Physics Letters A 372 (2008) 394–400
www.elsevier.com/locate/pla
A new image encryption algorithm based on hyper-chaos
Tiegang Gao
a,∗
, Zengqiang Chen
b
a
College of Software, Nankai University, Tianjin 300070, PR China
b
Department of Automation, Nankai University, Tianjin 300070, PR China
Received 24 October 2006; received in revised form 17 July 2007; accepted 20 July 2007
Available online 26 July 2007
Communicated by A.P. Fordy
Abstract
This Letter presents a new image encryption scheme, which employs an image total shuffling matrix to shuffle the positions of image pixels and
then uses a hyper-chaotic system to confuse the relationship between the plain-image and the cipher-image. The experimental results demonstrate
that the suggested encryption algorithm of image has the advantages of large key space and high security, and moreover, the distribution of grey
values of the encrypted y image has a random-like behavior.
©
2007 Elsevier B.V. All rights reserved.
Keywords: Hyper-chaos; Image encryption; Image total shuffling matrix; Key space
1. Introduction
With the rapid developments in digital image processing
and network communication, electronic publishing and wide-
spread dissemination of digital multimedia data over the In-
ternet, protection of digital information against illegal copying
and distribution has become extremely important. To meet this
challenge, many new encryption schemes have been proposed
[1–4]. Among them, chaos-based algorithms has suggested a
new and efficient way to deal with the intractable problem of
fast and highly secure image encryption, and it has been proved
that in many aspects chaotic maps have analogous but different
characteristics as compared with conventional encryption algo-
rithms [5–10].
The chaos-based encryption was first proposed in 1989 [11],
since then, many researchers have proposed and analyzed a lot
of chaos-based encryption algorithms, these work all have been
motivated by the chaotic properties such as the sensitive de-
pendence on initial conditions and system parameters, pseudo-
random property, non-periodicity and topological transitivity,
etc. While classical encryption algorithms are sensitive to keys,
*
Corresponding author.
E-mail address: gaotiegang@nankai.edu.cn (T. Gao).
so some elaborated constructions are need to achieve satisfying
and safer chaos-based encryption.
It is well known that a good encryption algorithm should
be sensitive to the cipher keys, and the key space should be
large enough to make brute-force attacks infeasible [12].Re-
cently, in [13], a fast chaotic cryptographic scheme based on
iterating a Logistic map was proposed, and no random num-
bers need to be generated and the look-up table used in the
cryptographic process is updated dynamically. In [14],atwo-
dimensional chaotic cat map is generalized to 3D for designing
a real-time secure symmetric encryption scheme, which em-
ploys the 3D cat map to confuse the relationship between the
cipher-image and the plain-image. Also recently, authors in [15]
thought that the algorithm for encoding binary images using
one-dimensional chaotic map [16] is not secure enough, and
there is the same problem with the algorithm proposed in [17],
to overcome the drawbacks such as small key space and weak
security of one-dimensional chaotic map, a nonlinear chaos al-
gorithm is proposed in [18], which shows high-level security
and acceptable efficiency.
Recently, because hyper-chaos has more than one positive
Lyapunov exponent, and have more complex dynamical char-
acteristics than chaos, so secure communication schemes based
on hyper-chaotic systems have been investigated [19,20], but at
present, there is little work about the study of encryption algo-
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doi:10.1016/j.physleta.2007.07.040