How and Why Do I Choose Chaotic Cryptography as the Topic of My Dissertation

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How and Why Do I Choose Chaotic Cryptography as
the Topic of My Dissertation
Shujun LiVisiting Student at VC Group, Microsoft
Research Asia Institute of Image
ProcessingXian Jiaotong UniversityApril, 2002
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Table of Contents

• Background
• Chaotic Cryptography
• Something about My Research
• A Brief Introduction of Our Research
• Statistical Properties of Digital Chaos
• Analysis of Presented Chaotic Ciphers
• Design of New Chaotic Ciphers
• Analysis of Image Encryption Methods
• Digital Watermarking

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1. Background
Since 1970s, modern cryptology has been developed
and the following two milestones are well-known
the proposal and establishment of DES as a
commercial encryption standard, the proposal of
public-key encryption scheme and the emergence of
RSA system. From my viewpoint, modern cryptology
is a cross-discipline involving mathematics,
information theory, communications technology,
networking, etc. As the rapid progress of
networking technology, the security of encryption
systems have been confronted with effective
challenges. It has been reported that DES and RSA
were successfully attacked based on distributed
computing. Today, the key size of 128256 bits
are required to provide higher security (AES).
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Background Recent Progress
In Recent years, many new sub-disciplines of pure
cryptology has been emerged Biometrics, Network
Security, E-Commerce, Information Hiding, etc. As
a cross-discipline of cryptology and image/video
processing, image/video security has also
attracted much attention recently. The following
two topics are chiefly focused digital
watermarking of image and video, image/video
encryption. The former corresponds to information
hiding in cryptology, and the latter is an
application of pure cryptology to protect
multimedia contents. The fundamental requirements
of an image/video encryption method include fast
encryption speed, simple implementation together
with compression algorithms, and extended
avalanche property.
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Background Why Use Chaos?
The idea of using chaos to construct encryption
systems has been developed since 1989. Some works
are made on analog circuits with chaotic
phenomena, and others on digital circuits or
computers with finite precision effects. The
significance of introducing chaos into
conventional cryptology can be explained with the
following facts 1) some progresses in cryptology
are promoted by newly introduced theories (two
examples are Elliptic Curve Theory and Quantum
Mechanics) 2) chaos can also be used to enhance
the design of traditional ciphers, such as using
chaos to obtain S-Boxes without trapdoors 3)
well-established chaos theory will be useful to
analyze some essentially properties of
traditional ciphers 4) considerations on
patents, laws and national security.
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2. Chaotic Cryptography
Chaotic systems has many perfect dynamical
properties, which can be connected with some
requirements of a good cipher. Such properties
include exponential sensitivity dependent on the
initial conditions/control parameters, ergodicity
and mixing property, etc. The first paper about
chaotic cryptography is published in Cryptologia
(1989), and an early milestone paper about
chaotic secure communications occurred in
Physical Review Letters (1990). From the middle
of 1990s, cryptanalytic works has also been
developed and many presented chaotic ciphers
(especially the ones using chaotic
synchronization techniques) have been known
insecure.
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Chaotic Cryptography

• Generally speaking, there are two chief
  kinds of chaotic ciphers
• Secure communications or cryptosystems based on
  chaos synchronization technique of analog
  circuits
• Chaos-based ciphers realized on digital circuits
  or computers with finite precision effect.
• In addition, the use of chaos in some other
  areas can enrich the knowledge about the design
  and the performance analysis of chaotic ciphers
  chaotic communications (especially chaotic spread
  spectrum communications), chaotic pseudo-random
  number generations, chaotic signal estimation and
  detection, chaotic digital watermarking.

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Chaotic Cryptography Diagrammatic View of
Related Disciplines
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3. Something about My Research

• Why I choose Chaotic Cryptography as the
  topic of my dissertation? It is due to the
  following facts
• I became strongly interested in Chaos and
  Fractals since 1997.
• Because of some specific reasons, I had to cease
  my previous research topic about Intelligent
  Transportation Systems (ITS) in 2000.
• I found another interest applied cryptography in
  2000, and started to read some papers about
  chaotic cryptography.
• I noticed that some image encryption methods
  involve the use of discrete-time chaotic systems
  (especially 2-D ones).

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Something about My Research Directions

• Statistical Properties of Digital Chaotic Systems
• Analysis and Enhancements of Presented Chaotic
  Ciphers and Related Cryptanalytic Methods
• Some New Encryption Schemes Based on Digital
  Chaotic Systems
• Chaotic Stream Ciphers Based on CCS-PRBG (PRBG
  Based on Couple Chaotic Systems)
• A Very-Fast Chaotic Product Cipher Based on
  Multiple Chaotic Systems
• Image Encryption Methods
• Cryptanalysis of Chaotic Image Encryption Methods
• Digital Watermarking

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Something about My Research Related Publications

• Journal Paper(s)
• Improving Security of a Chaotic Encryption
  Approach, Physics Letters A, 290(¾) 127-133,
  2001
• Reviewed Conference Papers
• On the Security of Bit Recirculation Image
  Encryption Method, Just accepted by IEEE ICIP
  2002
• Cryptanalysis of a Chaotic Image Encryption
  Methods, Proc. IEEE ISCAS 2002, to be published
• Statistical Properties of Digital Piecewise
  Linear Chaotic Maps and their Roles in
  Cryptography and Pseudo-Random Coding,
  Cryptography Coding the 8th IMA Int. Conf.
  Proc., Lecture Notes in Computer Science, vol.
  2260, pp. 205-221
• Pseudo-Random Bit Generator Based on Couple
  Chaotic Systems and its Applications in
  Stream-Cipher Cryptography, Progress in
  Cryptology INDOCRYPT 2001, Lecture Notes in
  Computer Science, vol. 2247, pp. 316-329
• Chaotic Encryption Scheme for Real-Time Digital
  Video, Real-Time Imaging VI, Proceedings of
  SPIE, vol. 4666, 2002

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4a. Statistical Properties of Digital Chaotic
Systems
When a chaotic system is realized in digital
computers with finite computing precision, its
dynamical properties will be far different from
the ones of continuous-value systems. Typical
problems include short cycle length, degraded
distribution and correlation. Although some
researchers have noticed such a problem, there
are not yet an established theory to measure the
dynamical degradation of digital chaotic systems.
In many applications of digital chaos, no
special attention is paid on potential defects
that may be induced by the dynamical degradation.
Some remedies have been proposed to improve the
dynamical degradation. Since no theoretical tool
exist, experimental tests are widely used.
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Statistical Properties of Digital Chaotic Systems

• We focus this problem from two sides
• For different chaotic systems, whether or not can
  we exactly (mathematically) measure the dynamical
  degradation of their digital versions in finite
  precision?
• Now we have obtained some useful results for
  piecewise linear chaotic maps (PWLCM) which are
  widely-used in many applications of digital chaos
  4.
• How to estimate the performance of the
  improvement of a remedy to the dynamical
  degradation?
• We have made some qualitative analysis on digital
  piecewise linear chaotic maps and three known
  remedies, based on the results obtained in 4.

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4b. Analysis of Presented Chaotic Ciphers and
Cryptanalytic Methods
It is well-acknowledged that only cryptanalysts
can judge the real security of a cryptosystem.
I have made some cryptanalyses of some presented
chaotic ciphers, and given some suggestions to
improve some chaotic ciphers. In addition, I have
also found problems in some cryptanalytic works
proposed by other researchers. Here, we list the
ideas I have made and will make in the future.
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Cryptanalysis I

1. Cryptanalysis of a class of chaotic stream
   ciphers proposed by Hong Zhou Xie-Ting Ling
   (two manuscripts are under review)
2. Problems with the chaotic probabilistic cipher
   proposed by S. Papadimitrious et al. (one
   manuscript is under review)
3. Cryptanalysis of three image encryption methods
   based on chaotic systems proposed by J.-C. Yen
   J.-I. Guo at Taiwan (two manuscripts have been
   accepted 2,3 and another one has not yet been
   ready)

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Cryptanalysis II Improvements

1. Improving the security of the chaotic cipher
   proposed by E. Alvarez et al. in 1999 (based on
   the analysis of the four cryptanalyses presented
   by G. Alvarez et al. in 2000) 1
2. Re-visiting the security of the chaotic block
   cipher suggested at EuroCrypt91 and the
   feasibility of Bihams attacks (one manuscript is
   under review)
3. Performance analysis of Jakimoski-Kocarevs
   attack (2001) to Baptistas chaotic cipher (1998)
   (manuscript has not yet been ready)

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4c. Design of New Chaotic Ciphers

• Based on our above works, we can give some
  useful suggestions for the design of digital
  chaotic ciphers
• Some remedy SHOULD be adopted to avoid the
  defects induced by the dynamical degradation of
  digital chaotic systems
• To avoid the known/chosen-plaintext attack,
  minimize information leaking about the digital
  chaotic orbits as possible as you can
• Use multiple chaotic systems to make the
  ciphertexts more complicated
• Use simpler chaotic systems to obtain higher
  speed, easier implementation and lower cost.

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Design of New Chaotic Ciphers

• Following the above criteria, we have
  proposed two new encryption schemes based on
  digital chaotic systems (papers have been
  published).
• Chaotic stream ciphers based on CCS-PRBG
  (Pseudo-random bits generator based on couple
  chaotic systems) 5
• A very-fast chaotic product cipher based on
  multiple chaotic systems 6
• Both the above two schemes use multiple
  chaotic systems to realize more efficient
  performance of concealing the information about
  digital chaotic orbits, and PWLCMs to increase
  the encryption speed and reduce the system
  implementation.

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4d. Analysis of Image Encryption Methods
We have mentioned that many image encryption
methods involve the use of digital chaotic
systems, especially 2-D chaotic maps. The image
encryption schemes using chaos can be divided two
classes Scharinger-Fridrich scheme and Yen-Guo
scheme. Generally speaking, the former is more
secure but slower, and the latter is faster but
insecure. In regards to the insecurity of Yen-Guo
scheme, we have published two papers 2,3.
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Problems with Other Image Encryption Methods

• We have also found security defects of other
  image encryption schemes without using chaos.
• SCAN-based image encryption scheme proposed by
  N. G. Bourbakis and C. Alexopoulos (joint
  encryption/compression algorithm)
• Related paper are published in Pattern
  Recognition (1992, 2001), J. Electronic Imaging
  (1995) and some conferences IEEE ICIIS99, Proc.
  SPIE vol. 2914 (1995) and IEEE ICSMC97. In fact,
  in Information Processing Letters (1996), J. K.
  Jan and Y. M. Tseng have pointed out that
  SCAN-based encryption scheme is not secure enough
  and can be broken by the known-plaintext attack
  with only a pair of plain-image/cipher-image.

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Problems with Other Image Encryption Methods

• Image encryption scheme based on BS compression
  algorithm proposed by T. J. Chuang J. C. Lin
• Related paper is published in J. Electronic
  Imaging (1998). No cryptanalysis has been
  reported. But such a scheme cannot resist
  known/chosen-plaintext attack, and the base is
  too small to ensure high security.
• Quadtree-based joint encryption/compression
  algorithm proposed by H. K. C. Chang J. L. Liu
  and enhanced by K. L. Chung L. C. Chang
• Related papers are published in Signal
  Processing Image Communication (1997) and
  Pattern Recognition Letters (1998). Neither
  schemes can resist known-plaintext attack. Some
  analysis has been reported by H. Cheng X. Li.

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4e. Digital Watermarking
References have been collected and some ones have
been read. To tell the truth, I have not been in
the hall of watermarking till now. Some
researchers have suggested using chaos to
construct digital watermarking, such as the one
presented by G. Voyatzis and I. Pitas (Computers
Graphics - UK, 1998). Two basic ideas are
employed a) using chaos to generate
pseudo-random watermarking b) using chaos to
realize pseudo-random embedding of the
watermarking.
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Thanks For your watching and advice!