Journal of Discrete Mathematical Sciences and
Cryptography
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DNA encryption algorithm based on Huffman
coding
Mustapha Meftah, Adda Ali Pacha & Naïma Hadj-Said
To cite this article: Mustapha Meftah, Adda Ali Pacha & Naïma Hadj-Said (2020): DNA encryption
algorithm based on Huffman coding, Journal of Discrete Mathematical Sciences and Cryptography,
DOI: 10.1080/09720529.2020.1818450
To link to this article: https://doi.org/10.1080/09720529.2020.1818450
Published online: 27 Dec 2020.
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Journal of Discrete Mathematical Sciences & Cryptography
ISSN 0972-0529 (Print), ISSN 2169-0065 (Online)
DOI : 10.1080/09720529.2020.1818450
DNA encryption algorithm based on Huffman coding
Mustapha Meftah *
Adda Ali Pacha †
Naïma Hadj-Said §
Coding and Information Security Laboratory
University of Science and Technology Mohamed Boudiaf
Oran
Algieria
Abstract
Today, the transmission of hypersensitive data through public communication,
poses a real problem for an unauthorized recipient which makes information security very
important.
The basic idea behind the proposed research work is to exploit the robustness of the
genetic material in order to improve and outperform the performance of other conventional
algorithm.
In this paper, Huffman coding method has been adopted to develop a new and efficient
symmetric DNA encryption algorithm.
Firstly, the algorithm codifies the secondary DNA key which is extracted from the
main DNA key according to Huffman coding. Then an XOR is applied between the coded
DNA sequence and the plain-image. And in order to strengthen our algorithm, we have
performed diffusion with a permutation box.
Subject Classification: 11K45, 68P25, 81P94, 94A60, 94A62.
Keywords: DNA, Cryptography, Huffman, Algorithm, Encryption, Decryption, Coding.
1. Introduction
The security of traditional methods of secret key and public key
cryptography is based on the keys. The keys used are so big that a
*E-mail: meftah_m@hotmail.com (Corresponding Author)
†
E-mail: a.alipacha@gmail.com
§
E-mail: naima.hadjsaid@univ-usto.dz
©
2
M. MEFTAH, A. A. PACHA AND N. H. SAID
multitude of powerful machines computing at the same time would still
take many years to decipher a key. It is not a problem today, but it will be
soon, given the growth in computing power.
A new method of data security was born inspired from DNA called
DNA Computing. It was invented by Leonard Max Adleman in 1994 to
solve some known NP-complete problems such as the traveling salesman
problem and the Hamilton Road problem [1].
The concept of using DNA in cryptography has given new hope to
unbreakable algorithms [2].
Our proposed encryption algorithm is based on a Huffman coding of
DNA nucleotide bases. The characteristics of Huffman coding are as
follows:
•
Variable length coding.
•
Instant decoding
•
Unique decoding
•
Reversible decoding
•
Compact
It is widely used in data compression during source coding.
Aruna Malik, Geeta Sikka & Harsh K. Verman, proposed a
steganography method based on Huffman compression and color
coding [3]
Also and in order to strengthen our algorithm we used a spiral
rotation permutation box. In this context, Sanal Kumar & S. Anfino Sherfin
presented an encryption algorithm based on a spiral rotation [4].
Related works
During the last years, as DNA encryption has been cited as one of
the safest methods of data representation, extensive researches have been
devoted to develop novel algorithms to ensure data security
One of the algorithms suggested using a bi-serial DNA encryption
method in which the plaintext is converted to hexadecimal code and into
a binary code. This message is divided into two parts; one will be used as
a key and the other as a message. The XOR operation is also performed
in order to increase the compression factor. A DNA encoded message is
received after the application of the digital DNA coding, then the PCR
DNA ENCRYPTION ALGORITHM BASED ON HUFFMAN CODING3
amplification is implemented using two main pairs as the key and the
compression is performed for a variable data length [5].
Another algorithm proposed by Shreyas Chavan was plaintext
encryption using a DNA-based method and a One Time Pad (OTP). This
algorithm uses two keys. First key is a random string of nucleotides bases
used as DNA sequence; its length is similar to that of the plaintext. The
second key is a binary sequence used as OTP, its length is twice that of the
DNA sequence key [6].
Varma and Raju carried out an analysis study of different approaches
of DNA encryption based on the matrix and the secure key generation
scheme. [7].
On the other hand, Kang Ning proposed an approach of securing data
by a method called pseudo-cryptography DNA method by converting the
text into protein according to the table of genetic codes. [8].
Kritika Gupta and Shailendra Singh proposed an algorithm, which
convert the plaintext into its ASCII code, and in its binary form. Then,
these binary values are encoded in DNA sequences. After that, a DNA
sequence is chosen as a key and grouped into blocks of 8 nucleotidesbases. Depending on the positions of the characters in the key, a table is
created and, using this table and key, the produced data is converted into
an encrypted form [9].
Recently, Al-Wattar et al. proposed different methods of DNA
cryptography depending on the key for the Mix-Columns and Shift-Rows
transformations similar to that implemented in the AES algorithm. This
increases its resistance to attacks. [10] [11].
On the bases of these finding, we have proposed a symmetric
encryption algorithm based on DNA.
The proposed algorithm
a. Encryption process:
Both parties must first share a DNA strand (The main key) of their
choice. The secondary key is represented by three parameters: Start_ Pos,
Nbr_Bases and a number of round NR1.
Phase 1 : Coding of the encryption key
Let be a plain-image M with a length LM. Here is the process for
coding the encryption key:
We are going to extract a DNA sequence which starts from Start_Pos
position with a length of Nbr_Bases. Next we will calculate the probability
4
M. MEFTAH, A. A. PACHA AND N. H. SAID
of appearance of each short sequence represented by four (04) nucleotide
bases. This is to obtain the Huffman coding for each quadruple.
The next step is to positioning in the main key at the Start_Pos position
and start coding the short sequences of four bases with the Huffman
coding obtained until we obtain a binary sequence having the same image
length (LM).
After coding, we will obtain a binary key sequence S of length
LS = LM.
Phase 2 : XOR
In this step, we will proceed to an XOR between the sequence
obtained S and the plain-image M in its binary form which are of the same
length. As a result, we will obtain a binary sequence which represents an
encrypted-image C1.
Phase 3 : Diffusion
Reminder:
A group is said to be monogenic when it is generated by one of its
elements.
∃x ∈ G / G = < x > = {x m , m ∈ Z}.
(1)
Furthermore, if x is of finite order for n ≥ 1, we say that G is a cyclic
group of order n and we have:
=
G
{e , x , x 2 , x 3 , … x n −1 }[12].
(2)
Permutation in a set:
Let n ∈ N *, we call permutation of {1, 2, 3, …, n}, any bijection of {1, 2,
3, …, n} in itself. All of these permutations are noted Sn [13].
Notation : ∀ ∈ Sn :
 1,
2,
3,
…,
n 

 δ (1), δ (2), δ (3),  , δ (n) 
δ = 
(3)
In order to strengthen the encryption we are going to do a diffusion of
the message obtained and for that, we used a permutation box as follows:
The encrypted sequence C1 is divided into blocks of 16 bits which
will each constitute an entry in the permutation box. Based on 16 bits,
including 8 even positions (2, 4, 6, 8, 10, 12, 14, 16) and 8 odd positions
DNA ENCRYPTION ALGORITHM BASED ON HUFFMAN CODING5
(1, 3, 5, 7, 9, 11, 13, 15), our permutation function is defined in the
following way: We will first take the even positions in an increasing order
then the odd positions in a decreasing order.
1
2
3
4
5
6
7
8
9
10
Even bits descending
16
14
12
10
8
6
11
12
13
14
15
16
13
15
Odd bits ascending
4
2
1
3
5
7
9
11
Figure 1
Permutation box
In=
our case : G
{δ 0 , δ 1 , δ 2 , δ 3 , … , δ n −1 } is a cyclic group of order
n such that:
δ n is the permutation identity
δ 0 = {1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15, 16} (4a)
δp =
δ ⋅ δ ⋅ δ ( p times)
δn = δ0
(4 b)
(4 c)
After simulation of Sn (the entire set of permutations), we obtained
n = 240
Which implies that G is a group of order 240
δ 240 = δ 0
(5)
The number of round NR is obtained from the secondary key NR1
combined with the result of phase 2 as follows:
Let S1 and S2 be the sum of the values of the odd and even pixels
respectively of the image C1
NR =
[( NR1 + | S1 – S2 | ) Mod 239 ] + 1
(6)
NR ∈ [1...239]
∀NR : δ NR < > δ 0
We opted for this combination in order to obtain the avalanche effect
between the small modification of the plain-image and the encryptedimage obtained.
After the 1st round, we will shift one bit to the left, After the 2nd round,
we will shift two bits to the left, and after the 3rd round, we will shift three
bits to the left, Until complete the number of round NR.
6
M. MEFTAH, A. A. PACHA AND N. H. SAID
We will get a binary sequence which represents the encryptedimage C.
All the process of encryption is represented below in fig. 2.
Figure 2
Diagram of encryption algorithm
b. Decryption process
As being our approach is a secret key algorithm, the decryption
process is the reverse operation of the encryption process.
Figure 3
Diagram of decryption algorithm
DNA ENCRYPTION ALGORITHM BASED ON HUFFMAN CODING7
Validation of results
We downloaded ‘Zea mays cultivar B73 chromosome2’ from NCBI
https://www.ncbi.nlm.nih.gov [14] and used it as our main key. The main
key contains 244442276 nucleotide bases. The secondary key is:
Pos_Start = 1000000
Nbr_Base = 100000
Number of round NR1 = 8.
The image used is ‘Cameraman.tif’ of size 256x256. After implementing
the algorithm with Matlab R2015a. The results are obtained as follow:
Test 1 : Key size
Main-Key: 244442276 nucleotide bases.
Secondary keys:
Start_Pos = [1 .. 244442276] (244 * 106) ≈ 228.
Nbr_Base = [1 .. 244442276] (244 * 106) ≈ 228.
Number of round NR1 = [1..240] (28).
Key size = 28 + 28 + 8 = 64 bits
Test 2 : Histogram of Image
The histogram can be seen as a probability of appearance of each pixel
value. It is resistant to many image transformations; such as rotations,
translations, changes of point of view and changes of scale.
Referring to the results obtained (fig. 4 & fig. 5), we can see that plainimage histogram differs substantially from the corresponding encrypted
one. Moreover, the histogram of the encrypted-image is uniform which
makes it difficult to extract the values for statistical purpose.
Fig. 4
Plain-image “cameraman.tif” and his histogram
8
M. MEFTAH, A. A. PACHA AND N. H. SAID
Fig. 5
Encrypted-Image “cameraman.tif” and his histogram
Test 3 : Entropy
Shannon’s entropy is a function that corresponds to the amount of
information provided by an information source.
In the case of a source X, providing a random variable with n
characters, each character xi has a probability of occurrence Pi. The entropy
H of source X is defined as follows:
H (X ) =
Pi =
−∑ i =1 Pi .log 2 (Pi )
n
ki
n
(7 a)
(7 b)
In our case :
•
i Π[0..255]
•
n = 256 * 256 = 65536
•
ki : is the frequency of each value i
If a source provides 256 symbols and if these symbols are equiprobable,
the entropy of each symbol is: log2 (256) = log2 (28) = 8 bits, this means that
to transmit a symbol you need 8 bits.
The ideal entropy of the encrypted-image must have a value close to
an entropy of a source providing random variables.
In our approach, we got the followings results:
•
eM = 7,0097 : The entropy of the plain-image ‘cameraman.tif’.
•
eC = 7,9957 : The entropy of the encrypted-image.
DNA ENCRYPTION ALGORITHM BASED ON HUFFMAN CODING9
Test 4 : Correlation between the adjacent pixels
In statistics and probabilities, studying the correlation between
two variables is to evaluate the intensity of the connection that can exist
between these variables.
The correlation coefficient is between –1 and 1. These values represent
the degree of linear dependence between the two variables. The closer the
coefficient is to the values –1 and 1, the stronger the correlation between
the variables.
A zero correlation coefficient means that there is absolutely no
correlation between adjacent pixels. In our case, we took 2000 pixels
randomly and we studied the correlation between adjacent pixels.
Figure 6
Correlation between the adjacent pixels horizontally of the plain-image and
the encrypted-image.
Figure 7
Correlation between the adjacent pixels vertically of the plain-image and the
encrypted-image.
10
M. MEFTAH, A. A. PACHA AND N. H. SAID
Figure 8
Correlation between the adjacent pixels diagonally of the plain-image and the
encrypted-image.
Table 1
Correlation coefficient
Image
Cameraman.tif
Direction
Horizontal
Vertical
Diagonal
Plain-image
0.9505
0.9628
0.9098
Encrypted-image
- 0.0132
0.0027
-0.0083
Fig. 6, Fig. 7 and Fig. 8 summarize the correlation between the
adjacent pixels of the plain-image and corresponding encrypted-image.
After calculating the correlation coefficient (Tab 03), we see that the
adjacent pixels in the plain-image have a strong correlation (coeff.≈1),
whereas in the encrypted-image there is a very weak correlation (coeff.
≈ 0). This weak correlation between neighboring pixels in the encryptedimage makes our cryptosystem resistant to statistical attack.
Test 5 : Differential attack
To carry out a differential attack, the attacker makes a tiny modification
such as modifying only one pixel in the plain-image, then observe the
modifications made to the encrypted result.
In this way, he can discover a significant relationship between the
original image and the encrypted one. So, in the case where a minor
change in the plain-image causes a significant change in the encryptedimage, it means that the differential attack is ineffective.
DNA ENCRYPTION ALGORITHM BASED ON HUFFMAN CODING11
In our approach, to observe the result of one pixel change on the
encrypted-image, two measurements were used:
(1) The number of pixels change rate (NPCR)
(2) The unified average change intensity (UACI).
For this purpose, we will note two encrypted-images c1 and c2,
corresponding to the plain-images m1 and m2 knowing that the difference
between m1 and m2 is only one pixel. Label the pixel values on the matrix
(i, j) of c1 and c2 by c1(i, j) and c2(i, j) respectively and define a twodimensional array D having the same size as the encrypted-image [15].
=
D(i , j )
=
0 if c1(i , j ) c 2(i , j )
(8 a)
=
D(i , j )
1 if c1(i , j ) ≠ c 2(i , j )
(8 b)
NPCR : N (c1, c 2) =
 D(i , j )
∑  W .H
i; j


.100% 

(9)
Where, W and H are the width and height of encrypted-image c1 or
c2. NPCR measures the rate of pixel difference between the two images.
The NPCR value is between 0 and 1.
When NPCR = 0, it means that c1 and c2 are exactly the same.
When NPCR = 1, it means that all the pixels in c2 are modified
compared to those in c1. Therefore, it is very difficult to establish a
relationship between these two encrypted images c1 and c2 [16].
The UACI, which measures the average difference in intensity
between the two encrypted images, is defined as follows:
UACI : U (c1, c 2) =
 c1(i , j ) − c 2(i , j )



.100%
∑

255.W .H
i, j 


(10)
Tests were realized on the proposed algorithm, concerning the
influence of the change of one pixel on an image ‘cameraman.tif’ with 256
grayscale of size 256 * 256.
We have changed the pixel value which has position (150,150) in the
plain-image “cameraman.tif”, We put the value 144 instead of the value
143, to obtain two encrypted images c1 and c2 respectively with the
corresponding values. We got the following results:
•
MPCR = 99,6032715 %
12
•
M. MEFTAH, A. A. PACHA AND N. H. SAID
UAIC = 33,6073513 %
It is reported in literature that the ideal expectation values of
NPCR and UACI for a gray scale image are 99.6094% and 33.4635% [17]
respectively.
The obtained result of NPCR and UACI in our algorithm is 99.6032%
and 33.6073% respectively. This means that any minor change occurring
on the plain-image, would cause an obvious change on the encrypted
images. It is called ‘the avalanche effect’. It means that our algorithm
presents strong sensitivity of plaintext.
Conclusion
This study reports a simple, straightforward and efficient symmetric
DNA encryption algorithm with block cipher on the bases of 03 essential
points:
A variable length Huffman coding of the nucleotide bases, a logical
XOR between the coded sequences obtained and the plain-image, and a
diffusion of the result using a permutation box with a number of round
obtained by a sub-key combined with a number of round obtained from
the previous step.
Moreover, the robustness of our cryptosystem is based on:
a. The coding of the nucleotide bases is not fixed in advance.
b. The coding of the nucleotide bases is of variable length.
c.
The impossibility of establishing a relationship between the
encrypted images.
Finally, future research is needed to further improve the efficiency
and performance of DNA encryption to ensure better security of the
encrypted result.
References
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Received February, 2020
Revised June, 2020