Fingerprint Template Encryption Scheme Based on Chaotic Map and DNA … · 2018-03-15 ·...

Fingerprint Template Encryption Scheme Based on

Chaotic Map and DNA sequence

MR. Nithyakalyani1, V. Palanisamy

2, R. Anandhajothi

3

1,3Research Scholar,

2Professor & Head

1,2,3 Department of Computer Applications, Alagappa University

Karaikudi-600 003, Tamilnadu, India [email protected] ,

[email protected] ,

[email protected]

Abstract— A growth in the field of digital technology,

conserving the privacy of biometric data has become an

inseparable issue. In the proposed work, fingerprint image

encryption scheme based on DNA encoding and chaotic Logistic

map is presented. Initially, using the Logistic map chaotic

sequences are generated and scrambled them by performing

route cipher method. Further, shuffle the original image pixels

with regarding to location map of permuted chaotic sequences

then key masks are generated using original chaotic sequences.

Finally, XOR the two DNA sequence matrix which are obtained

by DNA encoded the permuted image and masks will gain the

encrypted image. Moreover, experimental analyses, image

quality evaluation and sensitivity analysis shown that it is

improved the encryption scheme along with the capability of

resisting exhaustive attack and statistical attack and differential

attack.

Keywords—Biometrics; Fingerprint; Security; Encryption;

DNA (Deoxyribonucleic acid); Nucleotide; Logistic map;

I. INTRODUCTION

Biometrics makes highest level of security over traditional methods like Passwords and PIN numbers. Biometric is the study of automated identification by use of physical (Fingerprint, Iris, Hand, DNA, Face, etc.,) or behavioral (Voice, Signature, Keystroke, etc.,) traits. Thus, the Biometrics has no risk of forgetting it. Among all the Biometric traits, Fingerprint is an essential proven technology for verifying personal identity. In fact, a fingerprint template is the most universal, constant and distinctive. While fingerprint systems have several advantages than traditional security systems, there are some issues of fingerprint data are arises which is vulnerable to attack. Thus, template security is very essential in the development of biometric system because unauthorized person can access this template, can be replaced or altered in the communication channel between the database and matcher [1]. Encrypting the templates (image) is the remedy to this susceptible attack. In practices, cryptography approach is used for encryption. In the area of cryptography, various algorithms such as DES, AES, IDEA, Rabin, Elgamal, RC4, ECC and Blow Fish etc., were designed in past years which is not

efficient for practical image encryption due to high processing power and time complexity of encryption/ decryption is high, high in data capacity and also high correlation among the adjacent pixels. The new research algorithms of image encryption are proposed aims to reduce image content‘s redundancy by special operations, e.g., the chaos-based ciphers [2-4] and DNA based encryption operations [5].

Chaotic system is aperiodic long-term behavior in a deterministic system that exhibits high sensitive dependence on initial criterion which is also used to expand the shuffling and substitution in an image. In the shuffling phase, permutations of image pixels are prepared in a secret demand, deprived of varying their values. The substitution phase is used to alter the pixel values in sequence so that a little alteration in one pixel is blowout to several pixels, with looking forward to the whole image. This chaos system possesses astonishing characteristics such as sensitivity to initial conditions, the pseudo random number , ergodicity [6], topological mixing [8], self-similarity [10], perodicity [9], dynamic instability [7], dense periodic orbits. Therefore, these characteristics make chaos based encryption is to be suitable for constructing cryptosystems with high level of secure.

Pareek et al. [11] have proficiently put forward the algorithm based on chaotic 1D logistic map inorder to encrypt the original secret image. However, the algorithm has smaller key space and lower security. Ren and Ren et al. [12] came out with chaotic algorithm on the basis of dispersion sampling for enciphering image and attained better confusion effect but it has smaller key space. Y.H.Zhang et al. [13] utilize the logistic and standard systems to shuffling the location and pixel values from the original image which is leads to better results but security analysis of the algorithm is not performed. Thus some efficient schemes for encrypting digital images have been recommended. Multidimensional chaotic maps was used by Lian et al. [14-16] for image encryption and analysis the security of the proposed algorithm in detailed manner to ensure that the algorithm have adequate security along with a less cost. A.N. Pisarchik et al. [39] have suggested algorithm with chaotically coupled chaotic maps. For encrypting image, the

International Journal of Pure and Applied MathematicsVolume 118 No. 7 2018, 297-305ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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novelty algorithm based on the multiple chaos system was proposed by both Zuo et al. [18] and Liu et al. [19]. Their algorithms have large key space, strong sensitivity to keys and potential to resist against conventional attacks. Generally, scholars use complex chaotic behavior system or use the combination of new algorithm with previous chaotic algorithm inorder to enhance the security. Nevertheless, some chaotic algorithm was proved to be insecure [20-22].

In 1994, L.Adleman et al. [40] have been credited for introduced DNA (Deoxyribonucleic acid) Computing. After that, features such as massive parallelism, huge storage, ultra-low power consumption of DNA computing is employed in cryptography and many researchers being research on DNA cryptography. DNA cryptography is born as new emerging research topic in cryptographic area in which DNA used as an information carrier. Ashish Gehani et al. [5] proposed first experimental model of DNA Cryptography in which use two methods are substitution and bitwise XOR OTP cryptosystem for encrypt messages and also give the solution for OTP storage problem. C.T. Celland et al. [24] hid the secret message by using DNA microdots. Each character is encoded as three nucleotides i.e. ‗A‘ is denoted by CGA. However, it is tedious to implement and also not have a potential choice for encrypting image. Kang Ning et al. [25] have been proposed pseudo DNA cryptography. This scheme has better in encryption and moreover, real biological operation is not required but it is only applicable to enciphering the character information. Recently, Qiang Zhang et al. [26] have been credited with development of another novel algorithm for image encryption by using the DNA sequence addition combined with chaotic maps. The superior algorithm is developed by Lili Liu et al. [27] for encoding color image in which not need to biological experiment and provide high level of security than other DNA based algorithms. Hongjun Liu et al. [28] have suggested novel method based confusion and diffusion for encrypting images. The method based DNA and chaotic map technique for securing the Iris was suggested by Anil Johny et al. [29]. The novel hybrid method based DNA, Genetic algorithm and logistic map is suggested by Rasul Enayatifar et al. [30] and reduce correlation, increase entropy are the merits of this novel scheme. Babaei et al. [31] also proposed novel algorithm using the combination of chaos theory and DNA coding for encoding text and image. Saranya et al. [36] have been developed method in which use the hybrid combination of chaos and DNA to secure the image.

II. BASIC THEORY OF THE PROPOSED ALGORITHM

A. DNA Coding

This modern technique has the capability of vast storage capacity than traditional approach and the aim of the DNA coding is to encrypting secret data in DNA strands.

TABLE I. EIGHT KINDS OF DNA MAP RULES

1 2 3 4 5 6 7 8

A 00 00 01 01 10 10 11 11

G 01 10 00 11 00 11 01 10

C 10 01 11 00 11 00 10 01

T 11 11 10 10 01 01 00 00

DNA is composed of four nucleotides such as ‗A‘ terms Adenine, ‗C‘ terms Cytosine, ‗T‘ terms Thymine, and ‗G‘ terms Guanine [32, 33]. In Encryption process, two bit binary is converted into DNA sequences with regarding 8 encoding rules.

Table 1 introduces 8 encoding mapping rules of DNA sequence. Anyone of the rule could be employed to this proposed encryption scheme. For example: Fig.1. illustrated that suppose pixel value with a gray level of an image is 160, then it is represented in binary form 10100000 and encoded into DNA sequence is GGAA using Rule 2

Fig. 1. Example

B. DNA XOR operation

As the development of DNA computing, researchers have been proposed a lot of algebraic operations such as XOR based on DNA sequences with regarding to conventional XOR in the binary sequences. Corresponding to eight kinds of DNA encoding schemes, there also exist eight kinds of DNA XOR rules. In this proposed algorithm, XOR Operation is used to diffuse the original gray level fingerprint image pixels because of it‘s better for randomness and less correlation between adjacent pixels. For example: Assume that two DNA sequences are [AACT] and[GATC], use one kind of XOR operation is shown in Table.2 and produce the resultant sequence is [GAGG] . This XOR operation is reflexive and possesses the traditional property such as two inputs are same then output is 0. Otherwise it is 1. i.e. 00 01 = 01, 10 10 = 00. Thus, any one base in every row or column is unique, in other words, the results of XOR operation is one and only.

TABLE II. XOR OPERATION FOR DNA SEQUENCE

A G C T

A A G C T

G G A T C

C C T A G

T T C G A

C. Logistic map function

Recently, in image encryption schemes, one of the simple and most widely applied chaotic is 1D non linear logistic map because of low hardware complexity, low computation cost, simplicity and better pseudo random number generation which was recommended by R.M.May [38]. Mathematical

160

G G A A

10 10 00 00

International Journal of Pure and Applied Mathematics Special Issue

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representation for this definition is given in the following equation:

𝑥𝑖+1 = 𝜆𝑥𝑖(1 − 𝑥𝑖)

where, λ ∈ 0,4 , xi ∈ 0,1 , ‗i‘ is the number of iterations and x0 is set initially. The output chaotic sequence is produced by this logistic map function is regulated by the control parameter (λ) which is a positive real value sequence and the initial value respectively.

The system exhibits chaotic under the condition 3.569945< λ ≤ 4 as shown in Fig. 2 and chaotic sequences are highly sensitivity to initial value. When λ=4, the map is surjection and meanwhile xi is in the range of 0 and 1, the chaotic series of values have ergodicity.

Fig. 2. Logistic Map Function

The system exhibits chaotic under the condition 3.569945< λ ≤ 4 as showrn in Fig. 2. and chaotic sequences are highly sensitivity to initial value. When λ=4, the map is surjection and meanwhile xi is in the range of 0 and 1, the chaotic series of values have ergodicity.

D. Route Cipher

Route ciphers are transposition ciphers that begin by first writing the original secret data on a grid of given dimensions then read off in a pattern by a given key. The key would specify a direction ―spiral inward‖, ―clockwise‖, ―starting from the bottom right‖ that the route should follow when writing out the cipher data. Following Fig.3 is the illustration of route cipher.

R E I N F

O R C E M

E N T S A

R R I V I

N G N O W

Fig. 3. Route cipher example

Example: Encrypt ―REINFORCEMENTS ARRIVING NOW‖, Key: ―spiral from top right‖.

III. ALGORITHM DESCRIPTION

This section focusing the step by step procedure of a fingerprint template encryption algorithm incorporating DNA Encoding, DNA XOR operation, Chaotic Logistic Map and Route cipher. Initially, the chaotic sequences are generated through 1D Logistic map then route cipher is applied for transform the order of chaotic sequences. Further, secret

grayscale fingerprint image pixels are disturbed with regarding to the index of permuted chaotic. Then, using the chaotic sequences, each value of key mask is calculated by multiplying of X with 255. Finally, XOR the two DNA sequence matrix which are obtained by DNA encoding the permuted image pixels and key masks to obtained the encrypted image. The flow chart of the proposed algorithm is shown in Fig. 4.

Fig. 4. Flowchart for the proposed algorithm

Algorithm: Proposed Fingerprint Template Encryption

Step 1: Input Gray level fingerprint image, say, Fi.

Step 2: Generated the chaotic sequence of length M×N as the same size of the original image under the 1D Logistic map. Each number is used to encrypt each pixel.

Step 3: Route cipher is applied on this chaotic sequences to reorder the values.

Step 4: Then permuted chaotic sequence and Original chaotic sequence are compared and tabulated the index changes. Using this index, the secret image pixels are permuted.

Step 5: Using the original chaotic sequence, member of the key mask is created by following equation,

Kmask = Xi × 255

Step 6: Permuted image pixels is transformed into 8-bit binary sequences, Fbinary , as well as all member of the

aforementioned key mask, Kmask _binary .

Step 7: According to the table 1 DNA encoding rules, the binary sequences of image and masks are mapping into nucleotide base

FDNA = Fbinary DNA Nucleotide Table

Kmask _DNA = Kmask _binary DNA Nucleotide Table

Step 8: Finally, inorder to encrypt the fingerprint image, FEnc , regarding the DNA sequence XOR operation described in section 2.2 is performed between the DNA Encoded Mask and DNA Encoded image pixels.

FEnc = FDNA Kmask _DNA

Step 9: To decrypt the fingerprint image, DNA and chaotic based cryptography image is taken as an input and processing all encryption steps in reverse order.


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A. Step by Step Illustration

Following is the illustration of proposed algorithm to understand crystal clearly.

1. Generate Chaotic Sequence and read fingerprint image pixels

ChaoticSeq [X1= 0.9750, X2= 0.2841, X3= 0.1760, X4=

0.3780, X5= 0.1280, X6= 0.5460, X7= 0.8900, X8= 0.7250,

X9= 0.4321] Original Image Pixels

Fi = 190 54 130120 150 11072 180 170

2. It is arranged into grid and performs route cipher on this chaotic sequences,

3. Now, values in the grid are reordered and the encoded sequence is

Chaoticper =

0.4321 0.7250 0.8900 0.3780 0.9750 0.2841

4 1 2 3 6 5

Location Map

After that, permuted chaotic sequence and Original chaotic sequence are compared and the index change is noted.

4. Using the location map, the image is permuted and encoded into DNA bases

Fi = 170 180 72120 190 54130 110 150

Fbinary = 10101010 10110100 0100100001111000 10111110 0011011010000010 01101110 10010110

Confusion Matrix

FDNA = GGGG GTCA CAGACTGA GTTG ATCGGAAG CGTG GCCG

Mapping original image binary values of pixels into

nucleotide base according to the DNA Rule 2.

5. Now, Original chaotic sequence numbers are multiplied by 255,

6. Above Key is arranged in to matrix format and encoded into DNA bases according to Rule 2.

Kmask = 249 72 4596 33 139

227 185 110

Kmask binary = 11111001 01001000 0010110111000000 00100001 1000101111100011 10111001 01101110

Kmask _DNA =

TTGC CAGA AGTCTAAA AGAC GAGTTGAT GTGC CGTG

7. Finally, Perform XOR operation between KeyDNA and FDNA sequences according to the following table,

FEnc = CCAT TTTA CGCCGTGA GCTT GTTCCGAC TCCT TTGA

8. Now DNA code is transform back into decimal pixel to acquire encrypted fingerprint.

FEnc = 83 252 101

184 159 18997 215 248

IV. SIMULATION RESULTS AND ANALYSIS

The proposed method for fingerprint image encryption is implemented in Visual Studio 2010, C# language under the configuration of windows 7 operating system with Core-i3 and 3 GB RAM. In order to demonstrate the security and efficiency of the proposed algorithm, tested four fingerprint image samples from [36] which is composed of unique users‘ fingerprint images and set parameters x0= 0.25, λ=3.905. Table 3 shows that the experimental results of the original fingerprint images, enciphered images and deciphered images.

TABLE III. EXPERIMENTAL RESULTS ON FINGERPRINT IMAGE SAMPLES

Fingerprint Original

Image Encrypted Image Decrypted Image


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V. SECURITY ANALYSIS

An ideal image cipher algorithm that should has ability of resist against all kinds of attacks such as exhaustive, statistical and differential attacks. In this section, security analysis has been performed on the proposed algorithm.

A. Resistance to exhaustive attack

In order to prove the encryption algorithm that resist against exhaustive attacks, it should have a large key space and high enough sensitive to the secret keys.

1) Secret key space analysis: In this algorithm, the initial

value and control parameter of the logistic map where 𝜆 ∈ 0,4 and 𝑥𝑖 ∈ 0,1 , DNA coding and XOR rules can be

seen as secret keys. For the logistic chaotic system, if the

precision is taken as 10-15 then 1015×1015 = 1030. Also,

there are eight kinds of DNA encoding and XOR rules so the

total key space is 1030×8×8 = 1030×64, which is sufficient to

resisting exhaustive attack.

2) Secret key's sensitivity analysis: A secure image

encryption algorithm should be sensitive to the secret key, i.e.

the tiny changes in the secret key causes significantly different

ciphered images are produced. The Logistic chaotic system is

sensitive to the control parameter and initial value. In order to

test the key sensitivity, using the secret key in Section 4 to

encode the fingerprint image, obtained encoded image as

shown in Table 3., then utilize the secret key (0.001 is added to

x0 so that equates to 0.251, 𝜆=3.905) to decode the encoded

image. The result of decoding is shown the Fig.5 (c) shows the

decoded image which can be concluded if encoding and

decoding keys are consistent then correctly retrieve the original

image.. The sensitivity of the other secret keys are equivalent

as ―x0―, we have not shown examples of them here. On the

basis of above argument, it is proved that proposed algorithm

has ability of resist exhaustive attack and strong sensitive to the

secret keys.

(a) (b) (c)

Fig. 5. Experimental result of secret key‘s sensitivity a) original image b)

encrypted image c) the decrypted image with x0 add 0.001

B. Resistance to statistical attack

Histogram and Information Entropy are investigated inorder to prove the proposed algorithm has capability of resisting against statistical attacks.

1) The grey histogram analysis: The histogram illustrates

distribution of pixel intensities of an image [34]. Here, Table 4

depicted the grey histogram of the fingerprint image1 on the

basis of statistical analysis of original image and encrypted

image. Unlike the uniformity of the encrypted image, the grey

histogram of the original image fluctuated can be seen as in

Table4. Thereby, proposed encryption algorithm should be

robust against statistical attack.

TABLE IV. HISTOGRAMS OF ORIGINAL IMAGE AND THE ENCRYPTED

IMAGE

Original Fingerprint

Histogram

Encrypted Fingerprint

Histogram

2) Correlation Coefficient Analysis: It is well known that

in image the less correlation among adjoining pixels the more

potent ability of resist against statistical attack. In order to

test the correlation among two adjacent pixels, randomly

select 4000 pairs of adjoining pixels (vertical, horizontal and

diagonal) in fingerprint‘s image with 256 ×256 dimension and

calculate their Correlation coefficient by employing the

following equation.

𝑟𝑥𝑦 =𝐶𝑜𝑣(𝑥, 𝑦)

𝐷(𝑥) × 𝐷(𝑦)


301

where,

𝐶𝑜𝑣 𝑥, 𝑦 =1

𝑁 (𝑥𝑖

𝑁𝑖=1 − 𝐸 𝑥 )(𝑦𝑖 − 𝐸 𝑦 ) is the

covariance of x and y,

𝐸 𝑥 =1

𝑁 𝑥𝑖

𝑁𝑖=1 is the mean,

𝐷 𝑥 =1

𝑁 (𝑥𝑖

𝑁𝑖=1 − 𝐸(𝑥))2 is the variance

Fig.6,7,8,9 illustrated correlation of adjacent pixels

(horizontally, vertically, diagonally) in the original fingerprint image and in the encrypted image, respectively. Achieved outcomes are listed in Table 5, we can see that correlation coefficient of the adjoining pixels of encryption image is near to 0 and hence, the proposed algorithm can effectively robust against correlation statistical attack.

Fig. 6. Correlation of adjacent pixels in the original and its encrypted images of Fingerprint Sample1

Fig. 7. Correlation of adjacent pixels in the original and its encrypted images of Fingerprint Sample2

Fig. 8. Correlation of adjacent pixels in the original and its encrypted images

of Fingerprint Sample3

Fig. 9. Correlation of adjacent pixels in the original and its encrypted images

of Fingerprint Sample4

TABLE V. CORRELATION COEFFICIENT OF ENCRYPTED IMAGE

Image Name Horizontal Vertical Diagonal

Fingerprint1 0.0017 0.0007 0.0001

Fingerprint2 0.0025 0.0015 0.0006

Fingerprint3 0.0019 0.0021 0.0008

Fingerprint4 0.0023 0.00012 0.0012

From the Table 5, we can see that the entropy values of encrypted various Fingerprint images get close to ideal value which ensures that proposed scheme highly resist against statistical attacks.

C. Resistance to differential attack

In general, enciphered image is completely differing from plain image. Such difference could be calculated by two criterions such as NPCR and UACI [35].


302

NPCR: Number of Pixels Changing Rate (NPCR) which means change rate of the no of pixels in image. If NPCR get close to 100% then plain image is highly encrypted.

100%NM

j)D(i,

NPCRji,

UACI: Unified Average Changing Intensity which is used to measuring the average intensity of pixels difference between the plain image and enciphered image. If UACI around 33% then it is more sensitive resist differential attack.

%100255

j)(i,Fj)(i,F

NM

1UACI

ji,

ENCi

Table 6 shows NPCR of original and encrypted Fingerprint images gets nearly to 99.68 and UACI values are around 33.38 respectively. This result ensures that the proposed algorithm should be vigorous against differential attack.

TABLE VI. NPCR AND UACI VALUES OF FINGERPRINT IMAGE SAMPLES

Image Name NPCR (%) UACI (%)

Fingerprint1 99.60 28.79




VI. CONCLUSION

Since the authentication of biometrics techniques over open network occurs more and more, security of such techniques is more important. In this proposed scheme, human fingerprint is encrypted by using the properties of DNA code and chaotic logistic map with route cipher which ensures preserving the privacy of the template. From the above discussing, 1D logistic map chaotic sequences are scrambled by using route cipher operation and original image pixels are scrambled according to the index of permuted chaotic sequences. Then, using the original chaotic sequence, key masks are generated. Then, XOR the two DNA sequence matrix which are obtained by DNA encoding the permuted image and key masks to obtained the encrypted image.

Through the numerical experiment and security analysis, it is proved that proposed algorithm has better encryption effect, large key space and high enough sensitive to the secret keys. Moreover, the proposed algorithm has ability of resist against all kinds of attacks such as exhaustive, statistical and differential attacks. All these prominent aspects depicts that the combination of 1D chaotic map with route cipher and DNA Cryptography could be suitable for authentication of fingerprint template efficiently and securely.

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