International Journal of Security and Its Applications
Vol. 10, No. 2 (2016), pp.205-216
http://dx.doi.org/10.14257/ijsia.2016.10.2.19
ISSN: 1738-9976 IJSIA
Copyright ⓒ 2016 SERSC
A Novel Lossless Image Encryption Method using DNA
Substitution and Chaotic Logistic Map
Shouvik Chakraborty
*1
, Arindrajit Seal
2
, Mousomi Roy
3
, Kalyani Mali
4
1,2,3
P.G. Student, Department of Computer Science & Engineering,
University of Kalyani, West Bengal, India
4
Professor and Head, Department of CSE,
University of Kalyani, Nadia, WB, India
1
shouvikchakraborty51@gmail.com,
2
arindrajit.seal@gmail.com,
3
iammouroy@gmail.com,
4
kalyanimali1992@gmail.com,
Abstract
Presently, there is a growth in the transmission of image and video data. Security
becomes a main issue. Very strong image cryptographic techniques are a solution to this
problem. There is a use of a randomly generated public key and based on that there is an
application of DNA algorithm. In the proposed method DNA algorithm based substitution
is used for spatial domain bit permutation. Here the chaotic logistic map is used for
generating a pseudorandom bit sequence. We have generated 48bit length sequences for
every pixel. After the substitution operation, a final layer of security is imposed to make
this process more fault tolerant. The For checking the strength of the work a series of
tests are performed and various parameters are checked like Correlation Coefficient
Analysis, analysis of NPCR and UACI values etc.
Keywords: Image cryptography, DNA Substituion, Lossless encryption, Logistic map.
1. Introduction
Information security plays an important part in every field, especially fields related to
confidential business and/or military affairs. Keeping data safe from unwanted access is
Data Security. Encryption works by jumbling up the information data into unreadable
form and then uses a key to right it for reading. Traditional image encoding algorithms are
generally not suited for image encoding due to their slow speed in real-time processing
and also handling various data formatting. Many chaos-based digital image encoding
algorithms have been suggested. The concept of chaos is mostly used for image encoding
because of its excellent cryptography characteristics. Various algorithms provide different
degrees of security and it is based on how hard they are to break. If the cost required to
decode an algorithm is more than the value of the encoded data then the algorithm
probably is thought to be safe. Modern high quality image encoding methods have several
errors and are exposed to heavy attacks by expert cryptanalyst. Thorough study and
analysis between these techniques are needed to ensure the performance and to choose the
better one for the intended application. For certain applications speed of encryption may
be the main concern and for some other cases the security will be important. There are
three types of encoding schemes namely substitution, transposition and permutation and
techniques which include both transposition and substitution. Substitution schemes
change the pixels while permutation just shuffles the pixels based on the algorithm. In
some cases both the methods are combined to improve security. Chaos theory has proven
to be a very good alternative to provide a fast and quite reliable image encoding scheme.
The method in [1] is chaos based using bit level permutation. Permutation at the bit level
Shouvik Chakraborty is the corresponding author.
International Journal of Security and Its Applications
Vol. 10, No. 2 (2016)
206 Copyright ⓒ 2016 SERSC
changes the value. In [2] a novel image encryption method based on total shuffling
scheme is illustrated. In [3] combinations of two logistic maps are used for improving the
security of encryption. Encryption in [4] uses multiple chaotic systems. But each of these
methods has some security issues. The algorithm in [5] combines the diffusion and
confusion operations and uses the spatial-temporal chaotic system for generating the key.
But this is time consuming. As the key space increases the security of the algorithm also
get improved. From [6] it is clear that this algorithm performs better as compared to the
techniques in [5]. Although some of the chaos based image encoding techniques are
resistant to these types of attacks to some extent; more secured solutions are needed for
further improvement. Replay attack is one of the main security attacks. It can be stated as
a network attack in which a legitimate data transfer is intentionally repeated or delayed. It
can be done by the source or by any other advisory. The common remedies for these
attacks are session tokens, one-time -password(OTP), addendum of MAC and
timestamps. The reference [7] describes the replay attack. [8] and [9] proposes remedial
methods. In [10], Denning stated a method for preventing replay attack by timestamps.
These methods prevent replay attacks in normal data transfer. The proposed system is all
about to prevent the replay attack on digital image transmission with the help of
timestamps. In [11] only permutation is used for encoding the grey scale image. Although
the proposed work betters the security of that algorithm by introducing a bit substitution
technique in [12] for encrypting color images. The remaining of this paper is organized as
follows. Section 2 describes the chaotic logistic map, section 3 describes DNA
substitution method, section 4 describes the proposed method, section 5 gives the
experimental results and analysis and section 6 gives the conclusion.
2. Chaotic Logistic Map
Chaos is an ubiquitous phenomenon existing in deterministic nonlinear systems which
exhibit high sensitivity to initial conditions and have random behavior. It was discovered
by Edward N.Lorenz in 1963.
To create a chaotic stream cipher, a random bit stream is to be generated using chaotic
system. Pseudo Noise (PN) Sequences : A pseudo random bit generator [13] (PRBG) is a
deterministic algorithm, which uses a truly random binary sequence of length k as input
called seed and produces a binary sequence of length l>>k, which is called pseudorandom
sequence. This pseudorandom sequence appears to be random. The output of a PRBG is
not truly random; in fact the number of possible output sequences is at most a small
fraction ( / ) of all possible binary sequences of length l. The basic idea is to take a small
truly random sequence of length k and expand it to a sequence of much larger length l in
such a way that an adversary cannot efficiently distinguish between output sequence of
PRBG and truly random sequence of length.
The logistic map is a polynomial mapping of degree 2, often cited as an
archetypal example of how complex, chaotic behaviour can arise from very simple
non-linear dynamical equations. Mathematically, the logistic map is written as given
in Equation 1.
(1)
where λ € (0,4) , n = 0,1…..
Response of logistic map for is given in Figure 1 and for is given in
Figure 2.
International Journal of Security and Its Applications
Vol. 10, No. 2 (2016)
Copyright ⓒ 2016 SERSC 207
Figure 1. Response of Logistic Map for λ=2.8
Figure 2. Response of Logistic Map for λ=3.2
A bifurcation diagram shows the values visited or approached asymptotically
(fixed points, periodic orbits, or chaotic attractors) of a system as a function of a
bifurcation parameter in the system. The bifurcation parameter λ is shown on the
horizontal axis of the plot and the vertical axis shows the set of values of the logistic
function visited asymptotically from almost all initial conditions. The bifurcation
diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc.
Each of these bifurcation points is a period-doubling bifurcation. The ratio of the
lengths of successive intervals between values of λ for which bifurcation occurs
converges to the first Feigenbaum constant. The diagram also shows period
doublings from 3 to 6 to 12 etc., from 5 to 10 to 20 etc., and so forth. Biufurcation
diagram of logistic map is given in Figure 3.
Figure 3. Bifurcation Diagram of Logistic Map
The pseudo random bit sequence is generated by comparing the outputs of two
chaotic logistic maps. The chaotic logistic map produces the binary sequences by
comparing the outputs of the piecewise linear chaotic maps in the way as given in
Equation 2.
(2)
4. DNA Substitution Method
There are two rules in chaotic DNA substitution:-
• Binary Coding Rule
• Complementary Rule
The binary coding rule transforms letters transforms binary codes into A, T, G, C
and vice-versa. In this method the following encoding is adopted A=00, C=01,
g(x
n+1
,y
n+1
) = 0 if x
n+1
<y
n+1
= 1
otherwise
International Journal of Security and Its Applications
Vol. 10, No. 2 (2016)
208 Copyright ⓒ 2016 SERSC
G=10, T=11. That means A is coded as "00", C as "01" etc. Each pixel value is then
transformed into binary sequence using DNA substitution.
In complementary rule , each letter x is assigned to a complement denoted C(x).
Here the C(x) represents the complement of x. This is how the complement
operation takes place:-
(AT)(TC)(CG)(GA), the complement rule states that C(A)=T,
C(T)=C,C(T)=G,C(G)=A. There are six allowable complementary transformation.
(AT)(TC)(CG)(GA)
(AT)(TG)(GC)(CA)
(AC)(CT)(TG)(GA)
(AC)(CG)(GT)(TA)
(AG)(GT)(TC)(CA)
(AG)(GC)(CT)(TA)
Initially we take a 12 bit key generated using chaotic logistic map sequence. We
divide the 12 bits into 6 groups of 2 bits each. We perform XOR operation of Grp1
& Grp 2. We get a value of 2 bits. We perform XOR with this intermediate value
with Grp3. Likewise, we progress by performing XOR operation with the
intermediate values and the groups up to group 6. The final 2 bits value after
performing XOR operation is then subjected to a mod 3 operation to get the iteration
number.
4. Proposed Algorithms
4.1. Encryption Algorithm
The process start off by choosing an image and convert a pixel value into 8 bit binary
format. Then this binary sequence is reversed. Now we make 4 pairs from these 8 bits,
reverse each pairs. Now take four initial parameters for the logistic map as key. For each
pair of bits generate a chaotic pseudorandom sequence of 12 bits length. Now divide the
key (i.e. 12 bit sequence) into 3 groups each of length 4bit initially. Then generate a
binary sequence of length 4 by performing XOR operation on 3 groups of key sequence.
This operation is depicted in Figure 4. Now reverse these 4 bits and find the decimal
value of it and calculate the mod 6 value to select a transformation sequence. Now divide
the same 12 bit sequence key into 6 groups each of length 2. Then generate a binary
sequence of length 2 by performing XOR operation on 6 groups key sequence. Now
reverse these 2bits and find the decimal value of it and calculate the mod 3 value to select
a iteration number. Choose the complementary value from the sequence and find the
encoding value in decimal. In this way we get 4 values and convert these values in binary
and reverse all these pairs. Now combine these pairs to get a 8 bit binary sequence.
Now for 4 pairs we get 48 bit key sequence. We divide it into 6 groups each of length
8. Then generate a binary sequence of length 8 by performing XOR operation on 6 groups
key sequence. Now perform XOR operation with these 8 bits and 8 bits sequence
generated in the previous step. This step provides an extra layer of security. Reverse the
generated sequence and find the decimal value and assign it as an encoded image pixel.
International Journal of Security and Its Applications
Vol. 10, No. 2 (2016)
Copyright ⓒ 2016 SERSC 209
Figure 4. 4 Bit Key Generation from 12 Bit Sequence
The encryption algorithm is given below.
Step 1: Input an image.
Step 2: Choose a pixel and convert it into 8bit binary and reverse it.
Step 3: Make 4 pairs of pixels, reverse each pair and convert it into decimal.
Step 4: Now for every pair, find 12bits sequence using chaotic logistic map.
Step 5: Now divide the key into 3groups each of length 4.
Step 6: Then generate a binary sequence of length 4 by performing XOR operation on 3
groups key sequence.
Step 7: Now reverse these 4bits and find the decimal value of it and calculate the mod 6
value to select a Transformation sequence.
Step 8: Now divide the key into 6 groups each of length 2.
Step 9: Then generate a binary sequence of length 2 by performing XOR operation on 6
groups key sequence.
Step 10: Now reverse these 2 bits and find the decimal value of it and calculate the mod 3
value to select a Iteration number.
Step 11: Choose the complementary value from the sequence and find the encoding value
in decimal
Step 12: In this way we get 4 values and convert these values in binary and reverse all
these pairs
Step 13: combine these pairs to get a 8 bit binary sequence
Step 14: Now for 4pairs we get 48 bit key sequence. We divide it into 6groups each of
length 8.
Step 15: Then generate a binary sequence of length 8 by performing XOR operation on 6
groups key sequence
Step 16: Now perform XOR operation with newly generated key and 8 bits sequence
Step 17: Reverse the generated sequence and find the decimal value and assign it as an
encoded image pixel
4.2. Decryption Algorithm
The decryption process follows exactly the reverse method of the encryption process.
At first, generate a 48 bit sequence for each pixel and divide it into 6 groups of 8 bits
each. Generate 8 bits by performing XOR operation among these 6 goups. Now convert
the encoded pixel value into 8 bit binary format and reverse it. Now perform XOR
operation between pixel and previous 8 bits. Make 4 pairs of pixels, reverse each pair and
convert it into decimal. Now for every pair, generate 12 bits sequence using chaotic
logistic map. Now divide the key into 3 groups each of length 4. Then generate a binary
sequence of length 4 by performing XOR operation on 3 groups key sequence. Now
reverse these 4 bits and find the decimal value of it and calculate the mod 6 value to select
a transformation sequence. Now divide the key into 6 groups each of length 2. Then
generate a binary sequence of length 2 by performing XOR operation on 6 groups key
(b1 b2 b3 b4) XOR (b5 b6 b7 b8) XOR (b9 b10 b11 b12)
r1 r2 r3 r4