Text encryption

IJSRSET1734120 | Received : 15 August 2017 | Accepted : 31 August - 2017 | July-August-2017 [(3)5: 579-585]
© 2017 IJSRSET | Volume 3 | Issue 5 | Print ISSN: 2395-1990 | Online ISSN : 2394-4099
Themed Section: Engineering and Technology
579
A Text Encryption Algorithm Based on Self-Synchronizing
Stream Cipher and Chaotic Maps
Dr. Ekhlas Abbas Albahrani, Tayseer Karam Alshekly
Department of Computer Science, Mustansiriyah University, Baghdad, Iraq
ABSTRACT
A new text encryption algorithm which is based upon a combination between Self-Synchronizing Stream Cipher and
chaotic map has been proposed in this paper. The new algorithm encrypts and decrypts text files of different sizes.
First of all, the corresponding ASCII values of the plain text are served as input to the permutation operation which
diffuses the positions of these values by using hyper-chaotic map. Secondly, the result values are input to
substitution operation via1D Bernoulli map. Finally, the resultant vales are XOR feedback with the key.The
proposed algorithm has been analyzed using a number of tests and the results show that it has large key space, a
uniform histogram, low correlation and it is very sensitive to any change in the plain text or key.
Keywords : Text encryption, Chaotic map, Self-Synchronizing Stream Cipher, hyper-chaotic, Bernoulli map,
Henon map
I. INTRODUCTION
Chaos theory reliably assumes a dynamic part in current
cryptography. The primary point of interest of the
chaos-based method lies on the arbitrary behavior and
its effect on the initial conditions along with control
parameters. A self-synchronizing or asynchronous
stream cipher is a stream cipher where the key stream is
a key function and a fixed number of previously
encoded text characters. [1] proposed a novel
symmetric text encryption algorithm based on chaos.
They used a 128-bit secret key, two logistics maps with
optimal pseudorandom sequences, original text
properties, and only one permutation diffusions round.
They presented in [2] a new symmetric key stream
image encryption method, by using three 2D chaotic
maps, recently proposed by authors, rather than one
chaotic map. These maps are derived from some plain
curves equations; their trigonometric forms ensure a
large key space. The proposed method is a bi-modular
architecture, in which pixels are mixed by the random
permutation generated by using a new efficient
algorithm and a diffusion phase, in which pixel values
are changed by using a new XOR scheme. According to
[3], a new image-encryption method based on a new
chaotic system consists of joining two chaotic maps: the
logistics map and the cubic map. This chaotic system is
used to encrypt the components of R, G, B from a color
image at the same time and the three components affect
each other. They proposed in [4], the method that
utilizes two 1-D logistic maps with different keys and a
Tinker bell 2-D map. The chaotic sequence generated a
mixed sequence from A and B of the Tinker bell map,
depending on the chaotic sequences of the two logistics
maps. In [5], a novel fast and secure encryption
technique which uses the chaotic map function to
generate the different multiple keys was proposed and it
showed that negligible difference in parameters of
chaotic function generates completely different keys as
well as cipher text. [6] proposed new algorithm for text
encryption based on block cipher and chaotic maps.
This proposed algorithm is encrypted and it decrypted a
block size of (8×8) byte. The nonlinear substitution is S-
box component that was previously designed, this
algorithm used 2d Logistic map and 2d Cross chaotic
map. First, each block is permuted by using Standard
map and then substituted by the bytes in S-box. The
resulting block is then Xored with the key. The
proposed random key generator is based on Tent map to
generate the key sequences that are used in the
encryption and decryption process.
In this paper, a new chaotic and Self-Synchronizing
Stream Cipher encryption / decryption system for text is
suggested. The proposed algorithm consists of three
operations which are implemented based on the chaotic

International Journal of Scientific Research in Science, Engineering and Technology (ijsrset.com)
580
system. These three operations are used to add the
diffusion and confusion properties to stream cipher.
The remaining part of the paper is sorted out as follows:
Section 1 presents the basic theory of the Self-
Synchronizing Stream Cipher and chaotic functions;
Section 2 explains the key generation method, Section 3
introduces the proposed algorithm and Section 4
presents the statistical and security analysis of the
proposed algorithm.
II. METHODS AND MATERIAL
1. Basic theory
In this paper, Self-Synchronizing Stream Cipher and
three chaotic maps have been used, and they are: hyper-
chaotic, 1D Bernoulli map, and 2D Henon map.
1.1 Self-Synchronizing Stream Cipher
Self-Synchronizing stream cipher was developed from
SOBER which was suggested by Rose in1998. This
cipher is designed to generate a secret key of up to 128
bits. It also provides message encryption, message
integrity, or both [7]. In a Self-Synchronous Stream
Cipher (SSSC), the key stream only relies on the key
and on a limited number of the last cipher text symbols
as shown in figure 1 [8].
Figure 1: Self Synchronizing Stream Cipher model
where represent the original message, represent
key stream, ƒ represent the function of key stream
generator and represent the cipher text
1.2.Hyper-chaotic system
A hyper-chaotic system that is generated from Chen’s
chaotic system consists of 4D and was modeled by [9]:
{
( )
( )
Where a, b, c, d and k are parameters, when a=36, b=3,
c=28, d=-16, and -0.7 k 0.7 then the system is
hyper-chaotic.
1.3.1D Bernoulli map
Bernoulli map is one dimensional and is described as
follows [10]:
{ ( )
Where – 0.5 0.5 and 1.2 r 2.
In this paper, the Bernoulli map has been normalized in
a directed manner by exchanging the x rang (– 0.5 x
0.5) in equation (2) into new rang (0 x 255) and the
map becomes:
{ ( )
1.4. 2D Henon map:
Henon Map was first discovered in 1978, which is
described in following equation [11]:
{ ( )
The system has two control parameters a and b, and the
system will show chaotic behavior when (a=1.4, b=0.3).
2.key generation:
The key stream for the proposed algorithm is generated
by using the Chaotic Key Stream Generator (CKSG)
that has been previously designed in [12]. CKSG is
designed based on 3D Henoun map and 3D Cat map. In
the proposed algorithm, the key generation algorithm
consists of the following steps:-
1- Inputting the initial parameters ( ) for
CKSG, which are floating point numbers where the
precision is 10−16
.
2- The CKSG generates the key stream that will be
used for encryption and decryption algorithm.

581
3- The initial parameters( ) are changed by
using simple Xor operation as shown in the
following equations:
{ ( )
The resulting values are used as new initial parameters
for CKSG in order to generate the necessary parameters
for the permutation and substitution operations in the
proposed encryption algorithm.
3.The proposed algorithm:
The proposed stream text encryption algorithm consists
of two major algorithms: encryption algorithm and
decryption algorithm. Each algorithm has four main
operations, these are:-
1- Key generation operations.
2- Permutation operations.
3- Substitutions operations.
4- XOR Feedback operation.
Each step will be described in details in the next section.
3.1 Encryption algorithm:
The main steps of the proposed stream text encryption
algorithm are: -
Step 1: Plain text file is imputed where ASCII values of
the plain text characters are stored in a one
dimensional array called N.
Step 2: Initial parameters ( ) are imputed for
CKSG to generate the key stream for
permutation operations, substitutions operations
and XOR Feedback operation. These parameters
numbers are floating point numbers with
precision of 10-16
and they are considered as the
keys of the algorithm.
Step 3: The following three operations are performed
on the array N:
1- Permutation operation:
 Hyper-chaotic map equation (1) is iterated 50
times and the results are ignored in order to
eliminate the transient effect of chaotic map.
 Hyper-chaotic map is iterated for number of times
equals to the size of N. In each iteration, the four
floating point outputs are converted to the four
integer numbers in the range [1…N]. These
numbers represent the new positions that will be
used to permute the original array N.
 The original array N is permuted by using the
resulting new positions.
2- Substitutions operation: Each byte in the permuted
array is substituted by a new byte in the following
way:
 Each byte of permuted array is imputed to the 1D
Bernoulli map equation (2).
 The output from 1D Bernoulli map is XORed
with position number of the current byte.
 These two steps are repeated on all permuted
array.
3- XOR Feedback operation: is performed on the
substituted array in the following way:
 The first byte in the resulted substituted array is
XORed directly with the first byte of key.
 The remaining bytes in the substituted array are
XORed with key bytes in the following way:
o 2DHenon map is iterated four times. The four
resulting floating point numbers are converted
into four integer number in the range [0…7],
which represent the positions of different
four-bits in byte.
o A new key byte is generated by XORing the
four bit in previous cipher text byte and four
bits in current key byte where their positions
are determined in the previous step
o The new key byte is Xored with the byte in
the substituted array. The result is a cipher
text byte.
3.2. Decryption algorithm:
The text decryption algorithm is a reverse of text
encryption algorithm where each operation can easily be
reversible.
 Reverse XOR Feedback operation is the same
operation in encryption algorithm where it is
performed by XORing the encrypted array to the
same key.
 Reverse Substitutions operation is performed in
the same way as in the encryption algorithm, but
the inverse of 1D Bernoulli map is used.
In reverse permutation operation, Hyper-chaotic map is
iterated in the same way as in encryption algorithm,
where each position defined by Hyper-chaotic map will

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be used as index to return byte in encrypted array to its
original position.
III. RESULTS AND DISCUSSION
Experiment result:
The proposed algorithm is implemented using visual
basic. Net programming language and the tests are
performed on a Laptop with an Intel (R) Core(TM)2
Duo CPU T8100 @2.10 GH and 2 GB RAM .
The Security Analysis:
Key space analysis: -An ideal text encryption
algorithm should have large key spaces. A key space
size smaller than 2128
is not secured enough [13]. The
proposed algorithm has a secret key with key space of
2213
that is sufficient and adequate to resist brute-force
attack according to the computing power of the current
PCs. Here, key space is constructed form the parameters
required for generating keys (initial values ),
these parameters are floating point numbers, where each
one belongs to [-1.18, 1.5]. If the precision of each
parameter is 10-16
, the total space of keys is 2213
((1016
)4
).
The key space is adequate enough, far reaching to
contradict an extensive variety of brute-force attacks.
Key Sensitivity Analysis :- Adecent
cryptosystem should be delicate to the secret keys; this
suggests that 2 cipher texts is generated with small
different secret keys needed to be altogether completely
different. The plaintext of size 490 characters is as
follows:-
This plain text is encrypted by using two keys with very
small difference as shown:
Key 1:
X0=1.5389241520346711
Y0=-0.9275413174568903
Z0=0.3489512706410170
V0=1.8234567891011124
The resulting cipher text is as follows:
Key 2:
X0=1.5389241520346712
Y0=-0.9275413174568904
Z0=0.3489512706410171
V0=1.8234567891011125
The resulting cipher text is as follows:
The cipher text with inaccurate key does not
demonstrate any data related with plaintext, hence the
proposed algorithm is sensitive to secret key, the
correlation of the two cipher text is equal to (-0.0215),
this means the two cipher text are different.
Statistical Attack Analysis:
The statistical analysis of the encrypted image and
plaintext can be considered by:
 Histogram analysis: - this indicates how
constantly a conception shows up in the content.
The histogram can tackle information on the
plaintext, the closeness to one chest key or both.
On the instance that the histogram of the all
images in figure content is reasonably equally
circulated over the scale, no data about the
plaintext can be accumulated through histogram
examination. The histogram of the plaintext of
size 6439 characters and its cipher text are shown
in Figure (2). The cipher text histogram is
uniform and does not indicate any information
about the original plaintext, so the proposed
scheme is powerful against histogram attacks in
addition to frequency attacks.

583
 Correlation coefficient analysis: - Correlation
assessment checks the relationship between
plaintext and cipher text. The correlation
distribution of two horizontally adjacent bytes in
the plaintext of size 6439 characters and its cipher
text are shown in Figure (3). This Figure shows
that the correlation distribution of cipher text is
uniform as compared with the plain text. Table (1)
shows the results of correlation coefficient of 10
plaintext and its cipher text files with different
sizes. These results indicate that the correlations
between the plaintext and its cipher text are very
small.
Differential attack analysis:
To implement plaintext sensitivity examination, a rival
may attempt to build up a relationship between the plain
text and its cipher text by watching the impact of a
slight change on the overall encryption output. With the
assistance of different examination strategies, the secret
key might be acquired. This type of cryptanalysis turns
out to be practically infeasible if such a slight change
can be adequately diffused to the entire ciphered text.
There are two measurements to decide this robustness
[14].
 NPCR (Net Pixel Change Rate): - it measures the
quantity of characters that are different between
two cipher texts C1 and C2 from two analogous
plaintext; the value of NPCR is represented in
percentage, where 100% means that both cipher
texts are totally different. The NPCR is calculated
with:
(a)
(b)
Figure (2): Histograms of: a) plaintext and b)
cipher text
Table 1: the result of correlation between text file
File name Correlation Size of file
in byte
Plaintext1 &
ciphertext1
0.0067 5116
Plaintext2 &
ciphertext2
0.0034 5479
Plaintext3 &
ciphertext3
0.0058 7278
Plaintext4 &
ciphertext4
0.0167 3595
Plaintext5 &
ciphertext5
0.0046 4001
Plaintext6 &
ciphertext6
-0.0136 12109
Plaintext7 &
ciphertext7
-0.0335 2786
Plaintext8 &
ciphertext8
-0.0008 6439
Plaintext9 &
ciphertext9
0.0092 11260
Plaintext10 &
ciphertext10
0.000001 8279
∑
( )
( )
Where N is the text length and
( ) {
( ) ( )
( ) ( )
( )

584
Where C1 (i) and C2 (i) are the symbol values
of the cipher text C1 and C2.
 UACI (Unified Average Changing Intensity): -
it is the intensity difference average between
two cipher texts C1 and C2.The UACI is
calculated as follows:
∑| | ( )
Table 2 demonstrates the result of NPCR and UACI.
These results are very close to ideal values of NPCR
and UACI which means that the proposed algorithm is
robust against differential attacks. In addition, these
results show that a small change in the original image
will result in a great change in the encrypted image; this
implies that the proposed algorithm has an excellent
capability to resist the differential attack.
(a)
(b)
Figure 3 : Correlation analyses: a) plaintext correlation
b)cipher text correlation.
Table 2: The results of UACI and NPCR
File name NPCR UACI
Ciphertext1 98.87643 32.658
Ciphertext2 98.67433 33.067
Ciphertext3 99.55001 33.143
Ciphertext4 99.05432 33.674
Ciphertext5 98.76534 32.775
Ciphertext6 98.60068 32.754
Ciphertext7 99.26086 33.077
Ciphertext8 99.64341 33.214
Ciphertext9 99.17743 33.430
Ciphertext10 99.45088 33.601
Information Entropy Analysis:
The encryption process must generate an unpredictable
message, similar to noise, and with high disturbance.
These characteristics are checked with the information
entropy examination: the higher entropy, higher
disturbance in the encoded text. In contrast, if the
encryption process is not sufficiently random, low
entropy and the cryptographic algorithm can be
responsible for the entropy attack, because there is a
certain level of predictability of the encryption
technique.The entropy H (m) of a message m can be
calculated as follows [15]:-
( ) ∑ ( )
( )
( )
Where N is the number of bits of the message m, 2N
means all possible symbols, p(mi) represents the
probability of mi and the entropy is expressed in bits. If
a message is encrypted with 2N
possible symbols, the
entropy should be H(m) = N ideally. Table (3)
demonstrates the result of entropy analysis of 10 text
files. These results are very close to ideal values of
entropy, which means that the proposed algorithm is
robust against entropy attacks.
Table 3: Results of entropy analysis of the proposed
algorithm
The ciphertext Entropy
Ciphertext1 7.9630
Ciphertext2 7.9699
Ciphertext3 7.9761
Ciphertext4 7.9485
Ciphertext5 7.9579
Ciphertext6 7.9877
Ciphertext7 7.9227
Ciphertext8 7.9703
Ciphertext9 7.9809
Ciphertext10 7.9785

585
IV. CONCLUSION
A self-synchronizing or asynchronous stream cipher is a
stream cipher where the key stream is a key function
and a fixed number of previously encoded text
characters, but it has little diffusion and confusion. The
proposed text encryption algorithm increased this
property by the combination of a Self-Synchronizing
Stream Cipher and chaotic map .The main idea is to
encrypt and decrypt a text file of any size based on
permutation, substitution and XOR feedback operation.
Security analyses indicate that the proposed algorithm
has desirable properties such as the key space analysis,
statistical attack analysis and differential attack analysis
that are performed numerically and visually. All the
experimental results showed that the proposed
encryption scheme is secure because of its large key
space; it is highly sensitivity to the cipher keys and
plaintext. All these agreeable properties make the
proposed algorithm a potential possibility for encryption
of multimedia data such as images, audios and even
videos.
V. REFERENCES
[1]. M. A. Murillo-Escobar, F. Abundiz-Perez, C.
Cruz-Hernández, R. M. López-Gutiérrez “A novel
symmetric text encryption algorithm based on
logistic map", Proceedings of the 2014
International Conference on Communications,
Signal Processing and Computers,215
[2]. R. E. BORIGA, A. C.DĂSCĂLESCU, and A. V.
DIACONU" A New Fast Image Encryption
Scheme Based on 2D Chaotic Maps", IAENG
International Journal of Computer, 30 November
2014
[3]. N.F.Elabady , H.M.Abdalkader, M. I. Moussa ,S.
F. Sabbeh" Image Encryption Based on New One-
Dimensional Chaotic Map ", IEEE,2014
[4]. G.Hanchinamani, L.Kulakarni" A Novel
Approach for Image Encryption based on
Parametric Mixing Chaotic System", International
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June 2014
[5]. A.A. Khare, P. B. Shukla and S. C. Silakari"
Secure and Fast Chaos based Encryption
Systemusing Digital Logic Circuit", Computer
Network and Information Security,vol 6,2014
[6]. E. A. Albhrany, Dr. L.F. Jalil, Prof. Dr. H. H.
Saleh" New Text Encryption Algorithm Based on
Block Cipher and Chaotic Maps", IJSRSET, Vol
2, 2016
[7]. TAYSEER S. ATIA," DEVELOPMENT OF A
NEW ALGORITHM FOR KEY AND S-BOX
GENERATION IN BLOWFISH ALGORITHM",
Journal of Engineering Science and Technology,
Vol. 9, No. 4 (2014).
[8]. P.Guillot and S.Mesnager," Non-Linearity and
Security of Self Synchronizing Stream Ciphers",
International Symposium on Nonlinear Theory
and its Applications, 2005
[9]. T.Gao , Z. Chen ,"A new image encryption
algorithm based on hyper-chaos",Elsevier,2008
[10]. Sheela S.and S. V. Sathyanarayana “Application
of chaos theory in data security-a
survey",ACCENTS Transactions on Information
Security,Vol 2(5), 2017.
[11]. K.Singh, K. Kaur" Image Encryption using
Chaotic Maps and DNA Addition Operation and
Noise Effects on it", International Journal of
Computer Applications, Volume 23, June 2011
[12]. Dr. E.A. Albhrany, T.K. Alshekly"A New Key
Stream Generator Based on 3D Henon map and
3D Cat map",International Journal of Scientific &
Engineering Research,Volume 8, Issue 1,
January-2017
[13]. W. Liu , K. Sun, C.Zhu “A fast image encryption
algorithm based on chaoticmap",ElsevierLtd,2016
[14]. C.Fu , J.B. Huang , N.N. Wang , Q.B. Hou and
W.M.Lei “A Symmetric Chaos-Based Image
Cipher with an Improved Bit-Level Permutation
Strategy",entropy,2014, 16
[15]. M.A. Murillo-Escobar , C. Cruz-Hernández, F.
Abundiz-Pérez , R.M. López-Gutiérrez
“Implementation of an improved chaotic
encryption algorithm for real-time emb e dde d
systems by using a 32-bit
microcontroller",Elsevier,2016

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