A Neural-Network Approach for Visual Cryptography

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


Overview

大同大學資工所

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

AccessScheme

The (2, 2) access scheme.

The Shares Produced by NN

Target Image(The Secret)

Share 2

Share 1Neural

Network

NeuralNetwork

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 ProbabilityShares

#1 #2Superposition 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






The Q’tron

NN Model


The Q’tron

i

(ai )

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiR

External Stimulus

( )ij j jj

T a QInternal Stimulus

Ni

Noise

Quantum Neuron

The Q’tron

i

(ai )

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiR

External Stimulus

( )ij j jj


Ni

Noise

Free-Mode Q’tron

The Q’tron

i

(ai )

i

(ai )

. . .

0 1 2 qi1

aiQiActive value

Qi{0, 1, …, qi1}IiR

External Stimulus

( )ij j jj


Ni

Noise

Clamp-Mode Q’tron

Input Stimulus

InternalStimulus

ExternalStimulus

Noise

NoiseFreeTerm

i

(ai )

i

(ai )

. . .

Noise

Level Transition

Running AsynchronouslyRunning Asynchronously

i

(ai )

i

(ai )

. . .

Energy Function

InteractionAmong Q’trons

Interactionwith

External Stimuli

Constant

Monotonically NonincreasingMonotonically 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.


Interface Q’trons

Question-Answering

Read answer when all interface Q’trons settle down.


Interface Q’trons


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


Energy Function for VC

Visual Cryptography

Image Halftoning

Image Stacking

+

Image Halftoning

Graytone 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 Halftoning

Graytone 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

Halftoning

Clamp-mode

Free-mode



Question

Answer

Image Restoration



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


Plane-GS1

Plane-HS1

User Share

Authority

Clamp-Mode

Free-Mode

Plane-HS2

Plane-GS2

Clamp-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.


Plane-GS1

Plane-HS1

User Share

Authority

Clamp-Mode

Plane-HS2

Plane-GS2

Clamp-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.


Plane-GS1

Plane-HS1

User Share

Authority

Clamp-Mode

Plane-HS2

Plane-GS2

Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode


Key Share

Key Share

User Share

VIP IP P

Producing other user shares.


Plane-GS1

Plane-HS1

User Share

Authority

Clamp-Mode

Plane-HS2

Plane-GS2

Clamp-Mode

Free-Mode

Plane-GT

Plane-HT

Clamp-Mode


Key Share

Key Share

User Share

VIP IP P

Key Share

User Shar

e

User Shar

e

User Shar

e

VIP

IP

P


General

Access Scheme


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


朝辭白帝彩雲間朝辭白帝彩雲間

朝辭白

帝彩雲

間

SharesTheoretically,

unrealizable.

We did it in

practical sense.

Theoretically,

unrealizable.

We did it in

practical sense.


S1 S2 S3

S1+S2 S1+S3 S2+S3 S1+S2+S3

Access Schemewith Forbidden Subset(s)

Anyone knows what is it?Anyone knows what is it?


人之初性本善人之初性本善

人之初

性本 X

善

Theoretically,

realizable.Theoretically,

realizable.

Shares


S1 S2 S3

S1+S2 S1+S3 S2+S3 S1+S2+S3


Conclusion


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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Documents

A Neural-Network Approach for Visual Cryptography