Neural Networks for Visual Cryptography --- with Examples for Complex Access Schemes Tatung University, Taiwan Presenter: Tai-Wen Yue CAINE-2000.

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