Neural Networks for Visual Cryptography --- with Examples for Complex Access Schemes Tatung University, Taiwan Presenter: 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 Shares Stacking all shares Stacking two shares (2, 2)(3, 2)Full

Traditional Approach Using codebooks An Example codebook: (2, 2) PixelProbability Shares #1 #2 Superposition of the two shares White Pixels Black Pixels

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 ’ tron Active value Weighted and multilevelled Each Q ’ tron represents a quantity --- a i Q i

Q ’ tron Active value Internal stimulus Input due to Q ’ trons ’ Interactions T ii usually is nonzero and negative

Q ’ tron Active value Internal stimulus External stimulus External input serves as bias

Q ’ tron Active value Internal stimulus External stimulus Escape local-minima Persistent noise --- no holiday

Q ’ tron External stimulus Active value Internal stimulus

State Transition Rule Q ’ tron ’ s Input Internal Stimulus External Stimulus Noise Free

State Transition Rule State Updating Rule: Running Asynchronously

Q ’ tron NN vs. Hopfield NN Running Asynchronously Noise Free T ii =0 q i =2 Noise Free T ii =0 q i =2 Q ’ tron NN = Hopfiled NN

Energy Function Interaction Among Q’trons Interaction with External Stimuli Constant Monotonically Nonincreasing

Problem Solving Using a Q ’ tron NN A given problem A optimization problem Reformulation Cost Function Energy Function Build Q’tron NN Mapping

Operation modes External stimulus Active value Internal stimulus Clamp-mode

Operation modes External stimulus Active value Internal stimulus free-mode

Why operation modes? Unstable Stable

Why operation modes? Clamped Free

Why operation modes? Clamped Free

Q ’ tron NN for Visual 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 Image Clamped

The Q ’ tron NN for (2, 2) Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) Target Image Clamped Share 1 + Share 2 Share 1

The Q ’ tron NN for (2, 2) Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) Target Image Clamped Share 1 + Share 2 Share 1 Halftoning Stacking Rule

Halftoning + Stacking Rules Halftoning Gray Images  Binary Images Gray Images: Target and Shares Stacking Rules Fulfill the Access Scheme

Halftoning Graytone Image Halftone Image Halftoning How? To make the average luminances of each cell-pair as close as possible.

Halftoning Gray Image Halftone Image Halftoning May have many solutions

Stacking Rules Gray Image Halftone Image Halftoning Share Images Stacking Rule One or more pixels black  Black

Energy function --- Halftoning A 3  3 halftone cell A 3  3 graytone cell The luminance difference (squared error)

Stacking Rules (The magic) s1s1 s2s h E2E s1s1 s2s2 h E2E2 Feasible Infeasible + = s1s1 s2s2 h

Stacking Rules (The magic) s1s1 s2s h E2E s1s1 s2s2 h E2E2 Feasible Infeasible + = s1s1 s2s2 h LowHigh

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 K 1 K2K2 Result

Energy Function--- Share Image Assignment

Total Energy Halftoning Stacking Rules Stacking Rules Share Images Share Images

Q ’ tron NN Construction Mapping

Experimental Results

Histogram Reallocation Needed + + Histogram Reallocation

The Procedure Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) The original taget image

The Procedure Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) The original taget image Histogram Reallocation Clamped

The Procedure Plane-G Plane-S1 (Share 1 ) Plane-H Plane-S2 (Share 2 ) The original taget image Histogram Reallocation Clamped Free

Experimental Result --- (2, 2) Share 1Share 2 Target Image Share 1 + Share 2

Generalized Access Scheme Experimental Results

Full Access Scheme Shares 朝辭白帝彩雲間 朝 辭 白 帝彩雲 間 Shares

Full Access Scheme 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 Shares S1S2S3 S1+S2S1+S3S2+S3S1+S2+S3

Access Scheme with Forbidden Subset(s) 人之初性本善 人 之 初 性本 X 善 Theoretically, realizable. Shares

Access Scheme with Forbidden Subset(s) S1S2S3 S1+S2S1+S3S2+S3S1+S2+S3

Access Scheme for Access Control S1S2S3 S4S1+S4S2+S4S3+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 scheme. Auto generation of the Q ’ tron NNs Histogram Reallocation is a nontrivial task. Extend to color images