Reversible Multiple Image Secret Sharing using Discrete Haar Wavelet Transform

International Journal of Electrical and Computer Engineering (IJECE)
Vol.8, No.6, December2018, pp. 5004~5013
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i6.pp5004-5013  5004
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Reversible Multiple Image Secret Sharing using Discrete Haar
Wavelet Transform
Ashwaq T. Hashim1
, Suhad A. Ali2
1
Department Control and Systems Eng., University of Technology, Iraq
2
Department of Computer science, Science College for women, Babylon University, Iraq
Article Info ABSTRACT
Article history:
Received Feb 2, 2018
Revised Jun 30, 2018
Accepted Jul 11, 2018
Multiple Secret Image Sharing scheme is a protected approach to transmit
more than one secret image over a communication channel. Conventionally,
only single secret image is shared over a channel at a time. But as technology
grew up, there is a need to share more than one secret image. A fast (r, n)
multiple secret image sharing scheme based on discrete haar wavelet
transform has been proposed to encrypt m secret images into n noisy images
that are stored over different servers. To recover m secret images r noise
images are required. Haar Discrete Wavelet Transform (DWT) is employed
as reduction process of each secret image to its quarter size (i.e., LL
subband). The LL subbands for all secrets have been combined in one secret
that will be split later into r subblocks randomly using proposed high pseudo
random generator. Finally, a developed (r, n) threshold multiple image secret
sharing based one linear system has been used to generate unrelated shares.
The experimental results showed that the generated shares are more secure
and unrelated. The size reductions of generated shares were 1:4r of the size
of each of original image. Also, the randomness test shows a good degree of
randomness and security.
Keyword:
Block Cipher
Haar DWT
Linear System
Multiple Secret Sharing
Pseudo Random Generator
Secret Sharing
Copyright © 2018Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Suhad A. Ahmed,
Department of Computer, Science College for women,
Babylon University, Babylon, Iraq.
Email: wsci.suhad.ahmed@uobabylon.edu.iq
1. INTRODUCTION
Due to its importance, image security fields grows faster and widely, leading to the inventing of
image steganography, image protection, image watermarking and the area of secret image sharing. Images
need to be protected from being revealed, from being copied or from losing its content if it was containing
valuable contents. By mentioning security, Cryptography is the main player in the whole field and it plays an
important role in the infrastructure of the modern computing. There is no exaggeration to say that no
application, even the real world one, requires no keys (such as passwords) in any part of it for serving the
purposes of confidentiality, authentication, and nonrepudiation [1].
The strength of any cryptographic applications relies mainly on its key secrecy and key strength,
because if the key got lost or falls in the wrong hands, this can lead to catastrophic consequences and nothing
is more disastrous than losing a confidential secret information, consider a case where a confidential
document that can lead to the defeat in a battle like war information or forces location. Thus, to tackle such
problem many cryptosystem designers suggest such a solution:
Consider a secret S (a phrase, a password or a key) is divided into n>1 parts (called secret shares)
and it satisfies these conditions:
1. The secret S can be easily restored from r shares where (r ≤ n) shares.
2. It is impossible to restore the secret S from less than r shares.
3. Share size should not exceed the size of the secret S.

Int J Elec& Comp Eng ISSN: 2088-8708 
Reversible Multiple Image Secret Sharing using Discrete Haar Wavelet Transform (Suhad A. Ahmed)
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This scheme is called a r out of n, (r, n) threshold cryptography scheme or simply a secret sharing
system. Secret sharing system provides a higher level of protection for the key from being lost or falls in the
wrong hands by providing secure backup copies to the secret key distributed over several servers or
locations. Moreover, secret sharing can be considered as a mechanism to transfer secret information using
public communication channels [2]. The secret sharing scheme is an advanced cryptography branch that
plays crucial role in defense passively, and it would be used to protect valuable or classified information and
documents against dangers like robbery and illegal accesses [2]. Multiple Secret Image Sharing or simply
(MSIS) is a secret image sharing scheme that protect more than one secret images at a time. Conventionally,
transmission of a single secret image is possible over a channel at a time. But as long as technology grows,
there is an enormous need to share more than one secret image at a time [3].
2. RELATED WORKS
In 1979, Shamir [4] introduced the concepts and theory of secret sharing. Shamir’s secret sharing
scheme was based on a n-degree polynomial, and shares were the points on that polynomial. In 2002, Thien
and Lin [5] proposed an extension of Shamir’s scheme where the secret image is shared by n shares, and any
r (r <n) shares can be used to reconstruct the secret. This scheme is started with a permutation technique to
shuffle the image’s pixels and de-correlate it, then shares were made by processing the image pixels or
patterns in the spatial domain, each participant receiveing his own share as a shadow image looks like a
random noise image holding partial information of the secret. Share size is just 1/r of the secret image. In
2007, Chin and Ching [6], introduced a way of share images based on the reversible integer-to-integer (ITI)
wavelet transform.
This method processes the transform coefficients in each subband, and each of the resulting
combination coefficients were divided into n shares. It was allowing the recovery of the complete secret
image using any r or more shares (r ≤ n). This method has larger shadow images without coding than those
belong to the methods that applying coding as a preprocessing for the inputting to the sharing phase. Also, in
this method, the data is encoded either by Huffman coding or by arithmetic coding before the data is sent to
the sharing phase. Also, in this method the Huffman coding or arithmetic coding have been used to encode
data before it is sent to the sharing phase. In 2007, Jun et al [7], proposed a scalable secure approach to share
and hide secret image. The secret image given first is divided into numerous nonoverlapping blocks, and each
block is then transformed into one-level discrete wavelet transform. Then, the wavelet coefficients have been
quantized into 256 gray levels. After that the gray value information of the quantized image was rearranged
by using a bit-plane scanning method. Finally, the image data is rearranged into n shadows by using multiple
thresholds. Finally, each shadow image of R, G, and B channels is hidden in the cover image.
The results of the test indicated that the increasing of the number of shadows can lead to recovery of
the secret image with better quality. In 2011, Yang et al [8], suggested a fast secret image sharing method
based on Haar wavelet transform and Shamir’s method. Firstly, they used discrete Haar wavelet transform to
reduce the secret image to its quarter size (i.e., 1-level LL subband). Then, the modified Shamir’s algorithm
has been applied to only this LL subband for generating the shadow images. In 2011, T. Hoang and et al [9],
proposed a (2, n) gray image secret sharing scheme. The proposed scheme is basis on three existing
approaches: block truncation coding (BTC), vector quantization (VQ) and discrete wavelet transform (DWT).
In this scheme, the set of generated shares have been much smaller than the original image. Any gray image
can be reconstructed by combining at least two shadows.
The quality of the reconstructed image ranged from 29.5 bears to 36.5 dB. In 2012, Sagar et al. [10]
proposed a new method to perform color visual cryptography based on wavelet transform. Wavelet transform
has been utilized to obtain a gray image from a color image where the intensity image (Y) formed from the
YCbCr color transform. Then, Error-Diffusion Filter has been applied on the obtained grey image. After that
the visual cryptography system (VCS) model was applied on the generated halftone image. In 2014, Ashwaq
and Loay [2] introduce a security secret color image sharing based on transform coding, using wavelet or
cosine transformation to produce secure secret shares by first compress the image using one of the transform
coding techniques mentioned earlier. The compressed stream is then subject to a data diffuser followed by a
random generator to shuffle the image into shares; a secret shares generator system is then applied on these
shares to produce the secret shares.
3. THE TINY ENCRYPTION ALGORITHM
The Tiny Encryption Algorithm (TEA) is a block cipher known as a simple of description and easy
to implement. This cipher was firstly introduced by (Wheeler and Needham 1994). TEA works on 64-bit
plaintext at a time and using 128-bit key. It is a Feistel network of 64 rounds, typically applied on pairs

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termed rounds. The key schedule was extremely simple by mixing all of the key material in exactly the same
way for each round. Various multiples of a magic constant have been utilized to prevent simple attacks on
basis of the symmetry of the rounds. The magic constant, 2654435769 or 9E3779B916 has been chosen to be
232/ϕ, where ϕ was the golden ratio [12].
Figure 1 shows the structure of TEA algorithm. TEA is a Feistel cipher that uses different
(orthogonal) algebraic groups - XOR, ADD and SHIFT in this instance. This is a truly ingenious way of
saving Shannon's twin properties of diffusion and confusion which are important for a secure block cipher,
without needing the explicitly of P-boxes and S-boxes respectively. It seems highly resistant to differential
cryptanalysis, and achieves complete diffusion (where a one bit difference in the plaintext will cause about
32 bit differences in the cipher text) after only six cycles [13].
4. THE PROPOSED SYSTEM
An approach of multiple image secret sharing for secret gray images for set of participants has been
proposed. In this approach, each participant can share a gray secret image with the other of participants in a
way that of all them can reconstruct your secret gray image if only k out of n shares have been collected. The
proposed approach is basis on: (i) Applying Haar DWT to reduce each input image to its quarter size, (ii)
Using proposed pseudo random generator to distribute the combined compressed streams into r subblocks
randomly and (iii) Performing the developed multiple image secret sharing based on linear system to
generate unrelated shares. Algorithm (1) shows the steps of proposed system.
ALGORITHM 1: MULTIPLE SECRET IMAGE SHARING
Input: I1, I2, …,Im// m gray images of equal size.
r // Threshold value
n // Number of generated shares
Output: Shares // n shares
Step1: Applying haar DWT on input images secret imagesI1, I2, …,Im. The subbandsLL1, LL2, …,LLm of the
transform images have been used to generate shares.
Step2: Combined the LL1, LL2, …, LLm subbands in one total image T.
Step3: Separate the total image T into r sub blocks randomly using proposed pseudo random generator
system
Step 4: Generate n shares Sh1, Sh2, …, Shn using Linear System
4.1. Proposed Pseudo Random Generator
Digital cryptography relies greatly on randomness in providing the security requirements imposed
by various information systems. Just as different requirements call for specific cryptographic techniques,
randomness takes upon a variety of roles in order to ensure the proper strength of these cryptographic
primitives. Block ciphers are the most popular cryptographic primitives; due to the standardization of DES
followed by AES, but also due to the fact that block ciphers constitute some of the fundamental building
blocks for pseudorandom number generators, stream ciphers, hash functions and message authentication
codes.
A pseudo random generator has been proposed.thw length of random sequence that has been
generated by proposed system is 192 bits. This step is to decorrelate the output result from compression
stage; it has been distributed into rsubblocks. By using a proposed pseudo random generator based on a
secret key, it will be generated a random sequence of numbers each has a length equal to the length of
combined secret data for all images after compression and the values of generated sequence are ranged to be
1..r, then the secret information will be permuted randomly into nsubblocks according to generated sequence.
Algorithm (2) illustrates the detail steps of the proposed pseudo random generator.
Figure 1 depicts the general structure of the pseudo random generator where the keystream
generator (KSG) is a pseudo random number generator based on block cipher and the keys (i.e., K1, K’1) is
the seed of the pseudo random generator.

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Figure 1. The proposed block cipher based pseudorandom generator
The KSG is a consecutive of two proposed block ciphers. Each of them is a cascaded design of TEA
block cipher, denoted by Cascaded TEA1 and Cascaded TEA2. The Cipher Block Chaining encryption mode
has been used in proposed block cipher where the input to the first Cascaded TEA is a public IV, and the
inputs to each of them is one of two master keys, denoted kiand k’i respectively, these keys is considered as a
seed for the pseudorandom generator. Figure 2 shows the block diagram of KSG.
Figure 2. The proposed keystream generator KSG
As notice the xi is the input to the first Cascaded TEA, and the mi is an intermediate. Then the output
of the KSG is yi. The detail of Cascaded TEA has been showed in Figures 3 and 4.
Figure 3. The proposed of Cascaded TEA Figure 4. The proposed of Feistel TEA

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ALGORITHM 3: PROPOSED PSEUDO RANDOM GENERATOR
Input: T // Combined the LL1, LL2, …, LLmsubbands
n // Length of T
r// Threshold value
K, K' // Master keys each of which 64 bits
Output: SBk // Generated rsubblocks
Step1: The new input for the first Cascaded TEA is:
xi= IV
(3)
Step2: The mi is computed as intermediate value:
mi= Cascaded TEAki (xi) (4)
Step3: The KSG output yi is computed as:
yi = Cascaded TEAk’i(mi) (5)
Step4: The new input for the next Cascaded TEA is:
xi+1= IV ⊕yi. (6)
Step5: In the KSG design, the internal state at each step has been used to update running keys such as
following
ki+1 = ki⊕ mi (7)
and
k’
i+1 = k’
i⊕mi (8)
The k and k’ represented the master keys and the ki and k’i the running keys.
Step6: Repeat step2 to step5 until generate yiwhere i=1..n
Step7: For each yi components (i.e.,C1, C2, and C3) where i=1..n, Do the following:
Step7-1:Let K = C1, I=n-1
Step7-2: While 1>1
K←(𝐶2 × K + 𝐶3) modular I
Swap b[I], b[K]
End loop I
Step8: For I=1 ⇾ n
X←b[I]
IF(X <> 0)
X←X× n / r
ENDIF
no←count[X]+1
w←X+ no
SBk[w]=S[I]
end loop I
4.2. Multiple Secret Image Sharing Based on Linear System
The input I1, I2, …, Im images have been reduced (i.e., to its quarter size) and shuffled randomly into
rsubblocks. In the multiple secret images sharing, the input content is composed by a set of equal sized
blocks (i.e., SBk1, SBk2,…, SBkr). Each of the blocks can be any type of content. For a block of data {Qj| j=1..r}
(i.e., each Qjis a byte from jth
block), the ith
share is calculated by using the linear equations adapted from [2]
and shown in (9):
Shi = cijQj + cijQj+ ..... +cijQj mod 255, i=1,…,n, j=1,..,r (9)

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Where, Shi is the ith
share which is generated for the subblockQ(), cij is the jth
coefficient belong to the linear
equation denoted the ith
share.
5. EXPERIMENTAL RESULTS AND DISCUSSION
Different tests were implemented to evaluate the proposed system algorithm performance. Six grays
of size 512×512 images (“Lena”, “Jet-plane”, “Splash”, “Peppers” and “Sailboat” and “House”) have been
used. The test images have different visual properties, like a natural scene, having lot of edges and having
high correlated sections. These six test images are shown in Figure 5.
Figure 5. Test images
Table 1 lists the PSNR after applying haar DWT; the only distortion of the proposed multiple secret
image sharing was due to the use of this step, no further loss was caused by the rest operations or functions of
the proposed system.
Table 1. The CR, Number of bytes and PSNR of each image when applying proposed compression scheme
Image PSNR
Lena 34.52
Jet_plane 30.01
Splash 33.35
Peppers 33.28
Sailboat 30.90
House 41.21
The results that have been listed in Table 1 showed that the size of each has been reduced, 1/4 of the
size of the original secret image and the qualities of all images were at acceptable level (i.e., greater than30
dB). So that the total size for all input images have been reduced to 1/4r after applying a (r, n) threshold
multiple secret image sharing.
The proposed Pseudo-random number generator depends on two master keys and an initial vector to
generate and many random numbers as needed. Many statistical tests have been applied to test the
randomness of a sequence, in general many sequences that considered random may be easy to predict. So it's
important to test the generators to prove its efficiency. Table 2 shows first three samples generated using the
specified initial vector and keys. Table 3 shows the differences between each two consecutive generated
sequences. Table 4 shows the results of randomness test of 18 random sequences that are generated in
table 2.

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Table 2. Three consecutive random sequences that is generated using different initial and master keys
Sample
no
Initial
vector
Master
Key 1
Master
Key 2
First random
sequence
Second random
sequence
Third random
sequence
1 0 0 0
0111110000000011
0011001000100010
0101111111101111
0011000110100110
0101110110110110
1101000001101111
0100000010001101
0001001101101101
1001100110000011
0000001001010001
1011110011101010
1000001001010010
1011011000111011
1010110100100000
1010011010001100
0111010111010111
0101001110001000
1110000101110010
0000000010000000
0010000111110110
1000100101000000
0010111111100001
1101000001010010
0000100000110111
0011100100000111
0100111011111011
0101010000101000
1011101010110101
1111001000001100
0001110110001011
1101011011000011
0010101000011110
1011000101110001
1101000101000110
1100001100001010
1010100101001111
2 0 1 0
0010010110111110
1100010001001101
0010010011001100
1010111001001011
1001111000110111
0111100110111001
1101101111101000
1101001100101111
0101111110101110
0111110100001001
1110010011011101
0101001100000110
0100001100100101
1000101100011111
1111001010110100
0001010011101101
1111101010000111
1011110111101101
1111000100000011
1011011111110101
0001000010101000
1011101011100001
1101110000000001
0101001001010111
0001111111001001
0101111111101110
1101001001001001
1100100111100000
0011110110101011
1001000111001110
0111011100011000
0011110111000101
0111010111010000
0100000100100001
1101110011001100
0101100011110001
3 0 0 1
1011110110001111
1001110110010000
0001011101010010
1100010100101110
0000010110110001
1101010000010010
1100111001101101
0101011100100101
0100000011010110
1000101100000001
0110100111100010
1010110001110000
1010001011010100
1111010001011100
0010110010011100
1100010111010000
1110101000110010
0110010111011101
0011010000001001
1111100100001111
0100111100011110
1001100100100010
1101001111011100
1110100110111011
1011101000001000
0101100111101001
0101010001110111
1101101000110011
1111010000101000
1011101001000111
1010100000101111
0001000101000001
1111111100110000
0100011001101011
0010001100101100
1001000110001111
4 1 0 0
1000100110110101
1110001010110110
1001100101000000
1011001101001010
1001111000110111
0111100110111001
1101101111101000
1101001100101111
1010101000100111
0111111010011111
0001101001110011
1100011110001110
0111100000100110
0110010011111010
0101100100110010
1110100011101101
1111111001100001
0101100010000001
0101111000101010
0101001101000101
1100001111011000
0110100000100010
0100110110100000
0101000111010000
0011111001011001
0011100111101110
0110011101111111
1101011000001100
1110010000110110
0000011100111101
1000110000111100
1010000110001011
1001110100100111
1101001011001011
0110110000011000
1000100101110010
5 0
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
1111111
0
1000101000110110
1110001000111110
0011000101101111
1110100001001110
1001111000110111
0111100110101001
1101101111101000
1101001000111111
0011000001110011
1000011110000110
0001101000000101
0101111010111011
1000011101111001
0111010111001011
1010010010101100
1010111010011111
0001011010011100
0100000101010100
0101100000010101
1101001001011010
0111010001010001
1000010101100010
1111001111011010
0001111111110011
0111111111111100
0101100000000001
0110011110100101
1011100001011100
0110000010010111
0110011100100011
1010101100100110
0110101100100001
0110010001011010
0100111101111010
0001001001101100
0001111111000011

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Table 2. Three consecutive random sequences that is generated using different initial and master keys
Sample
no
Initial
vector
Master
Key 1
Master
Key 2
First random
sequence
Second random
sequence
Third random
sequence
6 0 0
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
11111111111
111111
0001111001111000
1100100010001101
0010011010011001
1010111011010000
1001111000110111
0111100110111001
1101101111100100
1101001100110001
1001011011000100
0000000101001100
0101100111001011
1011100101010010
0010010111100101
0000110110110110
1111000101010001
1001011010011000
0011010111010010
0100001001010010
0000111111100001
0111101011010111
0110111100111011
0111111001011100
0100010011101110
0010101010100110
1001010101110101
0111100101111001
0100000110101111
0010110100110100
0001111101000011
1011011010110010
1011111011011111
0101010111100111
1101101010110110
1110101000000100
1101000110100010
0000100100101001
Table 3. Difference between consecutive generated sequences
Sample no
Differences between
1st and 2nd
Differences
between 2nd and
3rd
1 101 (52.6%) 99 (51.56%)
2 99 (51.56%) 92 (47.92%)
3 102 (53.13%) 97 (50.52%)
4 98(51.04% 103 (53.64%)
5 98 (51.04% ) 102 (53.13%)
6 105 (54.69%) 94 (48.96%))
Table 4. Results of NIST Statistical of generated random sequences
Frequency
(Monobit)
Frequency
Test within
a Block
M=16
Runs
Test
Longest
Run Of
Ones
Cumulative
Sums
Serial
M=3
Approximate
Entropy
M=2
Linear
Complexity
M=8
0.0123 0.2117 0.8537 0.3339 0.3981 0.9248 0.1860 0.8654
0.0233 0.0116 0.4577 0.1299 0.0267 0.7316 0.1423 0.0811
0.0417 0.5083 0.9023 0.4124 0.0432 0.9845 0.4119 0.5523
0.0405 0.0664 1.0000 0.4124 0.1175 0.9845 0.4119 0.8231
0.1472 0.6512 0.4232 0.7208 0.2543 0.8825 0.5218 0.0996
0.1157 0.0299 0.3422 0.7208 0.1783 0.6766 0.6006 0.3241
0.1371 0.6512 0.1907 0.7208 0.0781 0.8825 0.4646 0.0445
0.2527 0.0276 0.5752 0.7208 0.1046 0.6356 0.5760 0.2883
0.2146 0.6309 0.4230 0.7208 0.1772 0.2650 0.3002 0.8877
0.2777 0.0424 0.3286 0.7208 0.3251 0.4437 0.5427 0.7619
0.4563 0.4066 0.3269 0.7891 0.1362 0.1607 0.2709 0.3242
0.9542 0.0642 0.8124 0.6928 0.3524 0.4369 0.6103 0.0222
0.4871 0.5661 0.2540 0.7632 0.3697 0.1054 0.1664 0.4987
0.3222 0.0642 0.2348 0.7208 0.2765 0.1038 0.2532 0.3245
0.7234 0.5879 0.7236 0.7891 0.3555 0.1038 0.2990 0.7856
0.8234 0.0843 0.7655 0.8770 0.3241 0.2096 0.5089 0.4759
0.9271 0.6506 0.2767 0.8770 0.9977 0.3622 0.5500 0.8921
0.2333 0.6564 0.4766 0.6487 0.3777 0.4437 0.5919 0.5437
0.3532 0.4814 0.2435 0.9145 0.2341 0.2096 0.3294 0.7321
0.2821 0.6642 0.4210 0.6487 0.2342 0.4369 0.4737 0.5911
The result listed in Table 3 shows that most differences are greater than 50% of the length of
generated random sequences while Table 4 shows that all the P-values are greater than α (α = 0.01 )value. So
the proposed pseudo random generator output have passed NIST statistical test suite. Figures 6 and 7 show an
example of coding and decoding of proposed multiple image secret sharing phases.
Table 5 illustrates the time required to recover the secret images of size 512×512 when applying
(2,5) threshold multiple secret image using linear system and the sharing coefficient values for share1 are:
a11=131, a12=132 and for share2 the coefficient values are: a21=133, a22=135.

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Table 5. The time required to encode and recover multiple secret images using (2,5) threshold multiple secret
image using linear system
No. of
Secret
images
(m)
Size in
bytes
Time in Sec.
Haar
(DWT)
Encoding of
Linear
system
Revealing of
linear
system
Inverse of
Haar
(DWT)
Pseudo
Random
Generator
TOTAL
Encoding
Phase
TOTAL
Revealing
Phase
2 131072 0.04 0.014 6.72 0.020 0.026 0.08 6.766
3 196608 0.06 0.022 10.08 0.032 0.019 0.101 10.131
4 262144 0.08 0.029 13.45 0.040 0.026 0.135 13.516
5 327680 0.10 0.039 16.81 0.053 0.033 0.172 16.896
Figure 6. Example for encoding phase of proposed multiple secret image sharing
Figure 7. Example for revealing phase of proposed multiple secret image sharing

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6. CONCLUSION
In this paper, a (r, n)-threshold multiple image secret sharing based on linear system with the haar
wavelet transform has been proposed. The benefit of a small computation time of reduced data has been
exploited after applying haar wavelet. All secret images have been preserved of their quality (i.e., greater
than 30 Db) after the reduced their sizes to quarter size. The proposed system employed pseudo random
number generator to permute the transformed images data in pre-generated shares randomaly. The proposed
pseudo random generator based on block cipher technique which is depended on a re-keying approach to
overcome key schedule weakness in TEA algorithm and used the rounds of the TEA which is a highly
random block cipher algorithm. The developed multiple secret image sharing has been applied to generate
uncorrelated shares to store in different servers. If any r out of n shares have been collected, can be recovered
the m secret images.
REFERENCES
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