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VCPSS：A two-in-one two-decoding-options
image sharing method combining visual
cryptography (VC) and polynomial-style
sharing (PSS) approaches
Sian-Jheng Lin, Ja-Chen Lin
Pattern Recognition Society, 2007
指導老師：李南逸
Speaker：Tzu-Chen Huang
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Outline
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Introduction
Visual cryptography
PSS
Encoding
Decoding
Conclusion
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Introduction
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If the decoding computer is temporarily not
available, we can stack to get a vague blackand-white view of the secret image.
The computer is finally available, we can get
a much finer gray-valued view of the secret
image using the information hidden earlier in
the shadows.
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Visual cryptography
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Input: An integer threshold t , and an integer n
(t≦n).
Output: A pair of basis matrices [B0] and [B1]
Step : 1. Arbitrarily choose (n-t) integers {h j | 0  j  n  t  1}
and an integer h n-t  0
Step : 2. Copmute the integers {a i | 0  i  n} by the formula
min{i,n-t}
ai =

j=0
(i+j)!
(-1) h j
i! j!
i+j
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Visual cryptography
Step : 3. Create {G0 ,...,Gn }. The first column of Gi is formed
of i consecutive 1's followed by (n-i) consecutive 0's.
Step : 4. Initially, set both [ B0 ] and [ B1 ] to empty set ; set ai  a0 .
i) If (ai  0), then do nothing for this ai , just go to (iv).
ii ) If (ai  0), then repeatedly append Gi into [ B0 ] (repeat |ai | time).
iii ) If (ai <0), then repeatedly append Gi into [ B1 ] (repeat |ai | time).
iv) If i = n, go to Step 5; else, increment i by 1 and go to (i).
Step : 5. [ B0 ] and [ B1 ] are now the desired output.
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PSS
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To share an image by Thien and Lin’s sharing
scheme
Step : 1. Partitioned the image S into |S|/t sectors.
Step : 2. Each sector had the gray-values of t pixels.
The t confficients {a 0 ,...,a t-1} in the sector polynomial
p(x)=(a 0  a1 x  a 2 x 2  ...  a t-1 x t 1 ) mod 251
Step : 3. For each sector, shadow si recelved a value p(i).
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S
H
S ( comp )
si
ri
L
w
b
t
K
n
Secret image
Halftone binary version of the image S
Compressed version S ( comp ) of S
Shadows
Transparency
wb

 entries.
b
Table L which has
White elements
Black elements
Get the shared secret in n transparencies
A security key
Produced n transparencies
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Encoding
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The flowchart to summarize the idea of encoding
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Encoding
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Input :S,L,K
Output: ri , i  1, 2,..., n
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Step 1. Compressed S obtain a S ( comp )
number of bits in S
ratio 
1
( comp )
number of bits S

ratio  8n / t  log 2  bw b 
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
( comp )
Step 2. Use K to encrypt S
Step 3. create si , i  1, 2,..., n
Share S by a (t,n)-threshold PSS.
i) Partitioned S into |S|/t sectors.
ii) Each sector had the gray-values of t pixels.
The t confficients {a 0 ,...,a t-1} in the sector polynomial
p(x)=(a 0  a1 x  a 2 x 2  ...  a t-1 xt 1 ) mod 257
iii) For each sector, shadow si recelved a value p(i).
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Encoding
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Step 4. S transformed the halftone version (H).
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i  1, 2,..., n)
Step 5. H is created to ri .(　
Step 6. Partition the S to n regions (S/n block)
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Step 7. si is hidden in region i of the ri
i) si is a numerical file of base
 
wb
b
ii) S/n block in region i of ri correspond L in si .
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Decoding
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The flowchart of the decoding algorithm.
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Decoding of stacking
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Input：Any t of the n transparencies, L
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Output：H
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Step 1. Stack all t collected transparencies to get an
enlarged H.
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Step 2. By counting black/white elements of each block, we
get H.
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Decoding of extraction
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Input：Any t of the n transparencies, L,K
Output：S ( comp )
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Step 1. Extract the si hidden in region I of the ri
i) Use L inspecting the |S|/n blocks in region i of ri
Step 2. Get of the n shadows
wb

i) si is a digit string of |S|/n, and each digit is in
b 
wb
ii) each digit string from base  b 
Step 3. Recover (encrypted) S ( comp )from the t shadows { si}
i) Using the inverse processing of the PSS
ii) Recover the t coefficients { a 0 ,...,a t-1}
( comp )
Step 4. Decrypt S
by K
( comp )
Step 5. Get the gray-value secret image S
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Conclusion
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Proposed a new method which combines two
major branches of image sharing.
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In the decoding issue, this new method is
more flexible than applying VC or PSS.
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2007/8/29 meeting
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再找看看有沒有更新的Paper來看(2007年)。
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