EFFICIENT DIGITAL ENCRYPTION ALGORITHM BASED ON MATRIX SCRAMBLING TECHNIQUE

International Journal of Network Security & Its Applications (IJNSA), Vol.2, No.4, October 2010
DOI : 10.5121/ijnsa.2010.2403 30
EFFICIENT DIGITAL ENCRYPTION ALGORITHM
BASED ON MATRIX SCRAMBLING TECHNIQUE
{M. Kiran Kumar, S. Mukthyar Azam}1
, Shaik Rasool2
1
Dept. of Computer Science & Engg, R.V.R & J.C College of Engg, Guntur, India
kirankumar.rvr@gmail.com
1
Dept. of Research & Development, Synfosys, Hyderabad, India
mukthyar@live.in
2
Dept. of Computer Science & Engg, S.C.E.T., Hyderabad, India
shaikrasool@live.in
ABSTRACT
This paper puts forward a safe mechanism of data transmission to tackle the security problem of
information which is transmitted in Internet. We propose a new technique on matrix scrambling which is
based on random function, shifting and reversing techniques of circular queue. We give statistical
analysis, sequence random analysis, and sensitivity analysis to plaintext and key on the proposed scheme.
The experimental results show that the new scheme has a very fast encryption speed and the key space is
expanded and it can resist all kinds of cryptanalytic, statistical attacks, and especially, our new method
can be also used to solve the problem that is easily exposed to chosen plaintext attack. We give our
detailed report to this algorithm, and reveal the characteristic of this algorithm by utilizing an example.
KEYWORDS
Cipher text, Encryption, Decryption, Random Number Generator, Circular queue.
1. INTRODUCTION
With the rapid growth of Internet, global information tide expends the application of
information network technology. It also brings about great economic and social benefit along
with the extensive use of this technology. However, because Internet is an open system which
faces to public, it must confront many safe problems. The problems include network attack,
hacker intruding, interception and tampering of network information which lead huge threat to
Internet [3]. Information security becomes a hot problem which is concerned by our society.
Security of the information over the insecure mode of communication, Internet, has been an area
of research for years. There have been several techniques developed for encryption/decryption
of the information over the years.
This paper discusses a new technique of encrypting data which enables good diffusion and is
having a unique technique of decrypting it back to the plaintext and is easy to implement using
matrix scrambling technique. The encryption algorithm of magic cube projected by Yongwei et
al. which is implemented in three-dimensional space [5][11][4]. The algorithm is complicated
and difficult to understand. F. Y. LI Min. proposed queue transformation based digital image
encryption algorithm [6], which works efﬁciently with low time complexity compared to
Yongwei et al.. However, it still has some shortcomings. Firstly, the algorithm signifies some
certain regularity. According to F. Y. LI Min, algorithm, assume we randomly select one
element, (i, j), from the matrix, rows (columns) with row (column) ID smaller than i(j)
cyclically shifts leftward (upward) with increasing steps, and rows (columns) with row (column)
ID greater than i(j) cyclically shifts rightward (downward) with proceeding steps. This
regularity makes the encryption output represent some certain periodicity with the increasing of
steps, which make the algorithm vulnerable to attacks with ease of decryption. Secondly, one
operation to a n× n matrix will cause n(n − 2i − 1)/2 cyclic shifts. At least n operations is needed
for scrambling, which makes the time complexity of this algorithm be O(n3
).

31
By enhancing this algorithm, in this paper, we propose an Efficient Digital Encryption
Algorithm Based on Matrix Scrambling Technique which is based on random function, shifting
and reversing techniques of circular queue, with efficient time complexity.
2. ENCRYPTION ALGORITHM
The plaintext chosen is arranged into a Bi-directional circular Queue data structure [10],In the
matrix A of order m × n. Input an integer parameter, w, as the count of operations, say, the time
of transformation we made to matrix. To some certain degree, this parameter represents the
intensity of the encryption. However, this does not necessarily mean that the greater w is, the
more intensive the encryption is. Random() function is used to generate random positive integer,
this integer value has to be converted into a binary equivalent [9]. Depending on the binary bit
from least significant bit to most significant bit, the choice to select rows or columns is made. In
case of row, two rows r1 and r2 are selected randomly from the matrix similarly two random
values of columns c1, c2 are chosen to determine the range of rows on which transformation has
to be performed. To perform transformation operations, a value is calculated from Random( )
mod3, circular left shift, circular right shift and reverse operations on the selected rows is
performed depending on the value which may be 0,1 or 2 In case of column, two columns c1
and c2 are selected randomly from the matrix, two random values of rows r1,r2 are chosen to
determine the range of columns on which transformation has to be performed.. Then to perform
transformation operations similar to rows, a value is calculated from Random( ) mod 3, based
on it circular upward shift, circular downward shift and reverse operations are performed similar
as rows.
The entire process is repeated w number of times; if w ≤ length (binary sequence) then the
process is performed only w number of times from LSB to MSB else the binary sequence is
repeated from LSB to MSB until the w operations. In this manner, the entire matrix elements
are transposed. For each operation performed, the operation should be recorded as a sub~key in
a file, which becomes the key file. The key file should be maintained secret. The decryption
process is done by reading the operations in the key file in reverse order and applying necessary
operations on the matrix, which contains cipher text as to get plain text.
Here we make introduction to our encryption algorithm, which is given in figure 1. The function
Random(n) generates random positive integers less than or equal to n and Random(m) generates
random positive integers less than or equal to m, where m, n ϵ N and Random( ) be the random
function which generates random positive integers. These random numbers could be
implemented by technology of chaotic sequence, wavelet transformation, elliptic curve and so
on [8][1][7][2].The entire process of encryption is summarized below:
1. The original plain text is stored in an m × n matrix A, where m ϵ N, n ϵ N.
2. Input an integer parameter w, which represents no. of rounds of operations to perform.
Depending on w, w transformations are applied on the matrix. To some extent, this
parameter represents the intensity of encryption. However, this does not necessarily mean,
the greater w is, the more intensive encryption is.
3. Let i = Random(), hence ‘i’ is a random positive number which decides which
transformation is applied either row transformation or column transformation. The value of
i provides some sort of strength to the encryption. After choosing i , binary value of i is
calculated and placed in a vector b, b = Binary Sequence(i). The good choice of i gives
better binary sequence to perform transformations on the matrix.
4. Let k = Digit(bt), where ‘t’ is bit position, k value is either 0 or 1, which provides a way of
deciding either to perform row or column transformation. If k = 0, then A = RowTrans(A)
is performed i.e. row transformation operations are applied on the matrix as given below

32
(i). If k = 1, then A = ColumnTrans(A) i.e. column transformation operations are applied
on the matrix as given below (ii).
Figure 1: Encryption Algorithm
(i) We illustrate the process of row transformation operations i.e. A = RowTrans(A) in this
section, the algorithm is shown in figure 2,Two rows are selected randomly, r1 = Random
(m),r2 = Random(m) similarly two random values of columns c1,c2 are selected i.e.
c1=Random(n), c2=Random(n), to determine the range of rows on which transformation has to
be performed. The constraint here is r1 ≠ r2 and c1≠c2 Let x1 = min(c1,c2), x2 = max(c1,c2),
Here x1 and x2 becomes lowest index and highest index of the sub array selected in the rows r1
and r2 .
Let op = Random() mod 3, hence op takes three possible values 0 , 1 and 2. Thus three row
operations are performed on the matrix. If op = 0, then circular left shift operation is performed
on rows r1 and r2 on the sub portion of range x1 to x2. If op = 1, then circular right shift
operation is performed on rows r1 and r2 on the sub portion of range x1 to x2. If op = 2, then
perform reverse operation on the sub array of r1 and r2 in the range from x1 to x2.
For each operation a sub~key is constructed and recorded in a key~file. The sub~key is 6 tuple
and is given as follows, sub~key = (T, op, α1, α2, β1, β2) where

33
T = Transformation applied either row or column and takes values ‘R’ or ‘C’
Op = 0 or 1 or 2 (Meaning of these values changes for row and column operations)
α1, α2 = Two random rows or columns selected depending on the transformation
β1, β2 = min and max values of range for two selected α1, α2
In case of row transformation sub~key is recorded as, R op/r1/r2/x1/x2.
Figure 2: Process of Row Transformation
(ii) We illustrate the process of column transformation operations i.e. A = ColumnTrans(A) in
this section, the algorithm is shown in figure 3, Two Columns are selected randomly, c1 =
Random(n), c2 = Random(n) similarly two random values of rows r1,r2 are selected i.e.
r1=Random(m), r2=Random(m), to determine the range of columns on which transformation
has to be performed. The constraint here is c1≠c2 and r1≠r2 Let x1 = min(r1, r2), x2 = max(r1,
r2), Here x1 and x2 becomes lowest index and highest index of the sub array selected in the
columns c1 and c2 .
Let op = Random() mod 3, hence op takes three possible values 0 , 1 and 2. Thus three column
operations are performed on the matrix. If op = 0, then circular upward shift operation is
performed on columns c1 and c2 in the sub portion of range x1 to x2. If op = 1, then circular
downward shift operation is performed on columns c1 and c2 in the sub portion of range x1 to
x2. If op = 2, then perform reverse operation on the sub array of c1 and c2 in the range from x1
to x2.

34
Figure 3: Process of column transformation
5. Check whether binary sequence in vector b is completed. If it is completed, again start
from first digit in the binary sequence of b (LSB MSB).
6. Repeat steps 4 and 5 for w no of times.
7. Record all the sub keys sequentially in a key~file.
2.1. Case Study of the Encryption Process
In this section, we show the detailed process of our encryption algorithm by an example. Let the
data to be encrypted is taken as follows
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20.
Let us set m = 4, n = 5, w = 7, i = 14, b = 01110. In vector b only 5 digits of the binary sequence
is considered in the example. It depends on the user to consider how many bits to use without
changing the actual bits of the value z. This provides irregularity and is used to increase the
intensity of encryption. After the plain text is set into A, the layout of the matrix is shown in
figure 4. After w operations and based on binary values in b, sub~keys recorded in the key~file
is given in figure 5.
Figure 4: Layout of the plain text

35
R 1/2/1/2/4, C 0/4/1/0/3
C 1/3/0/0/3, C 2/1/2/1/2
R 1/1/2/0/4, R 2/3/1/0/2
C 1/2/0/0/1
Figure 5: Content of the key~file
The process of disordering or scrambling the matrix elements based on sub~keys is explained in
figure 6.
Figure 6: Process of obtaining cipher text using sub~keys in the key~file
The cipher text obtained after the entire process is given as
17,7,14,19,9,16,1,3,15,4,20,6,12,10,8,18,2,11,13,5
3. DECRYPTION ALGORITHM
The proposed algorithm is a kind of symmetric encryption algorithm, with decryption process is
done by reversing the operations done in the encryption process. The cipher text is arranged into
a matrix of the same order in the encryption as m and n. The algorithm for decryption is given
in figure 7.
The steps of the decryption process explained in brief as follows

36
1. The key file is partitioned by the R (row) operations & C (col) operations. A sub key starts
from R or C operation, ends at the start of another R or C operation or the end of the key
file.
2. The sub keys are decrypted one by one from the last sub key to the first sub key.
3. For each sub key T, op, α1, α2, β1, β2 values are obtained whose terms are already
explained in the encryption algorithm. Based on T value either R or C operation is decoded
which are given as A = InverseRowTrans(A) and A = InverseColTrans(A).
4. In InverseRowTrans(A) depending on the value of ‘op’ transpositions are performed. For 0
right shifts, for 1 left shift and for 2 reverse operation is performed on the columns.
5. In InverseColTrans(A) depending on the value of ‘op’ transpositions are performed. For 0
downward shift, for 1 upward shift and for 2 reverse operation is performed on the rows.
6. The process is done until the key file is completed and at the end of process matrix A
contains the required original message i.e. plain text.
Figure 7: Decryption algorithm
3.1. Case Study of the Decryption Process
In this section, we show the detailed process of our decryption algorithm with an example.
Consider the cipher text obtained after encryption as 17, 7, 14, 19, 9, 16, 1, 3, 15, 4, 20, 6, 12,
10, 8, 18, 2, 11, 13, 5. The layout of the cipher text after placing in matrix A of order m and n is
given in figure 10. The decryption is done by reading the sub keys in key file in reverse order
and sub keys in reverse order is given in figure 9.

37
The steps of the decryption are given as follows in figure 10.
Figure 8: Layout of the cipher text
C 1/2/0/0/1, R 2/3/1/0/2
R 1/1/2/0/4, C 2/1/2/1/2
C 1/3/0/0/3, C 0/4/1/0/3
R 1/2/1/2/4
Figure 9: sub keys in reverse order
Figure 10: Process of Decryption
4. SIMULATION AND EXPERIMENTAL RESULTS
We present here results generated from practical implementation of our algorithm. A plain text
of 20 characters is taken as the input to the algorithm. The various steps involved in the
encryption algorithm are carried out. The Random number generators, Binary sequence
generators are used in to full fill the need for generating random number and binary sequence in

38
the algorithm. The input plaintext and the Random number and Binary sequence generated is
shown in the figure 11.
As per the algorithm, binary sequence is processed and the row or column is selected. The
operation to be performed is done based on the random number generated by the random
number generator. The first three rounds of operations are shown in the figure 12 and the next
three rounds in the figure 13. Each round operation’s output is also shown in the figures. For
every round operation a sub~key is generated and after every round of the operation the
sub~key is stored in a separate text file which is kept secret.
Figure 11: Plaintext and Generated Binary Sequence
Figure 12: Resultant matrix for the operations of ‘w’ (w=1, 2, 3)
The contents of the key file are shown in figure 14. It can be seen that it contains the entire
sub~key’s generated after the completion of the encryption process. The number of sub~key’s
equal to the ‘w’ no of operations. This key file is sent along with the cipher text to the receiver.
Depending on the key file each sub~key is used in the reverse order for the decryption process
to get back the plaintext.
Now we present the graphs that represent the amount of text scrambled in the algorithm based
on the experimental results. The total count of operations is 6 and for every round the number of
transpositions performed can be seen in the figure 15. It can be observed form the figure that as

39
with the every round of operation is complete the amount of transpositions goes on increasing
resulting in the very good scrambled matrix. When the same plaintext is taken and when the
encryption is performed again then the transpositions will be different and resultant scrambled
matrix is also different. This can be observed in the figure 16.
Figure 13: Resultant matrix for the operations of ‘w’ (w=4, 5, 6)
Figure 14: Resultant Cipher text and Key~file
Thus it is hard that we will be getting same result when we process the same text again and
again i.e. the scrambling is not same. It shows the efficiency of the algorithm and strong
encryption that is not vulnerable to cryptanalysis.
Figure 15: Analysis of Plaintext Scrambled for w=6
The value of parameter ‘w’ plays an important role in control the intensity of the encryption.
‘w’ should not be too small or too large. For a matrix of order m and n, e ≤ w ≤ 2e is good

40
choice to scramble the matrix, where e = max(m, n). Under this condition, time complexity of
our algorithm is O(e).
Figure 16: Analysis of Plaintext Scrambled for w=6
The second parameter ‘i’ also plays an important role in strengthening the intensity of
encryption along with the parameter ‘w’. The binary digit sequence of ‘i’ chosen also avoids
regularity in the resultant cipher text. The good choice of ‘i’ gives better binary sequence, which
is used to scramble the matrix in both directions row wise and column wise efficiently.
Our algorithm is based on magic rectangle, and hence it is easy to understand and easy to
implement the proposed algorithm, which also has the following characteristics.
1. Running Speed: The algorithm belongs to classis shifting encryption algorithm and it uses
only 3 kinds of linear array operations, circular horizontal shifting(left, right) , circular
vertical shifting(up, down) and reverse operations. So it works efficiently with little system
resources.
2. Simple Algorithm: Depending on shifting operations and reverse operation of the bi-
directional circular queue, the algorithm could be implemented by software as well as
hardware, which relax the limitation that most encryption algorithm needs to be
implemented by hardware.
3. Strong Encryption Intensity: For an n × n matrix, the encryption intensity of the algorithm
is nw
5. CONCLUSION AND FUTURE WORK
In this approach the usage of random number selection firstly for generating binary sequence
and, secondly for row (column) and column (row) selections, thirdly for selecting the operations
for scrambling, avoids the regularity in the resultant cipher text which is transformed from plain
text matrix; and hence improves the difficulty for decrypting.
The algorithm can be applied to text encryption, image encryption, and multimedia encryption
and so on. In future work we will focus also on UMTS and GSM wireless transmission systems.
Consequently, we can expect rapid growth in this area. In particular, with respect to real time
applications, it will be interesting to see if the entertainment and telecommunication industries
will make extensive use of the new standards MPEG IPMP and JPSEC. From the more research
oriented perspective, the integration and interoperability of different multimedia security
techniques poses a huge amount of open questions. Therefore, more research can be done in this
field.

41
REFERENCES
[1] W. Y. YE Yongwei and YANG Qinghua, (2003) “Magic cube encryption for digital image using
chaotic sequence”, Journal of Zhejiang University of Technology, 31(2):173–176.
[2] Z. L. Z. X. feng and FAN Jiu-lun, (2007) “A digital image encryption algorithm based on
chaotic sequences”, Microelectronics & Computer, 2.
[3] Kui-He Yang and Shi-Jin Niu, “Data Safe Transmission Mechanism Based on Integrated
Encryption Algorithm”, Staffordshire University.
[4] C. C. LUO Pu, (2006) “An image encryption algorithm based on chaotic sequence”, Journal of
Information, 12.
[5] S.-J.-b. BAO Guan-jun and JI SHI-ming, (2002) “Magic cube transformation and its application
in digital image encryption”, Computer Applications, 11:22–25.
[6] F. Y. LI Min, (2005) “A new class of digital image scrambling algorithm based on the method of
queue transformation”, Computer Engineering, 01(31):148–149.
[7] Z. X. L. Z. G. Chuan, (2006) “A digital image encryption algorithm based on chaotic
sequences”, Computer Engineering and Applications, 19.
[8] G. J. HUANG Xiaosheng, (2007) “Image encryption algorithm based on compound chaotic
sequence and wavelet transform”, Computer Engineering, 14.
[9] M. Morris Mano, (2001) “Digital Design”, Third Edition, Prentice Hall, pages (5-30).
[10] W. W. Yan Weimin, (1992) “Data Structure”, Tsinghua University Press, Beijing.
[11] X. Y. CHEN Tao, (2005) “Design and implementation of encryption algorithm based on n-
dimension magic cube”, Journal Of In- formation, 2:13–14.
Authors
Macharla Kiran Kumar1
received the Bachelor of Technology in Computer
Science & Engineering from Acharya Nagarjuna University, Guntur, India in
2004, and Master of Technology in Computer Science & Engineering from
Acharya Nagarjuna University, Guntur, India in 2009. He is working as a
Lecturer at the Department of Computer Science in R.V.R & J.C College of
Engg, Guntur, India. His main research interests are Data mining, Information
Security, Biometrics, web Information Retrieval, Image Processing, Discrete
Structures, and Network Security.
S. Mukthyar Azam1
received the Bachelor of Technology in Information
Technology from Jawaharlal Nehru Technological University, Hyderabad, India in
2006, and Master of Technology in Computer Science & Engineering from
Jawaharlal Nehru Technological University, Kakinada, India in 2009.He did
Diploma in Embedded Systems Design from Centre for Development of
Advanced Computing (Scientific Society of Department of IT, Ministry of
Communications and IT, Govt. of India), Noida, India. He is working as a
Software Engineer at Research & Development Lab in Synfosys, Hyderabad,
India. His research interests are information security, Network access control,
Intrusion detection and prevention systems, vulnerable access Management, programming methodologies.
Shaik Rasool2
received the Bachelor of Technology in Computer Science &
Engineering from Jawaharlal Nehru Technological University, Hyderabad, India
in 2008. He is currently pursuing Master of Technology in Computer Science &
Engineering from S.C.E.T. and also working as Assistant Professor at the
Department of Computer Science & Engineering in S.C.E.T., Hyderabad, India.
His main research interest includes Data mining, Network Security, Biometrics,
Information Security, Intrusion Detection, Programming Language and security
and Artificial Intelligence.

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