Information Security using Genetic Algorithm and
Chaos
Anil Kumar, M. K. Ghose
[email protected],[email protected]
Sikkim Manipal Institute of Technology, Sikkim (INDIA)
ABSTRACT
Security, integrity, non-repudiation, confidentiality, and authentication services are the most
important factors in information security. Genetic algorithms (GAs) are a class of optimization
algorithms. Many problems can be solved using genetic algorithms through modeling a
simplified version of genetic processes. The application of a genetic algorithm (GA) to the field
of cryptology is rather unique. Few works exist on this topic. In this paper we have propose a
new approach of genetic algorithms (GA) with pseudorandom sequence to encrypt data stream.
The feature of such an approach includes high data security and high feasibility for easy
integration with commercial multimedia transmission applications. The experimental results of
the proposed technique confirm that high throughput rate needed for real time data protection is
achieved.
Keywords: Cryptography, Chaos, and Genetic Algorithms.
I. INTRODUCTION
In the advent of greater demand in digital signal transmission in recent time, the problem
of huge losses from illegal data access has become a burning issue. Accordingly, the data
security has become a critical and imperative issue in multimedia data transmission applications.
In order to protect valuable information from undesirable users or against illegal reproduction
and modifications, various types of cryptographic schemes are needed. Cryptography ―sciences
of the secret‖ has been reserved strictly to diplomatic and military surroundings (for more than
3000 years). But with the rapid advances in data processing and the evolution of the networks of
communications, cryptography has become a vital process in all domains. Cryptography offers
efficient solutions to protect sensitive information in a large number of applications including
personal data security, medical records, network security, internet security, diplomatic and
military communications security, etc. through the processes of encryption/decryption.
Encryption is used to convert a plaintext (original message) into cipher text (the coded message),
which can be decoded back into the original message. An encryption (or ciphering) algorithm
along with a key is used in the encryption and decryption of data. The degree of security offered
by the algorithm depends on the type and length of the keys utilized.
There are two types of cryptographic schemes: symmetric cryptography [1-2] and
asymmetric cryptography [3]. The symmetric scheme uses the same key for encryption and
decryption. Two keys is used in asymmetrical cryptography , one for encryption, known as the
public key, and the other for decryption, known as the private key. Asymmetric cryptography is
often used for key distribution and digital signature but its processing speed slow. The symmetric
cryptography is normally used to encrypt private data for its high performance. However, there
have been various data encryption techniques [4-6] on multimedia data proposed in the literature.
Only few works has been done exist on genetic algorithm [7-12] based information security.
In Section 2, a brief introduction to cryptography is given. Section 3 gives overview of
genetic algorithms and its general sequence of events such as selection, reproduction and
mutation operators. Section 4 gives overview and generation of the pseudorandom sequence,
conventionally used for generation of encryption/decryption keys. Section 5 covers the various
cryptography techniques based on genetic algorithm as available in the literature in chronological
order. In section 6, a new approach of genetic algorithms (GA) with pseudorandom sequence to
encrypt data stream is proposed. Section 8 represents the analysis of the security. Finally, section
9 gives the overall conclusions with special emphasis of highlighting the areas of further
research.
II. OVERVIEW OF CRYPTOGRAPHY
Cryptography is a science which is used from thousands of years. It concerns about the
encryption as well as decryption of secret data in such a way that valuable information will
remain safe from unauthorized users. Earlier the cryptography used in military and government.
Due to advent of internet technology over the past few years, people are now using internet as to
share information and for communication purpose. For this reason, secure communication is
main requirement for online trading because internet is an unsafe channel. Cryptographic
techniques are used to protect individual privacy as well as commercial secrets. Now a day
security, integrity, non-repudiation, confidentiality, and authentication services are the most
important factors in the field of the Cryptography.
The main objective of the cryptography is to ensure secure communication over
insecure channel (like Internet).
Figure 1: Basic Encryption and Decryption Model
The message which is normally a plaintext, is encrypted using the encryption key. The
encrypted data (Cipher Text) is sent over the communication channel to the receiver. On the
receiver side the cipher text is decrypted using decryption key.
The cipher text can be generated in the stream or block form. In stream cipher the
plaintext is encrypted bit by bit while in the block cipher data of the plaintext is divided into
blocks of specific size.
Goal of Cryptography
1. Confidentiality means to keep secret the content of information from all unauthorized users.
2. Data integrity is deal with the unauthorized modification of data. In order to assure data
integrity, one must have the ability to detect data manipulation (i.e. insertion, deletion and
substitution) by unauthorized parties.
3. Authentication means identification. It is applicable to both users and information itself.
When two users start communication then they should identify each other. Information delivered
over a channel should be authenticated as to origin, date of origin, data content, time sent, etc.
4. Non-repudiation is a service which prevents an entity from denying previous commitments or
actions.
Now a days the cryptography is classified into two categories, private-key and public-key
cryptography. In private-key cryptography, the encryption and the decryption are same. In
public-key encryption and decryption are different.
Private-key cryptography
It is referred as symmetric key cryptography because encryption and decryption are
performed using the same key. The key should keep secret between sender and receiver. A block
diagram is shown below using DES
Figure Taken from Stalling:
Figure 2: Symmetric Encryption and Decryption Model
There are various types of the encryption algorithms. Block ciphers are now widely used
in industry.
Data Encryption Standard (DES) was adopted in 1977 by National Institute of Standards
and Technology. The architecture of DES is based on Feistel cipher (developed by IBM), with
16 rounds of identical operations. In each round of DES, substitution and permutation are
performed by S-Boxes and P-Boxes. It is to provide confusion and diffusion in the encrypted
data. Now DES is no longer a secure encryption standard because of the short key and various
types of attacks.
Advanced Encryption Standard (AES) is issued by National Institute of Standards and
Technology in 2001 to overcome the problem of the DES. It is intended to replace DES. It
supports key lengths of 128, 192, and 256 bits and a block size of 128 bits. It does not use Feistel
Cipher structure. Here, each round use byte substitution, permutation, arithmetic operations over
a finite field, and XOR technique.
Public-Key Cryptography
This concept was introduced by Diffie and Hellman in 1976. This technique is referred as
asymmetric cryptosystem in which encryption and decryption is done using two different keys
(Public and Private Key). The private is secret and public key is open which anyone can use. The
pair is selected in such a way that private key determination on th basis of public key is
infeasible.
Figure 3: Asymmetric Encryption and Decryption Model
The main advantage of the public-key cryptosystem is that there is no needs of
transmission of secret key because private key is never transmitted hence there are any chance of
interception because secret key is not transmitted.
The main disadvantage is that the speed of encryption is very slow compare to private
key cryptography. Second the Certification Authentication is required those who are using Public
key. No public-key encryption has been proven to be secure. Integer Factorization Problem
(IFD), Discrete Logarithm Problem (DLP) and Elliptic Curve Discrete Logarithm Problem
(ECDLP) are the mathematical tools which are used in public-key cryptography system.
Rivest, Shamir and Adleman (RSA) uses the IFD concept for public-key cryptography
such as, is equivalent to find the prime factors p and q given a very large number n. Recently
RSA, depicted by a new hardware implementation.
Diffie and Hellman used the concept of DLP. Digital Signature Algorithm (DSA) issued
by the NIST to provide the authentication mechanism that enables communication parties for
proving and verifications.
ECDLP concept used in Elliptic Curve Cryptography (ECC). It is an emerging technique
alternative of RSA and DSA. Solving of the elliptic curve discrete logarithm problem is
infeasible.
III. GENETIC ALGORITHMS:
The genetic algorithm is a search algorithm based on the mechanics of natural selection
and natural genetics [13-14]. The genetic algorithm belongs to the family of evolutionary
algorithms, along with genetic programming, evolution strategies, and evolutionary
programming. The set of operators usually consists of mutation, recombination, and selection.
The main idea is that in order for a population of individuals to adapt to some environment, it
should behave like a natural system. The survival and reproduction of an individual being is
promoted by the elimination of useless traits and by growing the useful behavior. Genetic
algorithms (GAs) consider an optimization problem as the environment where feasible solutions
are the individuals living in that environment. The degree of adaptation of an individual to its
environment is the counterpart of the fitness function evaluated on a solution. Similarly, a set of
feasible solutions takes the place of a population of organisms. An individual is a string of binary
digits or some other set of symbols drawn from a finite set. Each encoded individual in the
population may be viewed as a representation of a particular solution to a problem. In general, a
genetic algorithm begins with a randomly generated set of individuals. Once the initial
population has been created, the genetic algorithm enters a loop. At the end of each iteration, a
new population has been produced by applying a certain number of stochastic operators to the
previous population. Each such iteration is known as a generation. A selection operator is applied
first. This creates an intermediate population of n ―parent‖ individuals. To produce these
―parents‖, n independent extractions of an individual from the old population are performed. The
probability of each individual being extracted should be (linearly) proportional to the fitness of
that individual. This means that above average individuals should have more copies in the new
population, while below average individuals should have few to no copies present, i.e., a below
average individual risks extinction. Once the intermediate population of ―parents‖ (those
individuals selected for reproduction) has been produced, the individuals for the next generation
will be created through the application of a number of reproduction operators. These operators
can involve one or more parents. An operator that involves just one parent, simulating asexual
reproduction, is called a mutation operator. When more than one parent is involved, sexual
reproduction is simulated, and the operator is called recombination. The genetic algorithm uses
two reproduction operators - crossover and mutation. To apply a crossover operator, parents are
paired together. There are several different types of crossover operators, and the types available
depend on what representation is used for the individuals. For binary string individuals, one-
point, and two-point, and uniform crossover are often used. For permutation or order-based
individuals, order, partially mapped, and cycle crossover are options. The one-point crossover
means that the parent individuals exchange a random prefix when creating the child individuals.
Two-point crossover is an exchange of a random substring, and uniform crossover takes each bit
in the child arbitrarily from either parent. Order and partially mapped crossover are similar to
two-point crossover in that two cut points are selected. For order crossover, the section between
the first and second cut points is copied from the first parent to the child. The remaining places
are filled using elements not occurring in this section, in the order that they occur in the second
parent starting from the second cut point and wrapping around as needed. For partially mapped
crossover, the section between the two cut points defines a series of swapping operations to be
performed on the second parent. Cycle crossover satisfies two conditions - every position of the
child must retain a value found in the corresponding position of a parent, and the child must be a
valid permutation. Each cycle, a random parent is selected. After crossover, each individual has a
small chance of mutation. The purpose of the mutation operator is to simulate the effect of
transcription errors that can happen with a very low probability when a chromosome is mutated.
A standard mutation operator for binary strings is bit inversion. Each bit in an individual has a
small chance of mutating into its complement i.e. a ‗0‘ would mutate into a ‗1‘. In principle, the
loop of selection-crossover-mutation is infinite. However, it is usually stopped when a given
termination condition is met. Some common termination conditions are:
1. A pre-determined number of generations have passed
2. A satisfactory solution has been found
3. No improvement in solution quality has taken place for a certain number of
generations
The different termination conditions are possible since a genetic algorithm is not guaranteed to
converge to a solution. The evolutionary cycle can be summarized as follows :
generation = 0
seed population
while not (termination condition) do
generation = generation + 1
calculate fitness
selection
crossover
mutation
end while
Many of these application areas are concerned with problems which are hard to solve but have
easily verifiable solutions. Another trait common to these application areas is the equation style
of fitness function. Cryptography and cryptanalysis could be considered to meet these criteria.
However, cryptology is not closely related to the typical GA application areas and, subsequently,
fitness equations are difficult to generate. This makes the use of a genetic algorithm approach to
cryptology rather unusual.
The crossover is the process in which the strings are able to mix and match their desirable
qualities in a random fashion. Crossover proceeds in three simple steps:
Two new random strings are selected in Figure 4a.
A random location in both strings is selected in Figure 4b.
The portions of the strings to the right of the randomly selected location in the two
strings are exchanged Figure 4c.
In this way information is exchanged between strings, and portions of two strings are exchanged
and combined.
1 0 0 0 1 0 1 0
0 1 1 0 1 0 0 1
(a)
1 0 0 0 1 0 1 0
0 1 1 0 1 0 0 1
(b)
1 0 0 0 1 0 0 1
0 1 1 0 1 0 1 0
(c)
Figure 4: Illustration of the Crossover Operation
IV. CHAOS THEORY
Chaos is a pseudo-random process produced in nonlinear dynamical systems. It is non-periodic
in nature, non-convergent and extremely sensitive to the initial condition.
The chaos theory has been developed, since early 60‘s from many research disciplines (such as
Mathematics, Physics, Biology, Chemistry and Engineering). There exists relationship between
the chaos and cryptography [15-16] such as 1) Ergodicity and confusion. 2) Sensitivity to initial
condition and diffusion with a small change in the secret key or plain text. 3) Mixing property
and diffusion. 4) Deterministic dynamics and deterministic pseudo-randomness. 5) Structure
complexity and Algorithm complexity.
As a result of the above relationships, a good number of chaos-based cryptosystems has
been proposed [17-19]; some of them lack robustness and security [20-22].
The general chaotic system model is given as below
1nxfnx (1)
where the )(nx is a chaotic sequence generated by the nonlinear )0((.),xf is the initial condition.
A simple and well-studied example of 1D map that exhibits complicated behavior is the
logistic map from the interval [0,1] into [0,1].
)1()( xxxf (2)
where )1,0(x and 40 .
The Tent map , sine map , and cubic map are other chaotic map used by Pareek et al. and
Tent map 5.0)1(
5.0)(
xifx
xifxxf (3)
Sine map )sin()( xxf (4)
Cubic map )1()( 2xxxf (5)
The control parameters of the above chaotic map are assigned as
59.2,99.0,97.1 and respectively.
The PWLCM (piecewise linear chaotic map) denoted as following equation
1)(2
1)),(1(
2
1)(
)2
1(
))((
)(0/)(
)),((
txptxT
txp
p
ptx
ptxptx
ptxT (6)
or
);1,5.0[)())(1(
];5.0,[)()5.0(
1))((
);,0[)(/)(
))((
)1(
nxifnxC
nxifnx
nxifnx
nxC
nx (6a)
where p is the control parameter and 2
10 p .
The PWLCM has uniform invariant density function and likecorrelation. It can be easily
realized by both hardware and software, since its iterations only involve divisions and additions.
V. LITERATURE SURVEY
Only few genetic algorithms based encryption have been proposed. A. Kumar et al [7] in
2004 describe encryption using the concept of the crossover operator and pseudorandom
sequence generator by NLFFSR (Non-Linear Feed Forward Shift Register). The crossover point
is decided by the pseudorandom sequence and the fully encrypted data they are able to achieve.
A. Kumar et al [8] in 2005 extend this work also used the concept of mutation and after
encryption. Encrypted data is further hidden inside the stego-image. A. Tragha et al.[9, 10], in
2005 & 2006 describe a new symmetrical block ciphering system named ICIGA (Improved
Cryptography Inspired by Genetic Algorithms) which generates a session key in a random
process. The block sizes and the key lengths are variable and can be fixed by the user at the
beginning of ciphering. ICIGA is an enhancement of the system (GIC) ―Genetic algorithms
Inspired Cryptography‖ [10]. ICIGA is a block cipher system whose secret key is generated
during each session using a random process. The user can fix the size of the blocks as well as the
length of the key. The operation of ICIGA depends on the length of the secret key selected by the
user. ICIGA uses this length to divide the plaintext into parts of equal size. During the ciphering,
the first part is broken up into blocks of the same size which are used to generate the secret key.
This key will then be used to cipher the other parts of the message. If the user did not set the
length of the secret key the plaintext is composed of only one part and ICIGA generates a key of
maximum length. The genetic operations of crossover and mutation used for ciphering in GIC
are improved by the new system ICIGA as follows:
- A left shift is added to each block that is processed, and
- Another left shift is added to the part being processed after the processing of its last block.
The number of bits to be shifted is determined by the parameters of the genetic operations. The
goal of these shifts is to reinforce resistance to cryptanalysis, and in particular to techniques of
exhaustive search.
M. Husainy [11] in 2006 proposes Image Encryption using Genetic Algorithm based
Image Encryption using mutation and crossover concept.
A. Tragha [12] at al in 2007, proposed a new encryption algorithm using genetic
algorithm approach. The only related work is the attack of the asymmetric ciphering ―Knapsack
Cipher‖. This is inspired by the resolution of back bag problem. Thus efficiency genetic
algorithms have been proven in cryptanalysis. The problem of ciphering a message M is modeled
as a combinatorial optimization problem. Then a genetic solution based on the method used to
solve the traveling salesman problem (TSP) is also proposed. In the second system SEC-EX , for
scrambling plaintext, they introduce a new technique, which consists to encode plaintext in
binary, chooses randomly an integer k and cuts plaintext into blocks of size k. These blocks are
treated in the same way that the characters constituting the plaintext in SEC.
VI. THE PROPOSED METHOD
The block diagram of the proposed method is shown in figure 5. It consists of pseudorandom
sequence generator, crossover operator, and encryption and decryption modules.
The Encryption Process
The encrypting process emulates the working of the crossover operator using pseudorandom
sequence. The steps for the data encryption as follows:
1. Generate the pseudorandom binary sequence using the chaos as nY .
2. Convert the binary pseudorandom sequence into decimal pseudorandom sequence ranging
from 0 to 7 as .
3. Read 16 consecutive bytes from the data file.
4. Initialize
5. Initialize
Encryption
Module Pixels
Pseudo Random Binary
Sequence Generator (1D
logistic map).
Mapped Pixels
Encrypted Image
Decryption
Module
Original Image
Decrypted Image
Figure 5: The Block diagram of the proposed Method.
6. Modify the consecutive bytes using byte substitution for creating confusion, as per AES
standard.
7. Take two consecutive bytes of the data stream as .21 AandA
8. Perform crossover on two consecutive bytes of the data stream as 21 BandB by using the
number iZ
9. Encrypt data as .21 CandC , where
7(a)
7(b)
7©
7(d)
10. 2ii and repeat steps 6 to 9 until
11. Repeat steps 5 to 10 until
12. Again perform the byte substitution over the encrypted 16 consecutive bytes for further
creating confusion.
13. Repeat steps 3 to 12 until end of the data.
E. The Decryption Process
The steps for decryption are just reversal of the encryption. First, generate the pseudorandom
sequence using chaos and then use the pseudorandom sequence and crossover operator to
decrypt the data.
VII. EXPERIMENTAL RESULTS
In the simulation, ten images are used. As representatives, only the images of ―lena‖, ―it_logo‖
are shown in figures 6(a) and 6(d), respectively. The most direct method to decide the disorderly
degree of the encrypted image is by the sense of sight. On the other hand, the fractal dimension
can provide the quantitative measure on the randomness of the encrypted image.
The encrypted result of the two representative images by this method is shown in figures 6(b)
and 6(e). According to the figure 6, the encryption results of the method are completely
disordered and cannot be distinguished from the original image. The figures 6(c) and 6(f)
respectively are the decrypted image of ―lena‖, ―it_logo‖. Since the proposed method is losable,
we can find that there would be no encryption/decryption errors in using the proposed technique.
(a) b) (c)
(d) (e) (f)
Figure 6a) Lena Image b) Encrypted Image c) Decrypted Image d) It Image e) Encrypted Image
f) Decrypted Image.
As an example, we consider two consecutive bytes of the data stream after byte substitution
21 & AA as
101110001A
011100102A
The pseudorandom sequence is generated as follows:
1. If the value of µ=3.57 and , and threshold then the output pseudo
random binary sequence generated by chaos is as:
2. The decimal value sequence is than calculated using equation 1 as:
3. The value of 3&2 1ii ZZ .
Now, perform crossover operation with the generated pseudorandom sequence, In the operation
the various values generated are
111000011B
110010102B
00100010iX
001100111iX
110000111C
111110012C
The values of 1C and 2C are two consecutive encrypted data.
VIII. ANALYSIS OF PROPOSED APPROACH
It is of interest to know if the proposed technique is easily decrypted or not. Since there
are 8 combinations for crossover of 2 consecutive data bytes and for XOR (exor) the number is
64, thus the number of possible encryption result is (128) (N/2)
, where N is the total number of the
data bytes to encrypt .
For example, consider a 256 color-image of size 256*256 pixels and color depth of 8 bit
per pixel. In this case N equals 65536. All the possibilities are 12832768
≈ .
Statistical analysis of the encryption:
An ideal cipher should be robust against any type of statistical attack; because many
ciphers have been successfully analyzed with the statistical analysis and various types of attacks
have been devised on them.
Histogram analysis: We analyzed the histograms of several encrypted as well as original
images. Figure 7(a) original image and its histogram figure 7(c). Figure 7(b) encrypted image
and its histogram figure 7(b). It is clear from figure 7 histogram of the encrypted image is nearly
uniform and quite different from the original image and hence it does not provide any clue to
employ any type of statistical attack on the proposed image encryption. The secret key is µ=3.57
and .
7(a) 7(b)
7© 7(d)
Figure. 7. Histogram analysis: (a) Original Image (b) Encrypted image (c) Histogram of
Original image (d) Histogram of Encrypted image
Time analysis of the encryption: The speed of the algorithm is the important factor for a good
encryption algorithm. We have measured the encryption/decryption rate for several gray scale
images of different size. The average time taken by the algorithm for different size of images is
shown in table 1.
Table 1: Average ciphering speed of a few different sized grayscale images
Image
size(in
pixels)
Bits/pixels Average
encryption/decryption
time(s)
8 0.009-0.012
8 0.036-0.042
8 0.071-0.108
Without the knowledge of the pseudorandom sequence no one will be able to extract the
message.
Acknowledgement: This work is part of the Research Project funded by All India Council of
Technical Education (Government of India) vide their office order: F.No:8023/BOR/RID/RPS-
236/2008-09
IX. CONCLUSIONS
In this paper, the various genetic algorithm & chaos based of information security has been
discussed, and a new approach has been proposed. For transmitting the secured data over the
channel there is requirement of the high throughput, in these cases the conventional encryption
techniques are not a feasible solution for this reason a high throughput and secure encryption
technique is proposed for real time data transmission like over the telephone link or video
transmission. The concept of Genetic Algorithms used along with the randomness properties of
chaos. This total way of transferring secret information is highly safe and reliable. The
simulation results have indicated that the encryption results are (1) completely chaotic by the
sense of sight, (2) very sensitive to the parameter fluctuation. In the future work, we are planning
128128
256256
512512
to design a sophisticated hardware based on this technique which will be targeted to use in highly
secure multimedia data transmission applications.
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