Image Encryption using Hybrid Transform Domain Scrambling...

© 2014, IJARCSMS All Rights Reserved 82 | P a g e

ISSN: 2321-7782 (Online) Volume 2, Issue 6, June 2014

International Journal of Advance Research in Computer Science and Management Studies

Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com

Image Encryption using Hybrid Transform Domain Scrambling

of Coefficients Dr. H. B. Kekre

1

Senior Professor

Computer Engineering Department

MPSTME, NMIMS University

Mumbai – India

Dr. Tanuja Sarode2

Associate Professor


TSEC, Mumbai University

Mumbai – India

Pallavi N. Halarnkar3

PhD Research Scholar



Mumbai – India

Debkanya Mazumder4

Student



Mumbai – India

Abstract: Security of Data is very important, when it comes to Digital images the bulkiness of the data makes the standard

data security methods unsuitable, so novel techniques have to be proposed to secure the image data. Image scrambling is one

of the methods, however it does not change the pixel value rather it just changes its position making it prone to attacks. In

this paper we have made use of Image scrambling technique in our framework, which results in encrypting the digital

images to make them more secure. Earlier to this Non-sinusoidal transforms were used; here we have explored all the

combinations of Hybrid Transforms using Kekre Transform as the base transform with other non sinusoidal transforms.

The experimental results obtained are good when compared to individual non-sinusoidal transforms.

Keywords: Image Scrambling, Image Encryption, Key Based Scrambling, Hybrid Transforms.

I. INTRODUCTION

Image scrambling only shuffles the pixel values of a Digital image using some reversible transformation, which may be

easy to descramble it from attacker’s point of view. Rather Image Encryption could be a better alternative to protect digital

images. Muhammad introduced an Asymmetric Image encryption scheme in gyrator transform domain using Schur

decomposition [1]. Firstly the R G and B planes of the color image are separated, then using different random phase masks are

multiplied to R G and B planes for modulating them. Convolution is applied to combine the R G and B plane to convert it into

grayscale. This grayscale image is gyrator transformed. The gyrator spectrum is then amplitude and phase truncated. The

asymmetric keys are generated for R G and B plane. The Phase truncated image is divided into U and T parts by applying Schur

Decomposition. These U and T parts are gyrator transformed to obtain the encoded images. Numerical simulation shows the

validity and security of the proposed approach.

Ch. Samson et al. proposed an Image Compression based Encryption technique [2]. In this method a Wavelet Transform is

applied to the RGB image to achieve compression. In order to achieve a further compression lossless predictive coding is

applied. This compressed image is encrypted using Secure Advanced Hill Cipher in addition to a pair of Involutory matrices, a

function called as mix and XOR operation. Decryption process results in the proper recovery of the original image. The

proposed method can be used for a secure and a reliable transmission of data.

Narendra Singh et al. proposed a new chaos based image encryption scheme based on canonical transforms [3]. The

technique makes use of three different canonical transforms, fractional Fourier transform, the extended fractional Fourier

transform and Fresnel transform. The three chaotic maps used to generate random phase masks are the tent map, Kaplan –Yorke

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Dr. H. B. Kekre et al. International Journal of Advance Research in Computer Science and Management Studies

Volume 2, Issue 6, June 2014 pg. 82-111

© 2014, IJARCSMS All Rights Reserved ISSN: 2321-7782 (Online) 83 | P a g e

map and the Ikeda map. The random phase mask generated using these chaotic maps are called as chaotic random phase masks.

Two experimental parameters have been calculated, MSE and SNR. Blind decryption has been evaluated to check the

robustness of the proposed method.

Qing Guo et al. proposed a color image encryption scheme using Arnold and discrete fractional random transforms in IHS

space [4]. The RCB color image is first converted into IHS space. The Intensity component is encrypted using discrete fraction

random transform. This maintains the secrecy of pixel value as well as pixel positions simultaneously. A position scrambling is

done by applying Arnold Transform on the Hue and Saturation component. When compared to classical double random phase

encoding DFRNT save storage of keys which needs to be stored for decryption purpose. In the proposed method, the fractional

order of DFRNT, the random matrix of DFRNT and the iteration number of Arnold transform are the encryption keys. The

performance of the proposed method is analyzed.

Zhengjun Liu et al. proposed a new approach for color image encryption in the Hartley transform domain [5]. The color

image is firstly distinguished into three components R, G and B plane. Hartley transform is applied over the planes. Two

random angle shifts are introduced to rotate the color vectors in the transform domain. This rotation shift of the two angles can

serve as the key for encryption.

Gaurav Bhatnagar et al. used the discrete fractional wavelet transform for multiple encryptions [6]. The fractional wavelet

transform is rotation of signals in the time-frequency plane. In addition to fractional wavelet, chaotic maps are also used for

encryption process. Experimental results show robustness and efficiency of the proposed method.

Liansheng Sui et al. proposed a double image encryption using discrete fractional random transform and logistic maps [7].

Firstly an enlarged image’s pixel positions are relocated and intensity values are changed by using the confusion and diffusion

process using a chaotic map. Doing so results in an Encrypted image. This Encrypted image is encoded into phase and

amplitude part of a complex function which is encrypted into a cipher text with stationary white noise distribution using discrete

fractional random transform. The initial condition of the chaotic map and phase distribution can be used as keys for image

encryption. The proposed method is resistant to conventional attacks such as chosen plain text attack, cipher-text attack.

Karl Martin et al. proposed a partial image encryption technique using Color-SPIHT compression [8]. Image encryption is

achieved by encrypting only bits of individual wavelet coefficients for k iterations of the C-SPIHT algorithm. Varying k

processing overhead and level of confidentiality is achieved. Adequate security is achieved at k=2.

Efficient scrambling of wavelet based compressed images is proposed by G. Ginesu et al. in [9]. The proposed method is

based on randomization of wavelet coefficients. The method considers mobile field as one of the application. Three different

methods called H methods are proposed. Proposed method achieves a very good scrambling efficiency and compression rate.

Computational complexity is also low. All these advantages make it suitable for Mobile Environment.

An image encryption algorithm using Haar wavelet transform is proposed in [10] by Sara Tedmori et al.. The image is

firstly converted to transform domain by applying Haar wavelet transform. The sub bands are encrypted such that it is

unbreakable. A reversible weighting factor is used for encryption purpose. The algorithm reverses the sign of the frequency

components before an inverse is applied over the frequency components. Experimental results show that the encrypted image

values are completely deviated from the original ones. The proposed method is robust against known attacks.

Madhusudan Joshi et al. used fractional Fourier Transform and radial Hilbert Transform in [11] for digital image

encryption. The image is first segregated into two parts/channels by applying Radial Hilbert Transform and image subtraction.

Each of this part is encrypted using double random phase encoding in the Fractional Fourier Transform Domain. The keys of

the encryption and decryption system are the fractional orders and random phase masks.




A wide variety of methods are been proposed in the literature based on fractional Fourier transform. A review of these

methods is provided by B. M. Hennelly et al. in [12]. The strength of these methods and the robustness level of the encryption

methods are discussed. A comparison study is also been provided. An implementation of optical methods is discussed.

Robustness of the system for blind decryption is also provided.

Yong Xu et al. proposed an Image Encryption system based on synchronization of two fractional chaotic systems in [13].

Pecora and Carroll (PC) synchronization and fractional order Lorenz like system, both form a master-slave configuration.

Conditions are derived between these two systems via the Laplace transformation theory. The image is encrypted using a non

linear function of a fractional chaotic state. Experimental results show good encryption and its recovery through the chaotic

signals. Verification of high security is done through cryptanalysis by histogram, information entropy, key space and sensitivity

to initial condition.

J.B. Lima et al. proposed an Encryption technique using finite field cosine transform in [14]. The image is divided into

several sub images. For every sub image finite field cosine transform is applied recursively. After which the sub images are

regrouped and an intermediate image is reconstructed. A secret key determines the positions of these blocks in the intermediate

image. The proposed method has advantage with respect to computational complexity.

J.B. Lima et al. introduced fractional Fourier Transform over the finite fields GF(p) where p= 1(mod 4) in [15]. This is a

finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms. The constructed

transform is then used as a base for encrypting digital images. Metrics used in the method show the robustness of the image

encryption scheme.

Nidhi Taneja et al. presented selective image encryption technique in fractional wavelet domain [16]. In this technique only

sub bands are encrypted using chaotic stream cipher. Selection of sub bands is based upon the relationship between normalized

information entropy and perceptual information in sub band. Experimental results show less computational complexity and

good cryptographic security.

An image encryption scheme using Discrete Fractional Fourier Transform with Random Phase masking is proposed by

Ashutosh et al. in [17]. The proposed method is so sensitive against the keys that it makes the retrieval of the original image

impossible without the right keys. Experimental results are shown on a number of parameters like security, sensitivity and

MSE.

Kekre et al. proposed a novel framework for Encryption of Digital Images using Non Sinusoidal [18] and Sinusoidal

Transforms [19]. In the proposed framework, the image is first converted to transform domain using the suitable transform, then

the transform coefficients are scrambled using key based scrambling technique [21]. Then an inverse transform is applied to

these scrambled transform coefficients. Since the transform coefficients are not in their proper positions application of the

inverse transform results in Image Encryption.

II. IMAGE ENCRYPTION USING HYBRID TRANSFORMS

This paper deals with an extension to earlier method of Image scrambling in Transform domain [18] [19]. In this paper a

hybrid transform with base as Kekre transform with other Non Sinusoidal Transforms i.e. Walsh, Haar and Slant is used for

Image Encryption. The reason for choosing Kekre transform as the base and other as local is that in the earlier work on Non

Sinusoidal transform, Kekre transform gave the best results for correlation of rows and columns in the encrypted images when

compared to original image.

The step by step procedure for Encryption is as follows

1) Read an Image.

2) If the image is a color image , then convert it to grayscale




3) Generate the desired Hybrid Transform using the desired pattern

4) Apply the hybrid transform over the image

5) Hybrid Transformed image coefficients obtained are now scrambled using Key Based Scrambling method with the

same key as is used in [18]

6) Apply Inverse Hybrid transform so as to convert the image back to spatial domain

The step by step procedure for Decryption is as follows

1) Read the Encrypted Image.

2) Generate the same Hybrid Transform using the same pattern as used in the encryption process

3) Apply the hybrid transform over the encrypted image

4) Hybrid Transformed image coefficients obtained are now descrambled using Key Based Scrambling method with

the same key as is used in Encryption process

5) Apply Inverse Hybrid transform so as to convert the image back to spatial domain to get the original image back

III. EXPERIMENTAL RESULTS

For Experimental purpose five images of size 256X256 grayscale were used. For generating hybrid transform, Kekre

Transform was used as the base transform and Walsh, Slant and Haar were used as local Transforms. The different patterns

considered for Generating the Hybrid Transform are 2X128 , 128X2, 4X64 , 64X4, 8X32 , 32X8 and 16X16. The results

obtained for all these are discussed below. The various parameters used to evaluate the method are Average correlation of rows

and columns, Image Entropy, Peak Average Fractional in Pixel value (PAFCPV)[22] and NPCR [23]

a) Original Image (b) Gray Image

Fig 1.

Fig 1.(a) shows the 24 bit color image and (b) shows the grayscale image. Fig 2, 3, and 4.shows the results for 2x128

pattern for Hybrid transforms. Fig 2(a) shows the encrypted image obtained by applying Kekre-Walsh row transform. Fig 2(b)

shows encrypted image obtained by applying Kekre-Walsh column transform. Fig 2(c) shows encrypted image obtained by

applying Kekre-Walsh Full transform. Fig 2(d-f) shows the decrypted images obtained for the same.

Fig 3(a) shows the encrypted image obtained by applying Kekre-Slant row transform. Fig 3(b) shows encrypted image

obtained by applying Kekre-Slant column transform. Fig 3(c) shows encrypted image obtained by applying Kekre-Slant Full

transform. Fig 3(d-f) shows the decrypted images obtained for the same.

Fig 4(a) shows the encrypted image obtained by applying Kekre-Haar row transform. Fig 4(b) shows encrypted image

obtained by applying Kekre-Haar column transform. Fig 4(c) shows encrypted image obtained by applying Kekre-Haar Full





2X128

(a)Kekre- Walsh Row

Transform Encrypted

(b)Kekre- Walsh Column

Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted

(d) Kekre- Walsh Row

Transform Decrypted

(e) Kekre- Walsh Col

Transform Decrypted

(f) Kekre- Walsh Full

Transform Decrypted

Fig 2.

2X128

(a)Kekre- Slant Row

Transform Encrypted

(b)Kekre- Slant Column

Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted

(d) Kekre- Slant Row

Transform Decrypted

(e) Kekre- Slant Col

Transform Decrypted

(f) Kekre- Slant Full

Transform Decrypted

Fig 3.




Fig 5, 6, and 7.shows the results for 128X2 pattern for Hybrid transforms. Fig 5(a) shows the encrypted image obtained by

applying Kekre-Walsh row transform. Fig 5(b) shows encrypted image obtained by applying Kekre-Walsh column transform.

Fig 5(c) shows encrypted image obtained by applying Kekre-Walsh Full transform. Fig 5(d-f) shows the decrypted images

obtained for the same.







2X128

(a)Kekre- Haar Row

Transform Encrypted

(b)Kekre- Haar Column

Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted

(f) Kekre- Haar Full

Transform Decrypted

Fig 4.

128X2

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig 5.




Fig 8, 9, and 10 shows the results for 4X64 patterns for Hybrid transforms. Fig 8(a) shows the encrypted image obtained by







128X2

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig 6.

128X2

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig 7.







4X64

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig 8.

4X64

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig 9.




Fig 11, 12, and 13 shows the results for 64X4 patterns for Hybrid transforms. Fig 11(a) shows the encrypted image obtained by










4X64

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig 10.




64X4

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 11

64X4

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 12




Fig 14, 15, and 16.shows the results for 8X32 pattern for Hybrid transforms. Fig 14(a) shows the encrypted image obtained

by applying Kekre-Walsh row transform. Fig 14(b) shows encrypted image obtained by applying Kekre-Walsh column

transform. Fig 14(c) shows encrypted image obtained by applying Kekre-Walsh Full transform. Fig 14(d-f) shows the decrypted

images obtained for the same.







64X4

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig. 13.




8X32

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig.14.

8X32

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 15




Fig 17, 18, and 19 shows the results for 32X8 patterns for Hybrid transforms. Fig 17(a) shows the encrypted image

obtained by applying Kekre-Walsh row transform. Fig 17(b) shows encrypted image obtained by applying Kekre-Walsh column









8X32

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig. 16




32X8

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 17

32X8

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 18




Fig 20, 21, and 22 shows the results for 16X16 patterns for Hybrid transforms. Fig 20(a) shows the encrypted image

obtained by applying Kekre-Walsh row transform. Fig 20(b) shows encrypted image obtained by applying Kekre-Walsh column









32X8

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig. 19




16X16

(a)Kekre- Walsh Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Walsh Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 20

16X16

(a)Kekre- Slant Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Slant Full

Transform Encrypted


Transform Decrypted


Transform Decrypted


Transform Decrypted

Fig. 21




A. Non Sinusoidal Results

Table No I. shows the correlation obtained in transformed images and Encrypted images. These results are averaged out

over five images used. They are Lena, Baboon, Cartoon, Pepper and Lotus. Considering the limitation of space, the results of all

the 5 images were averaged out and compared with the averaged results obtained for Hybrid transforms and their different

Pattern Combination.

TABLE I

Value of Average Correlation between rows and columns of Row Transformed Images, Row Transform Encrypted Images,

Column Transformed Images, Column Transformed Encrypted Images, Full Transformed Images and Full Transform Encrypted

Images averaged over five images.

B. Pattern 2X128 and 128X2

Table No II and III Shows the correlation obtained in Hybrid transformed images and Encrypted images for 2X128 and

128X2 Pattern. These results are averaged out over five images used and compared with Non Sinusoidal Transforms. Analysis

of the same is provided in Table No IV and V.

16X16

(a)Kekre- Haar Row

Transform Encrypted


Transform Encrypted

(c)Kekre-Haar Full

Transform Encrypted

v

(d) Kekre- Haar Row

Transform Decrypted

(e) Kekre- Haar Col

Transform Decrypted


Transform Decrypted

Fig. 22

Transforms

Row:

0.81398

Col: 0.77742

Row

Transform

Row

Transform

Encrypted

Column

Transform

Column

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Walsh 0.99254 0.34018 0.22332 0.37144 0.26538 0.42456

0.2039 0.3857 0.99266 0.35288 0.23984 0.43424

Slant 0.86658 0.80618 0.31644 0.59116 0.3937 0.60866

0.4468 0.22542 0.99204 0.7784 0.40856 0.58126

Kekre 0.9894 0.7757 0.77696 0.25596 0.91172 0.29276

0.7743 0.24314 0.9926 0.91004 0.89104 0.26792

Haar 0.8985 0.79726 0.22652 0.56872 0.26778 0.5835

0.2168 0.22892 0.99182 0.6907 0.27026 0.56872




TABLE III



Images averaged over five images. (Pattern 2X128) Patter

n

2x128

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transfor

m

Full

Transform

Encrypted

Kekre- Walsh

(Row) 0.99256 0.30172 0.20072 0.24984 0.2383 0.26984

(Col) 0.20058 0.32594 0.99264 0.2954 0.24114 0.27298

Kekre – Slant

(Row) 0.92948 0.78828 0.31066 0.44012 0.3877 0.44144

(Col) 0.43638 0.22436 0.99146 0.57192 0.40048 0.41552

Kekre – Haar

(Row) 0.93566 0.82214 0.20692 0.44708 0.25504 0.44626

(Col) 0.21136 0.22208 0.99178 0.52858 0.25822 0.42214

TABLE IIIII



Images averaged over five images. (Pattern 128X2) Pattern

128X2

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre- Walsh

(Row) 0.98586 0.80842 0.20128 0.26026 0.24566 0.24766

(Col) 0.20268 0.29458 0.99212 0.79826 0.25948 0.24736

Kekre – Slant

(Row) 0.98586 0.80842 0.20128 0.26026 0.24566 0.24766

(Col) 0.20268 0.29458 0.99212 0.79826 0.25948 0.24736

Kekre – Haar

(Row) 0.98586 0.80842 0.20128 0.26026 0.24566 0.24766

(Col) 0.20268 0.29458 0.99212 0.79826 0.25948 0.24736

TABLE IVV

Comparison of Average Row and Column Correlation between individual Transforms and Hybrid Transforms for 2X128

Pattern Original

Transform

Hybrid

Transform

Analysis 2X128

Row Transform Encrypted Column Transform

Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh

Transform, a hybrid transform yields a marginal decrease in

row and column correlation

Compared to Walsh

individual Transform, a hybrid transform yields a

decrease in row and column

correlation

Compared to Walsh


higher decrease in row and

column correlation

Kekre Kekre-

Walsh

Compared to Kekre transform,

hybrid with Walsh results in

decrease in row correlation but a marginal rise in column

correlation

Compared to Kekre

transform, hybrid with

Walsh results in marginal decrease in row correlation

but a good decrease in

column correlation

Compared to Kekre


Walsh results in decrease in row correlation but a

marginal rise in column

correlation

Slant Kekre-Slant Compared to Slant Transform,

a hybrid transform yields a


correlation remains the same

Compared to Slant

Transform, a hybrid

transform yields a decrease

in row and column

correlation

Compared to Slant

Transform, a hybrid

transform yields a good


correlation

Kekre Kekre-Slant Compared to Kekre transform,

hybrid with Slant results in

marginal increase in row

Compared to Kekre


Slant results in increase in

Compared to Kekre






correlation but a marginal

decrease in column correlation

row correlation but a good

decrease in column

correlation

row and column

correlation

Haar Kekre-Haar Compared to Haar Transform,

a hybrid transform yields an

increase in row correlation and remains the same in column.

Compared to Haar

Transform, a hybrid

transform yields a decrease in row and column

correlation

Compared to Haar

Transform, a hybrid


correlation

Kekre Kekre-Haar Compared to Kekre transform,

hybrid with Haar results in

increase in row correlation but

a marginal decrease in column correlation

Compared to Kekre

transform, hybrid with Haar

results in increase in row

correlation but a good decrease in column

correlation

Compared to Kekre



and column correlation

TABLE V

Comparison of Average Row and Column Correlation between individual Transforms and Hybrid Transforms for 128X2

Pattern Original

Transform

Hybrid

Transform

Analysis 128X2


Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh

Transform, a hybrid transform yields an increase in row and


Compared to Walsh


decrease in row and

increase in column

correlation

Compared to Walsh



column correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields a marginal rise in row and

column correlation

Compared to Kekre

transform, hybrid with Walsh results in same row

correlation but a good

decrease in column

correlation

Compared to Kekre

transform, hybrid with Walsh results in marginal


correlation


a hybrid transform yields a marginal increase in row and

column correlation remains the

same

Compared to Slant

Transform, a hybrid transform yields a decrease

in row and marginal

increase in column

correlation

Compared to Slant

Transform, a hybrid transform yields a good


correlation


hybrid with Slant results in increase in row and column

correlation.

Compared to Kekre

transform, hybrid with Slant results in increase in


Compared to Kekre

transform, hybrid with Slant results in marginal


correlation



increase in row and column correlation

Compared to Haar

Transform, a hybrid

transform yields a decrease in row and an increase in

column correlation

Compared to Haar

Transform, a hybrid


correlation


hybrid with Haar results in

increase in row correlation but

a marginal decrease in column correlation

Compared to Kekre


results in marginal increase

in row correlation but a good decrease in column

correlation

Compared to Kekre


results in decrease in row


C. Pattern 4X64 and 64X4

Table No VI and VII Shows the correlation obtained in Hybrid transformed images and Encrypted images for 4X64 and

64X4 Pattern. These results are averaged out over five images used and compared with Non Sinusoidal Transforms. Analysis of

the same is provided in Table No VIII and IX.




TABLE VI



Images averaged over five images. (Pattern 4X64). Pattern

4X64

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre- Walsh

(Row) 0.99176 0.45234 0.1991 0.20162 0.23072 0.20258

(Col) 0.19762 0.24532 0.99188 0.2746 0.24486 0.20922

Kekre – Slant

(Row) 0.96042 0.78018 0.30734 0.31652 0.38854 0.32268

(Col) 0.4292 0.2195 0.9916 0.40484 0.39816 0.33296

Kekre – Haar

(Row) 0.95776 0.80626 0.20824 0.32438 0.24838 0.32572

(Col) 0.20738 0.22262 0.99188 0.41798 0.25734 0.33182

TABLE VVI




64X4

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre- Walsh

(Row) 0.98434 0.7994 0.21298 0.30448 0.26742 0.27276

(Col) 0.21856 0.30326 0.9918 0.69132 0.27168 0.26142

Kekre – Slant

(Row) 0.98072 0.7976 0.28302 0.34842 0.37742 0.33274

(Col) 0.3936 0.23512 0.99182 0.73774 0.39576 0.33034

Kekre – Haar

(Row) 0.97788 0.81034 0.27384 0.33864 0.37432 0.3177

(Col) 0.25892 0.24024 0.99184 0.78466 0.36678 0.31256

TABLE VIVII

Comparison of Average Row and Column Correlation between individual Transforms and Hybrid Transforms for 4X64 Pattern

Original

Transform

Hybrid

Transform

Analysis 4X64


Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh Transform, a hybrid transform

yields an increase in row and


Compared to Walsh individual Transform, a

hybrid transform yields a


correlation

Compared to Walsh individual Transform, a



column correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields a decrease in row correlation

and same in column

Compared to Kekre

transform, hybrid with Walsh results in decrease in

row and column

correlation

Compared to Kekre





decrease in row and marginal decrease in column correlation

Compared to Slant

Transform, a hybrid


correlation

Compared to Slant

Transform, a hybrid

transform yields a good decrease in row and column

correlation



marginal increase in row and

marginal decrease in column correlation.

Compared to Kekre



row and decrease in column correlation

Compared to Kekre


Slant results an increase in


Haar Kekre-Haar Compared to Haar Transform, Compared to Haar Compared to Haar





increase in row correlation and

remains the same in column

Transform, a hybrid


in row and column

correlation

Transform, a hybrid


in row and column

correlation


hybrid with Haar results in increase in row correlation but

a marginal decrease in column

correlation

Compared to Kekre

transform, hybrid with Haar results in marginal increase

in row correlation but a

good decrease in column

correlation

Compared to Kekre

transform, hybrid with Haar results an increase in row


TABLE VIIX

Comparison of Average Row and Column Correlation between individual Transforms and Hybrid Transforms for 64X4 Pattern Original

Transform

Hybrid

Transform

Analysis 64X4


Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh



Compared to Walsh


decrease in row and an

increase in column

correlation

Compared to Walsh



column correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields an increase in row and column

correlation.

Compared to Kekre

transform, hybrid with Walsh results in increase in

row and decrease in column

correlation

Compared to Kekre





decrease in row and marginal increase in column correlation

Compared to Slant

Transform, a hybrid

transform yields a decrease in row and a marginal

decrease in column

correlation

Compared to Slant

Transform, a hybrid

transform yields a good decrease in row and column

correlation



marginal increase in row and marginal decrease in column

correlation.

Compared to Kekre


Slant results in increase in row and decrease in column

correlation

Compared to Kekre


Slant results an increase in row and column

correlation



increase in row and column

correlation

Compared to Haar

Transform, a hybrid


in row and an increase in column correlation

Compared to Haar

Transform, a hybrid


in row and column correlation


hybrid with Haar results a

marginal increase in row

correlation and remains the

same in column.

Compared to Kekre



correlation but a good


Compared to Kekre


results an increase in row


D. Pattern 8X32 and 32X8

Table No X and XI Shows the correlation obtained in Hybrid transformed images and Encrypted images for 8X32 and

32X8 Pattern. These results are averaged out over five images used and compared with Non Sinusoidal Transforms. Analysis of

the same is provided in Table No XII and XIII.

TABLE X




8X32

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre- Walsh

Row) 0.99066 0.67794 0.20376 0.2791 0.2345 0.3044

(Col) 0.20052 0.2586 0.99166 0.52658 0.24678 0.31214

Kekre – Slant




(Row) 0.97188 0.82206 0.30644 0.33818 0.38622 0.37246

(Col) 0.4187 0.22272 0.99168 0.68682 0.39794 0.3723

Kekre – Haar

Row) 0.96582 0.80934 0.212 0.34642 0.25662 0.3677

(Col) 0.20388 0.21732 0.99156 0.64608 0.26004 0.36964

TABLE XI




32X8

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre- Walsh

(Row) 0.98688 0.78046 0.21402 0.33436 0.25696 0.36914

(Col) 0.21484 0.32782 0.99148 0.6181 0.26716 0.3598

Kekre – Slant

(Row) 0.9792 0.8115 0.30312 0.3622 0.38632 0.40738

(Col) 0.39694 0.22444 0.99158 0.7778 0.4028 0.40396

Kekre – Haar

(Row) 0.97518 0.80106 0.228 0.35598 0.29366 0.40008

(Col) 0.23034 0.22424 0.99158 0.73088 0.299 0.39844

TABLE XVIIII


Transform

Hybrid

Transform

Analysis 8X32

Row Transform

Encrypted

Column Transform

Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh



Compared to Walsh


decrease in row and an

increase in column

correlation

Compared to Walsh



correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields an

increase in row and a

marginal increase in column

correlation.

Compared to Kekre


Walsh results in marginal

increase in row and

decrease in column

correlation

Compared to Kekre


Walsh results in increase in



a hybrid transform yields a marginal increase in row and

remains the same in column.

Compared to Slant


in row and column

correlation

Compared to Slant



correlation


hybrid with Slant results an

increase in row and a marginal decrease in column

correlation.

Compared to Kekre


Slant results in increase in row and decrease in column

correlation

Compared to Kekre



correlation




marginal decrease in column correlation

Compared to Haar

Transform, a hybrid


in row and a marginal decrease in column

correlation

Compared to Haar

Transform, a hybrid


in row and column correlation


hybrid with Haar results an

increase in row correlation and

a marginal decrease in column.

Compared to Kekre



correlation but a good decrease in column

correlation

Compared to Kekre


results an increase in row





TABLE XIIXI


Transform

Hybrid

Transform

Analysis 32X8


Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh

Transform, a hybrid transform

yields an increase in row and a

marginal decrease in column correlation

Compared to Walsh

individual Transform, a


marginal decrease in row and an increase in column

correlation

Compared to Walsh

individual Transform, a


decrease in row and column correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields an

increase in row and column

correlation.

Compared to Kekre



row and a good decrease in column correlation

Compared to Kekre




Slant Kekre-Slant Compared to Slant Transform, a hybrid transform yields a


remains the same in column.

Compared to Slant Transform, a hybrid


in row and remain the same

in column.

Compared to Slant Transform, a hybrid

transform yields a good


correlation


hybrid with Slant results an increase in row and a marginal

decrease in column

correlation.

Compared to Kekre

transform, hybrid with Slant results in increase in

row and decrease in column

correlation

Compared to Kekre

transform, hybrid with Slant results an increase in

row and column

correlation



marginal increase in row and remains the same in column.

Compared to Haar

Transform, a hybrid


increase in column

correlation

Compared to Haar

Transform, a hybrid


correlation



increase in row correlation and a marginal decrease in column.

Compared to Kekre


results in increase in row correlation but a good

decrease in column

correlation

Compared to Kekre


results an increase in row and column correlation

E. Pattern 16X16

Table No XIV Shows the correlation obtained in Hybrid transformed images and Encrypted images for 16X16 Pattern.

These results are averaged out over five images used and compared with Non Sinusoidal Transforms. Analysis of the same is

provided in Table No XV.

TABLE XIV




16X16

Row

Transform

Row

Transform

Encrypted

Col Transform Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre-Walsh

(Row) 0.98906 0.67984 0.20828 0.27642 0.24656 0.27538

(Col) 0.20974 0.27366 0.9914 0.57898 0.25542 0.27136

Kekre-Slant

(Row) 0.97898 0.80404 0.30384 0.30936 0.3871 0.3325

(Col) 0.4113 0.22784 0.99158 0.71024 0.40072 0.3266

Kekre – Haar

(Row) 0.97094 0.80388 0.21498 0.31798 0.26602 0.33046

(Col) 0.21592 0.2178 0.9915 0.75404 0.2679 0.32188




TABLE XV

Values Comparison of Average Row and Column Correlation between individual Transforms and Hybrid Transforms for

16X16 Pattern

Original

Transform

Hybrid

Transform

Analysis 16X16


Encrypted

Full Transform

Encrypted

Walsh Kekre –

Walsh

Compared to Walsh

Transform, a hybrid transform yields an increase in row and a


Compared to Walsh


marginal decrease in row

and an increase in column

correlation

Compared to Walsh



correlation

Kekre Kekre-

Walsh


hybrid with Walsh yields a decrease in row and a marginal

increase in column correlation.

Compared to Kekre


increase in row and a good

decrease in column

correlation

Compared to Kekre


decrease in row and

marginal increase column

correlation


a hybrid transform yields a the same correlation in row and

column

Compared to Slant


in row and column

correlation.

Compared to Slant



correlation


hybrid with Slant results an

increase in row and a marginal decrease in column

correlation.

Compared to Kekre


Slant results in marginal increase in row and

decrease in column

correlation

Compared to Kekre



correlation



marginal increase in row and a marginal decrease in column.

Compared to Haar

Transform, a hybrid


increase in column

correlation

Compared to Haar

Transform, a hybrid


correlation



increase in row correlation and a marginal decrease in column.

Compared to Kekre


results in increase in row correlation but a good

decrease in column

correlation

Compared to Kekre


results an increase in row and column correlation

Table No XVI and XVII Shows the Entropy obtained in Hybrid transformed images and Encrypted images for 2X128 and

128X2 Pattern. These results are averaged out over five images used.

TABLE XVI

Values of Entropy in Row Transformed Image, Row Transform Encrypted Image, Column Transform Image, Column

Transform Encrypted Image, Full Transformed Image and Full Transform Encrypted Image for 2X128 Pattern 2X128

Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Original

7.398

Kekre – Walsh

4.753 3.524 4.756 3.573 4.754 3.104

Kekre – Slant

4.900 5.103 3.955 3.200 3.939 2.814

Kekre – Haar

5.059 4.676 4.070 3.446 3.965 3.027

TABLE XVII



Row

Transform

Row

Transform

Encrypted

Col

Transform

Col Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre – Walsh




Original

7.398

6.112 3.493 4.139 3.506 3.917 3.105

Kekre – Slant

6.112 3.493 4.139 3.506 3.917 3.105

Kekre – Haar

6.112 3.493 4.139 3.506 3.917 3.105

Table No XVIII and XIX Shows the Entropy obtained in Hybrid transformed images and Encrypted images for 4X64 and


TABLE XVIII



Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Original

7.398

Kekre – Walsh

4.812 3.495 4.751 3.562 4.755 3.090

Kekre – Slant

5.097 4.802 3.968 3.219 3.964 2.848

Kekre – Haar

4.878 4.609 4.081 3.458 3.974 3.058

TABLE XIX



Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Original

7.398

Kekre – Walsh

4.848 3.265 4.240 3.326 3.958 2.825

Kekre – Slant

5.449 4.367 4.184 3.202 3.823 2.660

Kekre – Haar

5.105 4.287 4.457 3.331 3.831 2.823

Table No XX and XXI Shows the Entropy obtained in Hybrid transformed images and Encrypted images for 8X32 and


TABLE XX



Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Original

7.398

Kekre – Walsh

4.764 3.453 4.450 3.492 4.545 3.040

Kekre – Slant

5.027 4.643 4.276 3.188 3.984 2.797

Kekre – Haar

4.837 4.526 4.249 3.400 4.000 3.015




TABLE XXI



Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Original

7.398

Kekre – Walsh

4.583 3.258 4.247 3.295 4.174 2.847

Kekre – Slant

5.013 4.456 4.099 3.142 3.906 2.661

Kekre – Haar

4.851 4.410 4.252 3.293 3.927 2.859

Table No XXII Shows the Entropy obtained in Hybrid transformed images and Encrypted images for 16X16 Pattern. These

results are averaged out over five images used.

TABLE XXII


Transform Encrypted Image, Full Transformed Image and Full Transform Encrypted Image for 16X16 Pattern 16X16 Row

Transform

Row

Transform

Encrypted

Col

Transform

Col

Transform

Encrypted

Full

Transform

Full

Transform

Encrypted

Kekre – Walsh

Original

7.398

3.352 4.670 3.365 4.363 2.960 4.345

Kekre – Slant

4.513 4.914 3.239 4.054 2.736 3.895

Kekre – Haar

4.466 4.439 3.315 4.205 2.945 3.923

Table No XXIII, XXIV, XXV, XXVI, XXVII, XXVIII, XXIX Shows the PAFCPV and NPCR results obtained in Hybrid

transformed Encrypted images for 2X128, 128X2, 4X64, 64X4, 8X32 and 32X8 and 16X16 Pattern. These results are averaged

out over five images used.

TABLE XXIII

Values of PAFCPV and NPCR in Row Transform Encrypted Image, Column Transform Encrypted Image, and Full Transform

Encrypted Image for 2X128 Pattern PAFCPV Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5625 0.5629 0.5637

Kekre – Slant 0.5595 0.5440 0.4869

Kekre – Haar 0.5507 0.5375 0.4865

NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 99.99 99.99 100

Kekre – Slant 100 100 100

Kekre – Haar 99.99 100 100

TABLE XXIV



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.4834 0.5038 0.4778

Kekre – Slant 0.4834 0.5038 0.4778

Kekre – Haar 0.4834 0.5038 0.4778




NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 100 100 100


Kekre – Haar 100 100 100

TABLE XXV



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5750 0.5626 0.5636

Kekre – Slant 0.5335 0.5506 0.4894

Kekre – Haar 0.5604 0.5369 0.4864

NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 99.99 100 100

Kekre – Slant 99.99 100 100

Kekre – Haar 99.99 100 100

TABLE XXVI



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5493 0.5167 0.4853

Kekre – Slant 0.5056 0.5040 0.4818

Kekre – Haar 0.5390 0.5035 0.4811

NPCR Row

Transform

Encrypted

Col Transform

Encrypted

Full

Transform

Encrypted


Kekre – Slant 99.99 100 100

Kekre – Haar 100 100 100

TABLE XXVII



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5758 0.5752 0.5374

Kekre – Slant 0.5318 0.5259 0.4899

Kekre – Haar 0.5725 0.5291 0.4899

NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted


Kekre – Slant 99.99 100 100

Kekre – Haar 99.99 100 100

TABLE XXVIII



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5704 0.5385 0.4934

Kekre – Slant 0.5455 0.5149 0.4854

Kekre – Haar 0.5586 0.5216 0.4868




NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted



Kekre – Haar 99.99 100 100

TABLE XXIX



Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted

Kekre-Walsh 0.5769 0.5574 0.5109

Kekre – Slant 0.5540 0.5170 0.4840

Kekre – Haar 0.5934 0.5136 0.4821

NPCR Row

Transform

Encrypted

Col

Transform

Encrypted

Full

Transform

Encrypted


Kekre – Slant 99.99 100 100

Kekre – Haar 99.99 100 100

IV. CONCLUSION

From the experimental results it can be concluded that Hybrid Transforms when compared to individual transforms

definitely gives good results from average row and column correlation. In this paper we have used all the possible combinations

for Hybrid transforms considering the image size 256X256. The reason for choosing Kekre as the base transform and others as

local was decided looking at the correlation results obtained for individual Non sinusoidal transforms where Kekre transform

performed the best.

The hybrid transform patterns which gave good results in terms of correlation for Row Transform, Column Transform and

Full transform are 2X128- Kekre-Slant, 128X2-Kekre-Walsh, 4X64- Kekre-Walsh and Kekre-Slant, 64X4- Kekre-Walsh and

Kekre-Slant and 8X32-Kekre-Walsh. For Image Entropy in Encrypted image a minimum value of 2.660 was obtained in Kekre

–Slant Full Transform 64X4 pattern.

A maximum value of PAFCPV 0.5934 was obtained in Kekre-Haar for Row Transform 16X16 pattern. NPCR values are

good across all the combination Pattern of different Hybrid Transforms. Hence we can conclude that based on the requirement

of the encrypted image quality, a wide variety of options can be used to encrypt the digital images. The proposed method gives

good encrypted images which can be seen from the experimental results.

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AUTHOR(S) PROFILE

Dr. H. B. Kekre has received B.E (Hons.) in Telecomm Engineering from Jabalpur University in

1958, M.Tech (Industrial Electronics) from IIT Bombay in 1960, M.S.Engg. (Electrical Engg.) from

University of Ottawa, Canada in 1965 and Ph.D. (System Identification) from IIT Bombayin 1970.

He has worked as Faculty of Electrical Engg. and then HOD Computer Science and Engg. at IIT

Bombay. After serving IIT for 35 years he retired in 1995. After retirement from IIT, for 13 years he

was working as a professor and head in the Department of Computer Engg. and Vice Principal at

Thadomal Shahani Engineering. College, Mumbai. Now he is Senior Professor at MPSTME,

SVKM‟s NMIMS University. He has guided 17 Ph.Ds, more than 100 M.E./M.Tech and several

B.E./ B.Tech projects, while in IIT and TSEC. His areas of interest are Digital Signal processing,

Image Processing and Computer Networking. He has more than 450 papers in National /

International Journals and Conferences to his credit. He was Senior Member of IEEE. Presently He

is Fellow of IETE, Life Member of ISTE and Senior Member of International Association of

Computer Science and Information Technology (IACSIT). Recently fifteen students working under

his guidance have received best paper awards. Currently eight research scholars working under his

guidance have been awarded Ph. D. by NMIMS (Deemed to be University). At present eight

research scholars are pursuing Ph.D. program under his guidance.

Dr. Tanuja K. Sarode has received M.E. (Computer Engineering) degree from Mumbai University

in 2004, Ph.D. from Mukesh Patel School of Technology, Management and Engg. SVKM’s NMIMS

University, Vile-Parle (W), Mumbai, INDIA. She has more than 11 years of experience in teaching.

Currently working as Assistant Professor in Dept. of Computer Engineering at Thadomal Shahani

Engineering College, Mumbai. She is member of International Association of Engineers (IAENG)

and International Association of Computer Science and Information Technology (IACSIT). Her

areas of interest are Image Processing, Signal Processing and Computer Graphics. She has 150

papers in National /International Conferences/journal to her credit.

Ms. Pallavi N.Halarnkar has received M.E. (Computer Engineering) degree from Mumbai

University in 2010, currently persuing her Ph.D. from Mukesh Patel School of Technology,

Management and Engg. SVKM’s NMIMS University, Vile-Parle (W), Mumbai, INDIA. She has

more than 8 years of experience in teaching. Currently working as Assistant Professor in Dept. of

Computer Engineering at Mukesh Patel School of Technology, Management and Engg. SVKM’s

NMIMS University, Vile-Parle (W), Mumbai. She has 20 papers in National /International

Conferences/journal to her credit.

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