will receive the audio file.
2) If the recipient belongs to the actual intended class
he can use the polynomial to get the hidden audio file
3) If the recipient belongs to a class lower than the
Actual intended class in the hierarchy, he will not be able
to derive the key .The polynomial derivation method will
give a null value.
4) If the recipient belongs to a higher class he can de-
rive the key and hear to the audio file and in case a text
message was sent it can be seen.
5) The users at the same class can transfer messages
among them.
6) When a user leaves or joins. The new polynomials
are given by the server and the private keys also get up-
dated according to the new polynomial. Other classes are
not affected by this.
7) Service messages can be sent from higher class us-
ers to lower class users.
The above steps are explained pictorially in “Figure
Stego data
Trusted receiver
belonging to
higher class
Derives key of
lower class
Trusted receiver
belonging to
Lower class
Symmetric polynomial gives
null value
Not allowed to
generate keys
Audio could not
be intelligible
Start listening
to audio
Polynomial Module
Generate Key for
User Class
Operation on key
to find frame no x
Figure 3. At the receiver.
Copyright © 2010 SciRes. JIS
4.1. Features of our Model
Solutions of a synchronized steganography have been
given in past [8]. In this once the stego data reaches the
destination the audio can be listened by the trusted re-
ceiver. Our contributions are
1) The key is used during the embedding process also.
2) The key is not a simple key it identifies a class of
3) If the key used belongs to a low level group in the
hierarchy, the higher level class of user can derive the
key using the symmetric polynomial approach and listen
to it.
4) There can be normal message transfer among the
Group elements and also service messages from higher
5) Forward and backward secrecy is maintained.
6) It is a dynamic one where new hierarchies can be
introduced, User level and class level dynamics are taken
5. Synchronized Audio to Audio
The data to be sent is not available. It is recorded in real
time before starting the steganography scheme. When the
covering media is being played at the same time the au-
dio file is recorded and put into the cover file. The stego
bit stream is then transmitted to the receivers. Multilevel
Access control using symmetric polynomial is used at
this stage to generate the key to make secure transmis-
sion of the audio file. According to the hierarchy the
trusted users are able to retrieve the hidden audio file.In
this system, both of cover data and secret data are di-
vided into fix-sized frames according to pulse code
modulation setting. To cover low size and high phonetic
quality the sampling rate of the hidden audio is set to 8
kHz. Three main processes are involved in the synchro-
nized audio to audio steganography.
1) Using data sampling, acoustic signals are embedded
into another audio.
2) Bit Embedding: The key used helps in hiding the
audio file in bit positions and once the bit positions are
found data is hidden after performing an operation on
secret data and the key.
3) Synchronized Process: Malicious and intentional
attacks can be avoided as the secret data is real time.
5.1. Algorithm
Step 1: Record the Secret Speech Data: The audio files
are divided into fix-sized frames and set to be specific
PCM format. PCM quantification is decided by sampling
rate, sampling size, and sampling channel. The PCM
property of cover audio wav is set to be 32kHz-16bit-2ch,
while the secret wav data is 16kHz-8bit-1ch.
Formula used for steganography:
Steganography process:
cover_medium + hidden_data + stego_key
= stego_medium
Part of The Wave File Format opened using Notepad:
52 49 46 46 24 40 01 00 57 41 56 45 66 6D 74 RIFF $
Wave Fmt10 00 00 00 01 00 02 00 11 2B 00 00 44 AC
00 00 ……. + …D…04 00 10 00 64 61 74 61 00 40 01
00 00 00 00 00 …. data. @..........
Wave_Format_PCM: 01 11 channel count: 02 00
Samples: 11 2B 00 00 bytes: 44 AC 00 00
Block align: 04 00 bits per sample: 10 00
Step 2: Use Symmetric Polynomial to calculate key of
the class
Step 3: Perform calculation and decide the frame from
which the data is to be embedded.
Step 4: Decide two bit locations in each frame and clear
the bit in the locations.
cmask1 = (2loc11) xor (keybit)
cmask2 = (2loc21) xor (Keybit)
cmask = cmask1 cmask2
hide the secret data bits into these bit locations by again
performing an operation on the secret data along with the
key. The cover media has two channels so data is written
on both the channels. Other bits are not changed.
Step 5: The next set of data will go to the next frame.
Step 6: Do the repetitive process till the recoding is over.
Step 8: Transmit using sockets.
Step 9: At the receiving end, use the key and play the
Step 10: If the receiving user belongs to higher class, he
can derive the key and listen to the audio.
6. Symmetric Polynomial Approach
6.1. Symmetric Polynomial
A CA selects a large positive integer P as the system
modulus, p need not be a prime and a threshold number t
so that less than t + 1 users cannot collaborate together to
disclose their ancestors’ keys. Then, the CA can ran-
domly generate a symmetric polynomial in m variables
with co-efficient from Zp in which the degree of any
variables is at most t as:
12,,, 12
00 0
,,, mod
tt ti
ii i
Px xxaxxxP
 
 
 
where 12
ii i
a are randomly generated coefficients by
the CA. The polynomial function
Pxx x is
kept as a secret to the CA. Every class in the hierarchy
Copyright © 2010 SciRes. JIS
has a polynomial function which is derived from
Pxx x and the polynomial function is trans-
mitted to each class securely by the CA.
Example for Symmetric Polynomial
The following polynomial function is a suitable example
for symmetric polynomials.
,, n
ww i
xxa xx
 
where 12 12
,,, (,,,)
ii iii i
For all permutations π of {1,…n}
For example,
suppose n = 3 and w = 2,
Let i1, i2, i3 be as follows
a0,0,0 = 13
a0,0,1 = a0,1,0 = a1,0,0 = 3
a0,0,2 = a0,2,0 = a2,0,0 = 7
a0,1,1 = a1,0,1 = a1,1,0 = 4
a0,1,2 = a0,2,1 = a1,0,2 = a2,0,1 = a2,1,0 = 8
a0,2,2 = a2,0,2 = a2,2,0 = 9
a1,2,2 = a2,1,2 = a2,2,1 =11
a2,2,2 = 5
6.2. Polynomial Function
To derive proper keys in the hierarchy, the CA generates
some publicly known numbers
1) n random numbers si associated with Ci for i = 1,
2, ... n and 2) and (m 1) additional random numbers rj
for j =1, 2, ..., m – 1
(Note: si and rj belong to Zp).
For each class Ci with an ancestor set i
{, ,, }
ii i
CC C where ij is an ordinal number such that
1 ij i n, class Ci is given a polynomial function, gi
derived by the CA as,
(,,,) ,,,,,
ii m
immmii ii
mm m
xxx Pssss
xx x
A symmetric polynomial based scheme:
A is an set of n classes – {C1, C2, C3,…, Cn}
B is a set of ancestral classes of set A.
B = {S1, S2, S3, …, Sn}
mi is calculated as the number of the ancestral classes mi
= |Si|. We choose m such that m max{m1, m2, …, mn} +
1. Here m is the number of parameter in the polynomial
function P, where P is to construct our multi level access
control scheme.
We illustrate with a sample hierarchy “Figure 4
Here we have nine classes
{C1, C2, C3, C4, C5, C6, C7, C8, C9}
Ancestral classes’ sets are
S1 = {φ}, S2 = {φ}, S3 = {C1, C2}, S4 = {C2}
S5 = {C2}, S6 = {C1, C2, C3},
S7 = {C1, C2, C3, C4}
S8 = {C2, C3, C5}, S9 = {C2, C5}
From the previous step, we need to choose m such that
m max{m1, m2, m3, …, m9}. Let us choose m = 7, it
will allow to expand the hierarchy without changing the
value of m.
Symmetric polynomial, we are using here is as follows
12 12
, ,...
00 0
,, mod
tt t
ii i
ii i
Px xxa
xx P
 
 
Here t is threshold number. We can classify our work
into two Key Calculation and Key Derivation.
Key Calculation:
We can calculate key Ki of class Ci as follows
12 12 --1
,,,, ,',',,'
iii iimm
KPsss ssss (1)
Key Derivation:
In key derivation, we are using a term Sj/I which is
 
jIj ii
i jijirj
Consider a class Ci which is ancestor to class Cj and key
Kj can be calculated by Ci as,
 
 
12 --2-
12 --2-
,,, ,,',', ,'
,,,,,, ,,,,,
', ',, '
ij mmr
ji jijir
ijiiii ji jijir
mm r
Ps ssssssss
ss s
Example Key Derivation
Consider that C3 is an ancestor class to class C7.
Figure 4. A typical hierarchy.
Copyright © 2010 SciRes. JIS
Then K7 can be derived by C3 in the following steps.
371241 2
Key Calculation for the Classes using Equation (1)
1 2 31234
5 1 21234
8123 451
Ps rrrrrr
Psss rrrr
Ps ss rrrr
Pssss rrr
Ps ss s s rr
Ps ss s s s r
Key Derivation of class 7 by class 3 using Equation
 
33 123
3/7 4
Which is equal to the key calculated by class7 itself.
Key Derivation of class 3 by class 7 using Equation
 
7 1234
It can be seen that when the class derives its own key
and when a ancestor of this class derives the key same
parameters are passed in the polynomial but the combi-
nation differs when a wrong ancestor derives the key, the
parameters are not the same.
The default values, we have taken are
m = 7, P = 2147483646, s1 = 5, s2 = 10, s3 = 13, s4 = 9, s5
= 6, s6 = 22, s7 = 18, s8 = 30, s9 = 39, r1 = 11, r2 = 12, r3 =
13, r4 = 14, r5 = 15, r6 = 16, r7 = 17, r8 = 18, r9 = 19 (in-
stead of s’ we have used r)
For a small Hierarchy “Figure 5”, with more than two
classes, we can easily illustrate our key calculations,
where each class consists of several users.
Figure 5. Sample hierarchy to illustrate calculations.
Key Calculations:
The parameters to be passed for calculating group key
class 2 are 2123456
( ,,,,,,)PSr rrrrr
Group key class C2 = 699615258
1) Private key for user 21 = 699615258 + (699615258/21) =
2) Private key for user 22 = 699615258 + (699615258/22)
= 731415951
3) Private key for user 23 =699615258 + (699615258/23) =
4) Private key for user 24 = 699615258 + (699615258/24)
= 728765893
Key Derivation:
Deriving the group key of class C4 using its ancestral
class C2
Sj|i can be calculated as
4|22 2
SsSUC Set Difference S4|2 = {Ф}
The parameters to be passed for deriving the key of class
C4 using C2
Key,,, ,, ,10,9,11,12,13,14,15
pssrr rr rp
Private Keys are used for local communication.
6.3. Class Level Dynamics
6.3.1. Adding a Class
When a new class Cr is added, we need to verify whether
m value satises the new node constraints
1) If m < max{m1, m2, ..., mn, mr} + 1, a new m value
will be generated so that m max{m1, m2, ..., mn, mr} + 1.
Also, the CA will regenerate a new polynomial functions
Pxx x accordingly. In addition, all polyno-
mial functions of classes are recomputed and retransmit-
ted securely.
Copyright © 2010 SciRes. JIS
2) If m max{m1, m2, ..., mn, mr} + 1, the CA selects a
random number sr for the new class Cr so that a new
polynomial function gr can be computed and transmitted
to class Cr securely. However, if class Cr is added as a
parent class of any existing classes, we need to modify
keys of Crs descendant classes to prevent class Cr from
obtaining old keys of its descendant.
6.3.2. Deleting a Class
When a class Cr is removed from the hierarchy, we need
to determine whether the class Cr is a leaf node or a par-
ent node. Here, a leaf node is dened as a node without
any descendant:
1) class Cr is a leaf node: The CA can simply discard
the public parameter sr without changing any other keys.
2) class Cr is a parent node: Once class Cr is deleted
from the hierarchy, we cannot allow it to compute keys
of Cr’s descendant classes using polynomial function gr.
We need to prevent class Cr from accessing its descen-
dants’ resources.
6.3.3. Moving a Class
A class Cr can be moved from one node to another node
in the hierarchy. There are four cases:
1) leaf node to another leaf node: the CA simply re-
computes new polynomial function gr according the new
hierarchy and securely transmits gr to Cr.
2) leaf node to parent node: the CA recomputes poly-
nomial functions of class Cr and Cr’s new descendant
classes according to the new hierarchy. The CA securely
transmits polynomial functions to the affected classes;
3) parent node to leaf node: the CA recomputes poly-
nomial functions of previous descendant classes of Cr
and class Cr according to the new hierarchy and then,
securely transmits these polynomial functions to the af-
fected classes
4) parent node to parent node: the CA recomputes
polynomial functions of previous and present descendant
classes of Cr and class Cr according to the new hierarchy
and then, securely transmits these polynomial functions
to the affected classes.
6.3.4. Merging a Class
Two or more classes can merge together and become one
class Cr. Similarly, the CA needs to find previous and
present descendant classes of the merging classes. The
CA randomly chooses a new number sr and then, gener-
ates polynomial functions for all corresponding classes.
6.3.5. Splitting a Class
A class Cr splits into two classes Cr1 and Cr2. Depending
on whether Cr is a parent node or leaf node, the CA has
to determine what previous and present descendant cla-
sses are associated with these classes (Cr, Cr1 and Cr2).
The CA then selects two new numbers sj1 and sj2 and
generates polynomial functions for these affected classes.
6.3.6. Adding a Link
If two classes Cr and Ck are linked together, we establish
a new direct parent-child relationship between two
classes, say class Cr is the parent of class Ck. There are
two different cases: 1) class Cr was an ancestor of class
Ck through other classes. The CA does not need to per-
form anything; and 2) class Cr is the only parent for class
Ck in the new hierarchy. The CA selects a new number Sk,
and generates new polynomial functions for class Ck and
its descendants classes. The CA securely transmits new
polynomial functions to these affected classes.
6.3.7. Deleting a Link
If two linked classes Cr and Ck are disconnected, we de-
stroy a direct parent-child relationship between two
classes, say class Cr will not be the parent of class Ck in
the new hierarchy. Again, there are two different cases: 1)
class Cr is still an ancestor of class Ck through other
classes in the new hierarchy. The CA does not need to
perform anything; and 2) class Cr is not an ancestor for
class Ck in the new hierarchy. The CA selects a new
number Sk, and generates new polynomial functions for
class Ck and its descendants classes. The CA securely
transmits new polynomial functions to these affected
6.4. User Level Dynamics
In this scheme, every class represents certain access
privileges. Also, a group of users in a class can share a
key if they belong to the same class. For example, all
users in class Cj can compute the keys of class Cj and its
descendant classes. Dynamic user operations deal with
how a user can join in a class or leave from a class, and
possible displacement from one class to a different class.
They all require the class key to be changed after any
user operation is completed so that the issue of backward
secrecy and forward secrecy can be addressed. Specifi-
cally, our scheme can revoke a user from a class Cj. It is
as quick and efficient as to join a user in the class Cj.
Both operations require that the CA randomly select a
new public parameter sj for Cj and recompute a new
polynomial function gj by using the new sj. Since the
polynomial function gj is newly produced, other polyno-
mial functions and keys are also recomputed for the de-
scendant classes of Cj. This will guarantee both back-
ward secrecy and forward secrecy. The efficiency can be
improved if backward secrecy or forward secrecy is not
required. Another common user operation is to allow a
Copyright © 2010 SciRes. JIS
user to move from one class Cj to another class Ck. Here,
the CA will randomly choose two new public parameters
sj and sk for Cj and Ck so that new polynomial functions
and keys are recomputed and transmitted to Cj, Ck and
their descendants respectively. Thus, both backward se-
crecy and forward secrecy are guaranteed.
6.4.1. User Join
Every time if a single user wants to join a group the CA
just allows the user to be added to the hierarchy and gen-
erates a private for that user by providing the corre-
sponding group key. When a new user joins the hierar-
chy, it should be provided with a group key and there are
no changes to be made on the user’s key.
6.4.2. User Leave
When a user wants to leave from the hierarchy the CA
change the group key by making changes on anyone of
the following changing the polynomial or changing the
value factor P.
7. Simulation Results
The system is developed using .NET and found to be
secure and fast. The system takes care of USER level and
class level dynamics. The large number of numbers pre-
vents a possible guessing. e.g., for a eight parameter
polynomial, 16 (i.e., 10922789888000) combinations
possible. Bursty leave and join operations also are possi-
ble and the system can be used for any hierarchy. The
outputs are shown in Figures 6-10.
8. Performance Analysis
Performance and security: Each user ui will receive
,... 2
, ,...,...
ii nn
ii n
fsxxgx x
The time complexity for computing the group key is O
(w2n). An important measure for a secure group com mu-
nication scheme is the number of rekeying messages.
Suppose that t users will be joining the group. The TA
will send k and gi to each of them respectively (2t mes-
sages) and broadcast one message to tell which users are
joining. The total number of rekeying messages is O (2t).
Suppose that t users are leaving the group. The TA only
broadcasts one message to tell which users are leaving,
thus the number of rekeying messages is O (1). Suppose
that t users are joining and another v users are leaving
the group, the total number of rekeying messages is still
O (2t).
As for the security of the scheme, if w + 1 class col-
lude, then they can Figure out the function f entirely.
Therefore, the scheme is w-resilient. Moreover, if less
than w + 1 classes collude, they cannot get any informa-
tion about the key, i.e., any value in the key space looks
like a valid and equiprobable key to these colluding users.
It follows that the scheme is unconditionally secure.
8.1. Memory
Each user will be able to calculate the key based on the
Figure 6. Users and classes.
Copyright © 2010 SciRes. JIS
Figure 7. Key calculation for all classes.
Figure 8. Communication among same class.
polynomial and hence very less memory is used. All pa-
rameters are publicly available and using the same
method keys of lower hierarchy can be derived by sub-
stituting the corresponding parameters as given by the
derivation module. The steganography module does not
involve any storage for storing the already recorded data
as always data is recorded and subsequently sent to the
receivers. The size of the cover medium does not in-
crease because only two bits are used in each channel.
8.2. Computation Cost
When the user joins there is no need for recalculation
because the recorded message has already been played.
When a user leaves a group key is recalculated and given
to the class. Private keys are generated from this. The
Copyright © 2010 SciRes. JIS
Figure 9. Hiding the message.
Figure 10. Recording the message.
value of the new key involves not a change of parameters
but a change of mod P value. Hence each class will be
able to get a new polynomial value by passing the same
parameters. Any left user will not be able to get the key.
Only one key is used during creation of stego data. The
higher class users need not remember the keys of all their
descendant classes but rather using a simple scheme de-
rive the exact parameters to generate the key. Hence the
computation cost is reduced.
8.3. Communication Cost
The P value is changed by the Trusted Authority and
when the users try to calculate the key the new key will
be generated. The computation cost is reduced because,
the class users are not bothered about the key transmis-
Copyright © 2010 SciRes. JIS
sion. Once the polynomial is given the users can calcu-
late their own key.
8.4. Dynamics
Class joining, Class leaving, Dynamic Hierarchy and New
user joining a class are all done by the trusted authority
in a phased manner thereby allowing the scheme to scale
to greater hierarchy. Additionally local messaging and
service messages are taken care in this system.
8.5. No of Rekeys
To calculate the no of changes might be made on the
user’s key based on user join/leave. Key must be chang-
ed when a new user is being joined/left from the hierar-
chy In the Hierarchy “Figure 11” for analyzing the no.
of rekeys there are 50 classes and Let every classes con-
sists of four users each, then we can calculate an unique
key for every class based on this group key, we can gen-
erate a private key for every single user.
Totally fifty classes of eight levels
Figure 11. Hierarchy analyzed for calculating the no. of
Every class is consists of 4 users
User joins:
Every time if a single user wants to join a group the
CA just allows the user to be added to the hierarchy
and generates a private for that user by providing the
corresponding group key. The secrecy is maintained as
the audio is real time.
User leave:
When a user wants to leave from the hierarchy the CA
change the group key by making changes on anyone of
the following Changing the polynomial, or by Chang-
ing the value factor P. The total no of key changes to
be made = No. of Ancestor classes + 1 as shown in
Table 1.
9. Conclusions and Future Work
9.1. Conclusions
Thus in this Paper, Design And Implementation Of Mul-
tilevel Access Control In Synchronized Audio To Audio
Steganography Using Symmetric Polynomial Scheme is
implemented successfully .The implementation results
show that any type of hierarchy can be introduced and all
dynamics can be done. For a 8 parameter polynomial that
can have use 8 among the 16 values there are 16 com-
binations. Also, nodes can derive their descendants’ keys
without involvement of the CA once polynomial func-
tions were distributed to them. In addition, the storage
requirement and computation complexity at the CA are
almost same as that at individual nodes, thus, the CA
would not be a performance bottleneck and can deal with
dynamic operations efficiently.
Table 1. No of rekeys for user leaving from a corresponding
Class 1: 1Class 11:4Class 21:5 Class 31:7 Class 41:8
Class 2:2Class 12:4Class 22:6 Class 32:7 Class 42:9
Class 3:2Class 13:4Class 23:6 Class 33:7 Class 43:9
Class 4:2Class 14:4Class 24:6 Class 34:7 Class 44:9
Class 5:3Class 15:4Class 25:6 Class 35:8 Class 45:9
Class 6:3Class 16:5Class 26:6 Class 36:8 Class 46:9
Class 7:3Class 17:5Class 27:6 Class 37:8 Class 47:9
Class 8:3Class 18:5Class 28:6 Class 38:8 Class 48:9
Class 9:3Class 19:5Class 29:7 Class 39:8 Class 49:9
Class 10:4Class 20:5Class 30:7 Class 40:8 Class 50:9
Copyright © 2010 SciRes. JIS
9.2. Future Work
1) The Trusted authority can still made secure by chang-
ing the value of the parameters.
2) A symmetric polynomial can be changed by the
trusted authority.
3) Bit selection for steganography can be made by us-
ing some pseudo random generator.
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