In modern society, digital information plays an important role in our daily life, and
among them images show a greater attraction than ever before. Many of them are
private, so, how to make a protection is an important issue. Cryptography approaches
have been studied extensively to hide the secret information. However, traditional text
encryption algorithms such as AES (Advanced Encryption Standard), DES (Data
Encryption Standard), and IDEA (Internatinal Data Encryption Algorithm), cannot be
applied directly. Aiming to the special characteristics of digital image, some encryption
schemes are proposed and designed in this thesis using chaotic systems.
Generally, the structure of permutation and diffusion is commonly used in the
image cipher. Because of the low security existing in permutation or diffusion operation
with only one round of iteration, mixture of the double functions with several overall
rounds of encryption should be considered to reach a required security level. The main
work of permutation is to exchange the pixel positions for an image and then reduce the
strong correlation among the adjacent pixels. To meet with the Shannon theorem, i.e.,
the effect of snow avalanche, a tiny change in the plain-image including even just onebit
difference, or small changes in initial keys, should lead to a totally different cipherimage.
Diffusion operation is adopted to connect the current pixel with next pixel in the
cipher-image.
Quite a lot of chaotic image encryption algorithms have been studied in recent
years. Many algorithms can indicate good effect in the gray distribution and large key
space. However, we find that all the chaotic values used in most of references are the
current state. That is to say, time-delay phenomenon is not considered in the encryption
process. To solve this problem, an image encryption scheme based on time-delay and
hyper-chaotic system is proposed. As is known, the time-delay phenomenon can be
commonly observed in daily life such as wave transmission. So it is incorporated in the
generation of pseudo-random chaotic sequences in our method. Furthermore, a structure
of forward plus backward diffusions is designed to achieve higher security.
We also find that for most of the references, either in stage of permutation or
diffusion, the values of keys iterated into chaotic maps remain the same in the whole
process in each round of iteration. To carry out the auto-updating for keys, like one-time
pad, an efficient self-adaptive model for chaotic image encryption is presented in both
stages. Moreover, using simple chaotic maps can avoid complex mathematical solving
methods such as Runge-Kutta method. So, much time is saved to solve highdimensional
ordinary differential equations. Numerical experiments show that the
proposed self-adaptive method can well resist chosen-plaintext and known-plaintext
attacks.
In the permutation stage, many image encryption algirhtms concentrate on the oneto-
one operation of pixel position exchange. As to the values generated from a chaotic
map, they first do the arrangement, for example, using the sort function for these values
from small to big. Then, we find the original position for each value and get an index set
for shuffling positions. As we know, it is a hard work to obtain the index set because it
costs us more time. As a remedy, a novel image encryption algorithm with diffusion
function only, instead of classical permutation plus diffusion operations, is proposed.
Consequently, the new method can supply us a fast encryption scheme. Compared with
that of the traditional architectures, it can reduce greatly the computation redundancy.
Normally, an attacker can break the encryption algorithm by statistical analysis if
the histogram of cipher-image cannot show a uniform distribution. Most researchers
studied the change function for pixel values in the operation of diffusion only. To reach
a higher level of security in the designed algorithm, a feedback chaotic image
encryption scheme based on both bit-level and pixel-level operations is proposed, in
which bit shifting in different bit-planes is implemented in the permutation stage. As a
result, both operations of permutation and diffusion can change the pixel values at the
same time compared with currently existing methods. SHA-3 (Secure Hash Algorithm-
3) algorithm is also employed to get hash value as output which is very sensitive to any
input message.
In conclusion, this thesis studies some new chaos-based image encryption schemes.
Making use of the characteristics of chaotic systems, such as control parameters,
ergodicity, and sensitivity to initial conditions, classical structure of confusion and
diffusion designed by Shannon theorem is employed in our works. Compared with other
references, this thesis shows some novelties, for example, the auto-updating function for
initial keys, keystream generation depending on the plain-image, and double functions
of diffusion effects due to bit shifting among different bit-planes. All experiments and
security analyses demonstrate the high security and high efficiency of the proposed
image encryption schemes.
| Date of Award | 15 Jul 2015 |
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| Original language | English |
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| Awarding Institution | - City University of Hong Kong
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| Supervisor | Kwok Wo WONG (Supervisor) |
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