A Neural-Network Approach for Visual Cryptography

虞台文大同大學資工所

Content Overview The Q’tron NN Model The Q’tron NN Approach for

– Visual Cryptography– Visual Authorization– Semipublic Encryption

General Access Scheme Conclusion

A Neural-Network Approach for Visual Cryptography

Overview

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What isVisual Cryptography and Authorization?

Visual Cryptography (VC)– Encrypts secrete into a set of images (shares).– Decrypts secrete using eyes.

Visual Authorization (VA)– An application of visual cryptography.– Assign different access rights to users.– Authorizing using eyes.

What is Semipublic Encryption?

Visual Cryptography (VC)– Encrypts secrete into a set of images

(shares).– Decrypts secrete using eyes.

Semipublic Encryption (SE)– An application of visual cryptography.– Hide only secret parts in documents – Right information is available if and only if a

right key is provided

The Basic Concept of VC

Target Image(The Secret)

Share 2

Share 1AccessScheme

The (2, 2) access scheme.

The Shares Produced by NN

Target Image(The Secret)

Share 2

Share 1NeuralNetwork

We get shares after the NN settles down.

Decrypting Using Eyes

Share 2

Share 1

Example: (2, 2)

Target image

Share image2

Share image1

Plane shares are used

Traditional Approach Naor and Shamir (2,2)

Pixel Probability Shares#1 #2

Superposition ofthe two shares

5.0p

5.0p

5.0p

5.0p

WhitePixels

BlackPixels

The Code Book

The VA Scheme

keyshare

user shares(resource 2)

user shares(resource 1)

stacking

stacking

…

…VIP IP P

…VIP IP P

Very Important Person.

…

The SE Scheme

智慧型系統實驗室資料庫使用者 Key江素貞 AB陳美靜 CD張循鋰 XY李作中 UV

public share(database in lab)

AB CD XY UV

stacking

usershares

keys

素貞

The SE Scheme

循鋰 美靜 作中

智慧型系統實驗室資料庫

使用者 Key江素貞 AB陳美靜 CD張循鋰 XY李作中 UV

智慧型系統實驗室資料庫

使用者 Key江素貞 AB陳美靜 CD張循鋰 XY李作中 UV

A Neural-Network Approach for Visual Cryptography

The Q’tron NN Model

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The Q’tron

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiRExternal Stimulus

( )ij j jj

T a QInternal Stimulus

Ni

Noise

Quantum Neuron

The Q’tron

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiRExternal Stimulus

( )ij j jj

T a QInternal Stimulus

Ni

Noise

Free-Mode Q’tron

The Q’tron

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiRExternal Stimulus

( )ij j jj

T a QInternal Stimulus

Ni

Noise

Clamp-Mode Q’tron

Input Stimulus

InternalStimulus

ExternalStimulus

Noise

NoiseFreeTerm

i

(ai )

. . .

Noise

Level Transition

Running Asynchronously

i

(ai )

. . .

Energy Function

InteractionAmong Q’tronsInteraction

withExternal Stimuli

ConstantMonotonically Nonincreasing

The Q’tron NN

Interface/Hidden Q’trons clamp-modefree-modefree mode Hidden Q’trons

Interface Q’trons

Question-Answering

Feed a question by clamping some interface Q’trons.

clamp-modefree-modefree mode Hidden Q’trons

Interface Q’trons

Question-AnsweringRead answer when all interface Q’trons settle down.

clamp-modefree-modefree mode Hidden Q’trons

Interface Q’trons

A Neural-Network Approach for Visual Cryptography

The Q’tron NNs for Visual Cryptography Visual Authorization Semipublic Encryption

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Energy Function for VC

Visual CryptographyImage Halftoning Image

Stacking

+

Image HalftoningGraytone Image

Halftoning

0

255

Halftone Image

0 (Transparent)

1

Graytone image halftone image can be formulated as to minimize the energy function of a Q’tron NN.

Image HalftoningGraytone Image

Halftoning

0

255

Halftone Image

0 (Transparent)

1

Graytone image halftone image can be formulated as to minimize the energy function of a Q’tron NN.

In ideal case, each pair of corresponding small areas has the `same’ average graylevel.

The Q’tron NN for Image Halftoning

Plane-G (Graytone image)

Plane-H (Halftone image)

Image Halftoning

HalftoningClamp-mode

Free-mode

Plane-G (Graytone image)

Plane-H (Halftone image)

Question

Answer

Image RestorationPlane-G (Graytone image)

Plane-H (Halftone image)

Restoration

Clamp-mode

Free-mode

Question

Answer

Stacking Rule

+ + + +

The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN.

Stacking Rule

+ + + +

The satisfaction of stacking rule can also be formulated as to minimize the energy function of a Q’tron NN.

The energy function for the stacking rule.

See the paper for the detail.

The Total Energy

+

Share 1 Target

Share 1

Share 2

TargetShare 2

TotalEnergy

Image Halftoning Stacking Rule

The Q’tron NN for VC/VA

Plane-GS1

Plane-HS1

Share 1

Plane-HS2

Plane-GS2

Share 2

Plane-GT

Plane-HT

Target

Application Visual Cryptography

Plane-GS1

Plane-HS1

Share 1

Plane-HS2

Plane-GS2

Share 2

Plane-GT

Plane-HT

Target

Clamp-Mode

Clamp-Mode

Clamp-Mode

Free-Mode Free-Mode

Free-Mode

Application Visual Authorization

Plane-GS1

Plane-HS1

User Share

Authority

Plane-HS2

Plane-GS2

Plane-GT

Plane-HT

Key Share

Key Share

User Share

VIP IP P

Application Visual Authorization

Plane-GS1

Plane-HS1

User Share

Authority

Clamp-Mode

Free-ModePlane-HS2

Plane-GS2Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode

Free-Mode

Key Share

Key Share

User Share

VIP IP P

Producing key Share & the first user share.

Application Visual Authorization

Plane-GS1

Plane-HS1

User Share

Authority

Clamp-ModePlane-HS2

Plane-GS2Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode

Some are clamped and some are free.

Key Share

Key Share

User Share

VIP IP P

Producing other user shares.

Application Visual Authorization

Plane-GS1

Plane-HS1

User Share

Authority

Clamp-ModePlane-HS2

Plane-GS2Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode

Some are clamped and some are free.

Key Share

Key Share

User Share

VIP IP P

Producing other user shares.

Application Visual Authorization

Plane-GS1

Plane-HS1

User Share

Authority

Clamp-ModePlane-HS2

Plane-GS2Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode

Some are clamped and some are free.

Key Share

Key Share

User Share

VIP IP P

Key Share

User Shar

e

User Shar

e

User Shar

e

VIP

IP

P

A Neural-Network Approach for Visual Cryptography

GeneralAccess Scheme

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Full Access Scheme 3 Shares

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)

Anyone knows what is it?

Access Schemewith Forbidden Subset(s)

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

A Neural-Network Approach for Visual Cryptography

Conclusion

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Conclusion Different from traditional approaches:

– No codebook needed.– Operating on gray images directly.

Complex access scheme capable. http://www.suchen.idv.tw/

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