Journal of Signal and Information Processing, 2011, 2, 238-244
doi:10.4236/jsip.2011.23033 Published Online August 2011 (http://www.SciRP.org/journal/jsip)
Copyright © 2011 SciRes. JSIP
Image Encryption Based on the General Approach
for Multiple Chaotic Systems
Qais H. Alsafasfeh, Aouda A. Arfoa
Electrical Engineering Department, Tafila Technical University, Tafila, Jordan.
Email: qsafasfeh@ttu.edu.jo, aouda@ttu.edu.jo
Received April 10
th
, 2011; revised July 5
th
, 2011; accepted July 13
th
, 2011.
ABSTRACT
In the recent years, researchers developed image encryption methods based on chaotic systems. This paper proposed
new image encryption technique based on new chaotic system by adding two chaotic systems: the Lorenz chaotic system
and the Rössler chaotic system. The main advantage of this technique is stronger security, as is shown in the encryption
tests.
Keywords: Lorenz Equations, Rossler Systems, Image Encryption, Chaos
1. Introduction
Recent researches of nonlinear dynamical systems have
been increasingly based on Chaos [1]. Image encryption
schemes have been increasingly studied to meet the de-
mand for real-time secure image transmission over pri-
vate or public networks. Conventional image encryption
algorithm such as data encryption standard (DES), is not
suitable for image encryption because of the special
storage characteristics of an image [2] and weakness of
low-level efficiency when the image is large [3].The
chaos-based encryption has suggested a new and efficient
way to deal with the intractable problem of fast and
highly secure, image encryption.
Chaotic systems have many important properties, such
as the sensitive dependence on initial conditions and sys-
tem parameters, the density of the set of all periodic
points and topological transitivity, etc. Most properties
are related to some requirements such as mixing and dif-
fusion in the sense of cryptography [4]. Matthews pro-
posed a chaotic encryption algorithm in 1989 [5], since
then, increasing researches of image encryption technol-
ogy are based on chaotic systems [4,6-12]. These meth-
ods have high-level efficiency but also weakness, such as
small key space and weak security and complexity to
overcome these drawbacks. This paper proposes a image
encryption scheme based on combining two chaotic sys-
tems (Lorenz and Rosslere) and compares the results
with the other techniques. The paper is organized as fol-
lows. Section 2 discusses the proposed scheme. Section 3
presents experimental results. Section 4 to Section 7 dis-
cuss and examine the new scheme by applying statistical
tests test also the security of the chaotic encryption is
discussed. Conclusions are drawn in Section 8.
1.1. Lorenz Chaotic System
The Lorenz equations are a fairly simple model in which
to study chaos.
x y x
y rx y xz
z xy z
(1)
The arbitrary parameters , r and b > 0 and for this
example are = 10, r = 28, b = 8/3. This system of
differential equations is then solved numerically using
Matlab’s ode 45 Runge Kutta routine. The results are
plotted in Figure 1 [12].
1.2. Rossler Chaotic System
A system of three differential equations has a simpler
strange attractor than Lorenz’s. That the Rossler system
has only one quadratic nonlinear xz numerical integra-
tion shows this system has a strange attractor for a = b=
0.2, c = 5.7 as shown in Figure 2 [12].
x y z
y x ay
z b zx c
(2)
2. The Proposed Scheme
First, most researchers used chaotic image encryption