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(r, n)-Threshold Image Secret Sharing Methods with Small Shadow Images
Xiaofeng Wang, Zhen Li, Xiaoni Zhang, Shangping Wang
Xi'an University of Technology, Xi'an, Shaanxi, 710048, P.R.China
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Outline
Introduction Proposed Scheme
Multi-Secret Sharing Mode Priority Sharing Mode
Experimental Results Conclusions
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Introduction(1/1)
the characters of the proposed methods : the sizes of generated shadow images are
smaller; provided a lossless secret image recovery
approach with smaller shadow images
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Multi-Secret Sharing Mode( 1/3)
Original image IDividing I into four non-overlapping sub-image: I1, I2 , I3, I4
Dividing each sub-image into 8×8 non-overlapping blocks
Generating difference matrix of each 8×8 blockHuffman coding
Generating row vectors:D1, D2 , D3, D4
Pre-processing
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Multi-Secret Sharing Mode( 2/3)
Generating sharing shareGenerating sub-shadow images si(1), si(2),si(3), si(4), si(5), si(6)
Combing the 24 sub-shadow images, generating four shadow images
Embedding these four shadow images to carrier images as watermark
Shadow generation
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Multi-Secret Sharing Mode( 3/3)
Taking a pixel from each of the shadow images
Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial
Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the pixels of difference image
Inverse difference transformation
Recovered secret image
Recovery
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Priority Sharing Mode(1/9)Pre-processing
Original image IDividing the secret image I into n bit-level images
0 1 1, , , nP P P
combing them to generate four combined bit-level images
1 2 3 4, , ,I I I I
1 7 6 2 5 4( ) , , ,B I b b B I b b
3 3 2 4 1 0( ) , , ,B I b b B I b b
Dividing into 2×2 image blocks, every minimum of blocks constructed matrix
1 2 3 4, , ,I I I I
iIM
ijkm
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Priority Sharing Mode(2/9)
Defining matrix that would be used in recovery phase, the elements of are as follows:
iDiD
j, k=1,2,…,N/2 i=1,2,3,4
ijkkj
ijkkj
ijkkj
ijkkji
jkmbmb
mbmbd
2,212,2
2,1212,12
Pre-processing
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Priority Sharing Mode(3/9)
( , ) 1, 1
, 1, 1, 1
, , 1
iui i
st u ui iu u
E s t s t
a E s t E s t s t
E s t E s t others
Dividing into 8×8 image blocks and computing the difference matrix
iIM iuE
ijkdiff
11 12 18
21 22 28
81 82 88
ijk
a a a
a a adiff
a a a
(i=1, 2, 3, 4)
Combining to generate matrix
ijkdiff
iDiff
u=1, ..., N/16×N/16 , )8,...,2,1,( ts
11 12 1, /16
21 22 2, /16
/16,1 /16,2 /16, /16
i i iN
i i iN
i
i i iN N N N
diff diff diff
diff diff diffDiff
diff diff diff
4,3,2,1i
Pre-processing
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Priority Sharing Mode(4/9)
Re-arranging elements of by row to generate a row vector, and compressing it by Huffman coding, then converting the output into 0~255 decimal numbers, noted as
iDiff
1 2 3 4, , ( ), ( )C I C I C I C I
Pre-processing(4/4)
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Priority Sharing Mode(5/9)Shadow generation
Taking every four pixels from as a sharing share, denoted as , then construct Lagrange polynomial for each sharing share
iC I 0 1 2 3, , ,a a a a
Generate six sub-shadow images , ks x 4,3,2,1k1,2,...,6x
Combining the 24 sub-shadow images, then generate four shadow images 1 2 3 4, , ,SH SH SH SH
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Priority Sharing Mode(6/9)
The algorithm of generating shadow images 1 2 3 4, , ,SH SH SH SH
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Priority Sharing Mode(7/9)Secret image reconstruction algorithm
Taking a pixel from each of the shadow images
Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial
Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the difference bit-level images 1 2', ',..., 'rG G G
Using inverse difference transformation to obtain the bit-level images 1 2', ',..., 'rM M M
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Priority Sharing Mode(8/9)
1
1
' , 1, 1
' , ' , 1, 1
' ,
i
j
i ij
k
ik
G j k j k
M j k G j k j k
G j k others
;,...,2,1 ri
2/,...,2,1, Nkj
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Priority Sharing Mode(9/9)
' , ' , ,
' , 1 ' , ,
' 1, ' , 1,
' 1, 1 ' , 1, 1
ii i
ii i
ii i
ii i
I j k M j k D j k
I j k M j k D j k
I j k M j k D j k
I j k M j k D j k
Accumulating and the corresponding matrix to obtain , and obtain the recovered secret image
'iMiD 'iI
'I
;,...,2,1 ri 2/,...,2,1, Nkj
1 2' ' ' ... 'rI I I I
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Experimental Results(1/4)
Fig. 1. Four shadow images generated by using the multi-secret sharing mode
(a) (b) (c) (d)
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Experimental Results(2/4)
(e) (f) (g) (h)
(i) (j) (k)
Fig. 2. Reconstructed images by using different numbers of shadow images in multi-secret sharing mode, where (a)-(f) are recovered images by using two shadow images, (g)-(j) are recovered images by using three shadow images, and (k) is recovered image by using four shadow images.
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Experimental Results(3/4)
Fig. 3. Shadow images generated by using the priority sharing mode.
(a) (b) (c) (d)
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Experimental Results(4/4)
(e) (f) (g) (h)
(i) (j) (k)
Fig. 4. The reconstructed images by using priority sharing mode. (a)-(f) are reconstructed images by using two shadow images, (g)-(j) are reconstructed images by using three shadow images, and (k) is reconstructed image by using four shadow images.
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Conclusions
Smaller shadow images Saving storage space and transmission time