Image Encryption Algorithm Analysis and Comparison

Agenda
 Encryption Introductory Concepts
 Encryption Algorithms
 Evolutionary Algorithms
 Chaos Theory
 Swarm Intelligence/Particle Swarm Model
1. Analysis and Comparison of Image Encryption Algorithms
2. From Chaos to Cryptography
3. From Chaotic Maps to Encryption Schemes
4. Survey - Image Encryption using Chaotic Cryptography Schemes
5. New Encryption Schema Based on Swarm Intelligence Chaotic Map
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Encryption Introductory Concepts
 Encryption is the process of transforming information using an algorithm to make it
unreadable to anyone except those possessing special knowledge
 Encryption has long been used by militaries and governments to facilitate secret
communication
 Encryption is now commonly used for protecting information within many kinds of
civilian systems
 Files on computers and storage devices
 Data being transferred via networks e.g. Internet, mobile telephones, wireless
microphones, wireless intercom systems, Bluetooth devices and bank automatic teller
machines
 The harder part in encryption is to ensure that people who are supposed to
decipher the encrypted message can do so with ease, yet only those authorized
are able to decipher it
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Encryption Algorithms (1/2)
 Encryption Algorithm is some mathematical operations to conduct substitutions
and transformations to the information to convert it to the encrypted form
 Encryption Algorithm main purpose is to provide:
 Authentication: Provding one's identity before granting access
 Privacy and Confidentiality: Ensuring that outsiders can’t read data intended for specific
parties
 Integrity: Ensuring that the message has not been modified in any way before it arrives to
the intended recipient
 Non-Repudiation: Ensuring that the message is truly originated from the sender
 Generally encryption algorithm consists of:
 Plaintext: The text message to which an algorithm is applied
 Encryption Algorithm: Mathematical operations to conduct substitutions and
transformations to the plaintext
 Secret Key(s): An input to the algorithm that dictates the encrypted outcome
 Ciphertext: The encrypted or scrambled message produced by applying the algorithm to
the plaintext message using the secret key
 Decryption Algorithm: The encryption algorithm in reverse, it uses the ciphertext and the
secret key to derive the plaintext message
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Encryption Algorithms (2/2)
 Symmetric Algorithms (Conventional, Private Key and Single Key Encryption)
 Enquire all communicating parties to share a common key
 Use single key to encrypt and decrypt data
 Work fast and are well suited for encrypting blocks of messages at once
 It is essential that the sender and the receiver have a way to exchange secret key in a
secure manner
 Asymmetric Algorithms (Public Key Encryption)
 Each sender and recipient has a private key
 There’s a public key, which can be known by anyone
 Each encryption/decryption process requires at least one public key and one private key
 Asymmetric Algorithms tend to be slower than their symmetric counterparts
 They aren't recommended for encrypting large amounts of data
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Evolutionary Algorithms (1/2)
 Artificial Intelligence “The study and design of intelligent agents”, it’s
the intelligence of machines, where an intelligent agent is a system that perceives
its environment and takes actions that maximize its chances of success
 Population is a set of organisms in which any pair of members can breed together,
this implies that all members belong to the same species and live near each other
 Evolutionary Computation is a subfield of artificial intelligence, it uses iterative
progress in a population such as growth or development, this population is
then selected in a guided random search using parallel processing to achieve the
desired objective
 Candidate Solution is a member of a set of possible solutions to a given problem,
a candidate solution does not have to be a likely or reasonable solution to the
problem, it is simply the set that satisfies all constraints
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Evolutionary Algorithms (2/2)
 Metaheuristic designates a computational method that optimizes a problem
by iteratively trying to improve a candidate solution with regard to a given measure
of quality
 Fitness Function is a function that prescribes the optimality of a solution so that
any solution may be ranked against all the other solutions
 Evolutionary Algorithms (EAs)
 EAs subsets of evolutionary computation, a generic population based
metaheuristic optimization algorithms
 EAs use some mechanisms inspired by biological evolution such as reproduction, mutation,
recombination and selection
 Candidate solutions to the optimization problem play the role of individuals in a
population
 EAs often perform well approximating to all types of problems because they ideally do not
take any assumptions about the underlying fitness landscape
 EAs show successes in fields as diverse as engineering, art, biology, economics,
physics, marketing, genetics, operations research, robotics, social sciences, politics and
chemistry
 Some of the most widely used EAs techniques are Genetic Algorithms, Particle Swarm
Optimization techniques
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Chaos Theory
 Dynamical System is a concept in mathematics where a fixed rule describes the
time dependence of a point in a geometrical space e.g. mathematical
models describing the swinging of a clock pendulum and the flow of water in a
pipe
 Chaos Theory
 Field of study in applied mathematics, with applications in several disciplines
including physics, economics, biology, and philosophy
 It studies the behavior of dynamical systems that are highly sensitive to initial conditions
 Small differences in initial conditions (such as those due to rounding errors in numerical
computation) yield widely diverging outcomes
 These systems are deterministic, meaning that their future behavior is fully determined by
their initial conditions
 Chaotic behavior can be observed in many natural systems, such as the weather
 Chaos-Based encryption technology has been studied for decades and it has
become an important branch of cryptography
 Attractiveness points of using chaos as the basis for developing cryptosystem are:
 Sensitivity to initial conditions
 The iterative values generated are completely random in nature, although limited between
bounds
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Swarm Intelligence/Particle Swarm Model
 A completely different approach to chaotic-based encryption based on artificial
intelligence has been proposed recently
 Swarm Intelligence
 Design framework based on social insects behavior
 Social insects such as ants, bees, and wasps are unique in the way these simple individuals
cooperate to accomplish complex, difficult tasks
 This cooperation is distributed among the entire population
 Particle Swarm Model
 Consists of swarm of particles moving iteratively through the m-dimension problem space
to search the new solutions (positions)
 Each particle adjusts its position according to its own experience and according to the
experience of its neighbors, making use of the best position encountered by itself and its
neighbors
 A certain quality measure “Fitness Function” f is defined making it possible for particles to
compare different problem solutions
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1. Analysis and Comparison of Image
Encryption Algorithms
 In this paper, we analyzed current image encryption algorithms and
compression is added for two of them (Mirror-like image encryption and
Visual Cryptography)
 A study of image compression is becoming more important since an
uncompressed image requires a large amount of storage space and high
transmission bandwidth
 Although we may use the traditional cryptosystems to encrypt images directly, it
is not a good idea for two reasons
 One is that the image size is almost always much greater than that of text
therefore, the traditional cryptosystems need much time to directly encrypt
the image data
 The other problem is that the decrypted text must be equal to the original text,
however, this requirement is not necessary for image data
 Image Encryption Algorithms
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 A Technique for Image Encryption using Digital Signatures
 The digital signature of the original image is added to the encoded version of the
original image. Image encoding is done by using an appropriate error control code,
such as a Bose-Chaudhuri Hochquenghem (BCH) code
 At the receiver end, after the decryption of the image, the digital signature can be used to
verify the authenticity of the image
 Lossless Image Compression and Encryption Using SCAN
 The compression and encryption schemes are based on SCAN patterns generated by
the SCAN methodology
 The SCAN is a formal language-based two-dimensional spatial-accessing methodology
which can efficiently specify and generate a wide range of scanning paths or space filling
curves
 A New Encryption Algorithm for Image Cryptosystems
 The images are first decomposed into vectors and then sequentially encoded vector by
vector
 Then traditional cryptosystems from commercial applications can be used
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 A New Mirror-Like Image Encryption Algorithm and Its VLSI Architecture
 Based on a binary sequence generated from a chaotic system, an image is scrambled
according to the algorithm
 Rearranging image pixels using swap function according to the binary sequence
 Color Image Encryption Using Double Random Phase Encoding
 New method to encrypt color images using existing optical encryption systems for gray-
scale images
 The color images are converted to their indexed image formats before they are
encoded
 In the encoding subsystem, image is encoded to stationary white noise with two random
phase masks, one in the input plane and the other in the Fourier plane
 At the decryption end, the color images are recovered by converting the decrypted
indexed images back to their RGB (Red-Green-Blue) formats
 Visual Cryptography for Color Images

 Comparison of Current
Algorithms
 Adding compression to MIE and VC
algorithms
13

 Compression is more important issue for visual cryptography because it produces 2
or more sharing images which are twice in size of dimensions of the original image
 JPEG (Joint Photographic Experts Group) is a standard compression algorithm
used to reduce memory requirement for the storage of digital images
 The JPEG standard allows to specify the desired quality of the encoded image by
varying a quality factor between 0 (lowest quality) and 100 (best quality)
 PNG is an extensible file format for the lossless, portable, well-compressed
storage of raster images
 While the jpeg compression has losses in the compressed image, in PNG
compression there is neither a change of colors nor a reduction of color depth
 Mean square error (MSE) is the cumulative squared error between original
and recovered image
 Lower value of MSE means lesser error
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 EXPERIMENTAL RESULTS
15

 As we can see from the experimental results jpeg with quality parameter set
to 100 does not compress grayscale image, besides size of the grayscale image
increases, because noise in the image can not be compressed productively
 Quality setting set to 90 or below reaches good compression ratios
 However jpeg is not suitable for color images (even with quality set to 100)
because of the loss in the color
 Lossless PNG compression with VC for gray-level and color images has a big
compression ratio because it has only one color plane to encrypt and saves
storage space and network bandwidth up to 92,4%
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3. From Chaotic Maps to Encryption
Schemes
 Many fundamental concepts in chaos theory such as:
 Mixing
 Measure Preserving Transformations
 Sensitivity to changes in initial conditions and parameters have been already applied for
a long time in cryptography
 Encryption algorithms are usually written in form of transformations:
where plaintext X, cryptogram Y and secret key Z are sequences of letters in
finite alphabets L x , L y , L z ,respectively, which are not necessarily equal to each
other
 A very common approach to creating diffusion and confusion is to use a product
cipher, a cipher that is implemented as a composition of simple ciphers
 Most commonly, product ciphers employ both permutation and substitution
ciphers as their component ciphers
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Schemes
 Deterministic chaotic discrete time dynamical systems
 k in Encryption Algorithm case was the key
 Considering maps which possess only unstable periodic orbits and chaotic
trajectories
 Two general principles which guide the design of practical ciphers are
 Diffusion
○ Diffusion means spreading out of the influence of a single plaintext digit over many ciphertext digits
so as to hide the statistical structure of the plaintext
 Confusion
○ Confusion means use of transformations which complicate dependence of the
statistics of ciphertext on the statistics of plaintext
28

Schemes
 Such maps usually have mixing property: any set of initial conditions of
nonzero measure will eventually spread over the whole phase space as the
system evolves
 We also assume that mixing property holds for a large set of parameters
 Most ciphers achieve the mixing property by means of round repetition
 Same logic applies when a chaotic map serves as a cipher’s basis, mixing property
of the chaotic map is not sufficient
 Mixing property of chaotic maps is closely related to property of diffusion in
encryption transformations (algorithms)
 The keys of an encryption algorithm represent its parameters
 Kind of “mixing property” should hold also in the parameter space of the
map, if we would like to use chaotic maps as encryption algorithm
 We should look for maps that have only chaotic trajectories in a large parameter
region
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Schemes
 Mixing maps are good candidates for encryption algorithms because both diffusion
and confusion are their immanent properties
 Every encryption algorithm possesses properties of confusion, diffusion, mixing
and sensitivity to changes in plaintext and secret key
 This almost guarantees that an extension of the domain of an encryption
algorithm from a N-dimensional lattice to a N-dimensional continuum will give
rise to a chaotic map
 Therefore, sensitivity to changes in initial conditions and parameters, and
mixing property of a chaotic map do not guarantee that its discrete version is a
good crypto-algorithm
 The notion of cryptographic security has no counterpart in chaos theory, and
the cryptographic security of a chaos-derived encryption algorithm can be
checked up only by means of crypto-tools
 Still, the area of cryptanalysis provides us with certain cryptanalytic tools and
attacks against which any encryption algorithm must be resistant
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4. Survey - Image Encryption using Chaotic
Cryptography Schemes
 This paper contributes by comparing and analyzing the performance of the past
chaotic image encryption schemes
 Properties of chaos including deterministic dynamics, unpredictable behavior and
non-linear transform
31

5. New Encryption Schema Based on Swarm
Intelligence Chaotic Map
 A new Swarm Intelligence Chaotic Map (SICM) is proposed to construct a robust
encryption algorithm
 The proposed scheme is described in details, along with the analysis of the
possibility to be used in image cryptography field
 Visual and computational experimental results are presented to demonstrate the
encryption quality of the proposed schema
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 At each time step t the velocity is
updated and the particle is moved to
a new position
 This new position is simply
calculated as the sum of the
previous position and the new
velocity
 The update of the velocity from the
previous velocity to the new velocity
is determined by:
 For a single individual particle swarm
the system is completely defined by
 The objective is to find pair of values
(c, t) so that M = I (where I is the
identity matrix) with long period t
 It means in particular that if we
generate a sequence of points in
this simplified particle swarm model
by using c values between 0 and 4,
we will obtain a pure random
sequence
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 Most of the existing Chaos-Based
encryption systems are built upon
m-dimensional mapping functions
called Chaotic Maps
 The procedure of the proposed
SICM cryptographic algorithm for
encryption and decryption
processes is all about:
 Obtaining a chaotic key
 This key is used for chaotic mixing of:
○ Image colors
○ Pixel position permutation
34

PSO Only
35
PSO
Vo
K(w,h,3)
Calculation
Yo Yt
Vt
R,G,B
Substitution
Position
Permutation
Cipher

Paper Algorithm – PSO + Logistic Map
36
PSO
Vo
Logistic
Map
K(w,h,3)
Calculation
Yo
cXo
Yt
Vt
R,G,B
Substitution
Position
Permutation
Cipher

3 Particles PSO + Logistic Map
37
PSO - RED
Vo
Logistic
Map
K(w,h,3)
Calculation
Yo Yt
Vt
R,G,B
Substitution
Position
Permutation
Cipher
PSO - GREEN
Vo
Yo Yt
Vt
PSO - BLUE
Vo
Yo Yt
Vt
Xo C

 Step 1 Generate Binary 192 bit
secret Key
 The secret key is divided into six
blocks KI (I=1: 6) of 32-bit each
 K00, K12, K34 and K56 are divided
into 16 blocks kjk (j=1:4, k=1:4) of
8-bit each
 The initial values for logistic map
and each dimension of SICM are
calculated
 Step 2 Encryption (Masking Step)
 Initialize Logistic Map by x0
 Initialize SICM by (v0[1], v0[2], y0[1],
y0[2])
 Get next value of Logistic Map to be
the parameter (c) of SICM
 For Each Pixel pi (i=1 to
Block Height X Block Width)
 Iterate SICM to get ith outputs vi[1],
vi[2], yi[1],and yi[2]
 Convert these outputs to the
equivalent binary form of 32 bit
length
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 Map the binary version of SICM
output
 Divide K1, K2 and K3 into 12 blocks
kjk (j=1:3, k=1:4) of 8-bit each and
Calculate encryption Keys for R, G
and B channels
 Encrypt/Decrypt the ith plain pixel
 Step 2 Encryption (Permutation)
 Fill the xpermutation vector by vi[1]
and the ypermutation vector by vi[2]
 Arrange xpermutation and
ypermutation vectors from large to
small values
 Permutate whole Image by
xpermutation and ypermutation
indexes
39

 Detailed security analysis of the proposed image encryption scheme is
presented
 Key Space Analysis: Key space size is 2^192, which is large enough to resist all kinds of
brute-force attacks with the current computing technology
 Statistical Analysis: Below histograms of R, G, and B channels confirms that ciphered
image looks completely random
40

 Correlation Coefficient Analysis: The correlation coefficient of the adjacent pixels in
original Lena image is very high, and the correlation coefficient in ciphered image
processed is very low, close to 0
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 Key Sensitivity Analysis: Ideally a single bit of difference between encrypting and
decrypting key should make it unable to decrypt ciphered image
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 The possibility of using simplified model of swarm intelligence as a chaotic map is
proposed
 The SICM parameter is controlled throw another logistic map to make the
proposed schema more robust
 The presented schema is applied in image encryption
 Experimental results demonstrated that the proposed schema has enough key
space to resist all kinds of brute-force attacks
 The encryption image has good statistical properties shown in histogram and two
adjacent pixel correlation analysis
 Although the proposed encryption schema presented in this paper focuses on
image encryption field, it can be used for secure transmission of various
information forms
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