neural networks for visual cryptography --- with examples for complex access schemes tatung...
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Neural Networks for Visual Cryptography --- with Examples for Complex Access Schemes
Tatung University, TaiwanPresenter: Tai-Wen Yue
CAINE-2000
Outline Introduction Neural Network Model --- Q’tron NN Q’tron NN for Visual Cryptography Experimental Results
Conclusions and Feature Works
Introduction
What is visual cryptography?(n, k)-scheme: k out of n
Decompose a secret image into a set of n shadow images called shares.
A share carries meaningless information.
Stacking k or more shares, printed on transparencies, reveals the secrete.
Decrypting using eyes
Example
Target image
Share image2
Share image1
Applications Key Management Message Concealment Authorization Authentication Identification Entertainment
Access Schemes
A A
A A A
A
E F G
CB D
AA A
A A A
A
A A AA A A
A
E F G
CB D
A
E F GE F G
CB DCB DShares
Stackingall shares
Stackingtwo shares
(2, 2) (3, 2) Full
Traditional Approach Using codebooks An Example codebook: (2, 2)
Pixel ProbabilityShares
#1 #2Superposition ofthe two shares
5.0p
5.0p
5.0p
5.0p
WhitePixels
BlackPixels
Our Approaches No codebook required Inputs are gray images
Target Image(s) Share Images
Outputs are halftone images that mimic the corresponding gray images
Applicable to complex access schemes
Neural Network Model
Q’tron NN
Q’tronActive value
iiQa
1iq0 i
i
a
• Weighted and multilevelled• Each Q’tron represents a quantity --- aiQi
Q’tronActive value
Internal stimulus
n
jjjij QaT
1
ii
a
iiT
• Input due to Q’trons’ Interactions• Tii usually is nonzero and negative
Q’tronActive value
Internal stimulus i
i
a
iI
External stimulus
• External input serves as bias
Q’tronActive value
Internal stimulus i
i
a
External stimulus
• Escape local-minima• Persistent noise --- no holiday
iN
Q’tron
iIExternal stimulus
iN
Active value
Internal stimulus
n
jjjij QaT
1
ii
a
iiT iiQa
1iq0
State Transition Rule
iI
iN
n
jjjij QaT
1
ii
a
iiT iiQa
1iq0
Q’tron’s Input
InternalStimulus
ExternalStimulus
Noise
NoiseFree
State Transition Rule
State Updating Rule:
Running AsynchronouslyRunning Asynchronously
Q’tron NN vs. Hopfield NN
Running AsynchronouslyRunning Asynchronously
Noise Free Tii=0 qi=2
Noise Free Tii=0 qi=2
Q’tron NN = Hopfiled NN
Energy Function
InteractionAmong Q’trons
Interactionwith
External Stimuli
Constant
Monotonically Nonincreasing
Problem SolvingUsing a Q’tron NN
A given problemA given problem
A optimization problemA optimization problemReformulation
Cost FunctionCost Function
Energy FunctionEnergy Function
Build Q’tron NNBuild Q’tron NN
Mapping
Operation modes
iIExternal stimulus
iN
Active value
Internal stimulus
n
jjjij QaT
1
ii
a
iiT iiQa
1iq0
Clamp-mode
Operation modes
iIExternal stimulus
iN
Active value
Internal stimulus
n
jjjij QaT
1
ii
a
iiT iiQa
1iq0
free-mode
Why operation modes?
Unstable
Stable
Why operation modes?
ClampedFree
Why operation modes?
Clamped Free
Q’tron NN forVisual Cryptography
Highlight the main concept by(2, 2)
The Q’tron NN for (2, 2)Plane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
The Q’tron NN for (2, 2)Plane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
Target ImageClamped
The Q’tron NN for (2, 2)Plane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
Target ImageClamped
Share 1+
Share 2
Share 2Share 1
The Q’tron NN for (2, 2)Plane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
Target ImageClamped
Share 1+
Share 2
Share 2Share 1
Halftoning
Stacking Rule
Halftoning + Stacking Rules Halftoning
Gray Images Binary Images Gray Images: Target and Shares
Stacking Rules Fulfill the Access Scheme
HalftoningGraytone Image Halftone Image
Halftoning
How?To make the average luminances of each cell-pair as close as possible.
HalftoningGray Image Halftone Image
Halftoning
May have many solutions
Stacking RulesGray Image Halftone Image
Halftoning
Share Images
Stacking Rule
One or more pixels black
Black
Energy function --- Halftoning
A 3 3 halftone cellA 3 3 graytone cell
The luminance difference(squared error)
Stacking Rules (The magic)
s1 s2
0
0
1
1
0
1
0
1
h
0
1
1
1
E2
0
0.25
0.25
0.25
0
0
1
1
0
1
0
1
1
0
0
0
2.25
1
1
1
s1 s2 h E2
Feasible Infeasible
+ =s1 s2 h
Stacking Rules (The magic)
s1 s2
0
0
1
1
0
1
0
1
h
0
1
1
1
E2
0
0.25
0.25
0.25
0
0
1
1
0
1
0
1
1
0
0
0
2.25
1
1
1
s1 s2 h E2
Feasible Infeasible
+ =s1 s2 h
Low High
Energy function --- Stacking Rules
Minimizing this term tends to satisfy the stacking rules
Share Image Assignment For simplicity, shares are plain images
S1 S2
Mean Gray level K1K2
Result
Energy Function---Share Image Assignment
Total Energy
HalftoningHalftoning StackingRules
StackingRules
ShareImagesShare
Images
Q’tron NN Construction
Mapping
Experimental Results
Histogram Reallocation Needed
+
+
HistogramReallocation
The ProcedurePlane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
The original taget image
The ProcedurePlane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
The original taget image
HistogramReallocation
Clamped
The ProcedurePlane-G
Plane-S1 (Share 1 )
Plane-H
Plane-S2 (Share 2 )
The original taget image
HistogramReallocation
Clamped
Free
Experimental Result --- (2, 2)
Share 1 Share 2TargetImage
Share 1+
Share 2
Generalized Access Scheme
Experimental Results
Full Access Scheme --- 3 Shares
朝辭白帝彩雲間朝辭白帝彩雲間
朝 辭 白
帝 彩 雲
間
Shares
Full Access Scheme --- 3 Shares
朝辭白帝彩雲間朝辭白帝彩雲間
朝 辭 白
帝 彩 雲
間
Shares
Theoretically, unrealizable.
We did it in practical sense.
Full Access Scheme --- 3 Shares
S1 S2 S3
S1+S2 S1+S3 S2+S3 S1+S2+S3
Access Schemewith Forbidden Subset(s)
人之初性本善人之初性本善
人 之 初
性 本 X
善
Theoretically,realizable.
Shares
Access Schemewith Forbidden Subset(s)
S1 S2 S3
S1+S2 S1+S3 S2+S3 S1+S2+S3
Access Schemefor Access Control
S1 S2 S3
S4 S1+S4 S2+S4 S3+S4
Target and Shares are Gray Images
S1
Armored knight
Target and Shares are Gray Images
S2
Man
Target and Shares are Gray Images
S1 + S2
Armored Knight + Man
= Lina
Conclusions and Future works
Conclusions How? NNs for visual cryptography No codebook. Uniform math for access schemes. Target images and share images are
graylevelled ones Share image size = Target image size
Future Works Design language to specify an access s
cheme. Auto generation of the Q’tron NNs Histogram Reallocation is a nontrivial
task.
Extend to color images