Probabilistic Visual Cryptography Schemes - Visual Cryptography and Secret Image Sharing - page 125

5

Probabilisti c Visual Cryptography Schemes

Stelvio Cimato
Universita degli Studi di Milano, Italy

Roberto De Prisco
Universita di Salerno, Italy

Alfredo De Santis
Universita di Salerno, Italy

CONTENTS
5.1

Introduction :::::::::::::::::::::::::::::::::::::::::::::::::::::: 127

5.2 Visual Cryptography Schemes ::::::::::::::::::::::::::::::::::: 129

5.2.1 The Deterministic Model :::::::::::::::::::::::::::::::: 129

5.2.2 The Probabilistic Model ::::::::::::::::::::::::::::::::: 131

5.3 Canonical Probabilistic Schemes ::::::::::::::::::::::::::::::::: 133

5.4 Probabilistic Schemes with No Pixel Expansion ::::::::::::::::: 135

5.5 Trading Pixel Expansion with Probabilities ::::::::::::::::::::: 138

5.5.1 Probabilistic Schemes with Given Pixel Expansion ::::: 138

5.6 Constructing Probabilistic Schemes ::::::::::::::::::::::::::::: 142

5.6.1 (n;n)-Threshold Probabilistic Schemes with Any Pixel

Expansion :::::::::::::::::::::::::::::::::::::::::::::::: 142

5.6.2 (2;n)-Threshold Probabilistic Schemes with Any Pixel

Expansion :::::::::::::::::::::::::::::::::::::::::::::::: 144

5.7 Probabilistic Schemes with Boolean Operations ::::::::::::::::: 147

5.7.1 (2,n) Scheme for Binary Images (Wang) :::::::::::::::: 147

5.7.2 (n,n) Scheme for Binary Images (Wang) :::::::::::::::: 149

5.8 Conclusions and Open Problems ::::::::::::::::::::::::::::::::: 150

Bibliography :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 151

5.1 Introduction
Visual cryptography schemes allow the encoding of a secret image, consisting
of black or white pixels, into n shares that are distributed to the set P of n