The Recent Developments in Visual Secret Sharing Chair Professor Chin-Chen Chang (張真誠) National Tsing Hua University (清華大學) National Chung Cheng University (中正大學) Feng Chia University (逢甲大學) http://msn.iecs.fcu.edu.tw/~ccc

Outlines Concept of Secret Sharing Concept of visual cryptography Visual cryptography for binary images Visual cryptography for grayscale images Meaningful visual cryptography for grayscale images Meaningful and progressive visual cryptography Visual cryptography for color images Authenticatable VSS Scheme

Traditional (t, n)-secret sharing (Shamir’s Method 1979) secret message (2, 3)-secret sharing Alice Bob Ken shadows secret retrieval Shamir, A. (1979): How to Share a Secret, CACM, Vol. 22, Nov. 1979, pp. 612-613.

How to Share a Secret (t, n)-threshold Scheme Ex: (2, 3)-threshold Scheme (The secret k=7) 3 shadows: (1, 9), (2, 0), (3, 2) y (3, 2) (2, 0) (1, 9) x

How to Share a Secret (t, n)-threshold Scheme Ex: (3, 5)-threshold Scheme (t=3, n=5, k=13, p=17) Alice Bob Ken Jesse Eva ID1=1 ID2=2 ID3=3 ID4=4 ID5=5 (1, 8) (3, 10) (5, 11) Lagrange Interpolation k

Concept of Visual Cryptography Traditional Cryptography Symmetric: DES, AES Asymmetric: RSA The encryption and decryption processes need high computation costs Need secret key for decoding Visual Cryptography low computation Fast decoding Without the secret key

The Secret Image: Airplane Hidden in Hidden in The Basis Image: Mickey The Counterfeit Image: Minnie

The Basis Image: Mickey The Counterfeit Image: Minnie The Expanded Counterfeit Image: Minnie-3X3 The Expanded Basis Image: Mickey-3X3

Mickey-3X3 Minnie-3X3 Airplane

Visual Cryptography for Binary Image Naor and Shamir (1994) proposed a (k, k)–VSS scheme Extend a secret pixel into a block of 22 sub-pixels Contain two white pixels and two black pixels for each block White pixel: transparent Black pixel: black

Secret pixel Share 1 Secret image stacked result Share 2

Visual Cryptography for Grayscale Image Transfer the grayscale image to the halftone image Utilize the density of black dots to simulate the content of grayscale image White area: low density of black dots Black area: high density of black dots

Share 1 Share 2

Meaningful Visual Cryptography for Grayscale Image secret image cover image shadow 1 shadow 2 camouflage stego image1 stego image2

shadow1 shadow1 transparent shadow2 shadow2 stego image1 stego image2 1 1 167 97 140 150 shadow2 shadow2 stego image1 1 1 167 170 83 140 stego image2 152 167 140 137 170 97 150 83 cover image

140 150 167 97 stego image1 stacked result 140 167 83 170 stego image2

Experimental Results shadow1 cover image1 stego image1 shadow2

stego image1 stego image2 stacked result

shadow1 cover image1 stego image1 shadow2 cover image2 stego image2

stego image1 stego image2 stacked result

Meaningful and Progressive Visual Cryptography Meaningful shares: friendly content Progressive visual cryptography Improve the stacked result progressively

Progressive Visual Cryptography (t, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Progressive & Meaningful Visual Cryptography Meaningful shares: friendly content … shadow 1 shadow n secret image camouflage cover image … stego image1 stego image n

extended secret image secret image cover image shadow image secret image cover image shadow image 1 shadow image 2 shadow image 3 shadow image 4

secret image cover image t =2 t = 3

Experimental Results (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Visual Cryptography for Color Image RGB: TV’s and Monitors CMY: Color Printing Press

Experimental Results shadow image 1 shadow image 2 stacked image 2

Authentication 32 Participant 1 Stack Share 1 Recovered secret image Hacker 32 Authentication Stack Participant 1 Share 1 Recovered secret image Original secret image Participant 2 Share 2 32

Authentication Legal extra Legal revealed confidential image secret image Correct stacking result Correct stacking result Share 1 Share 1 Share 2 Share 2 33

Authentication Tampered revealed Nothing secret image Tampered share 1 Tampered secret image Tampered secret image Tampered share 1 Tampered share 1 Share 2 Share 2 34

Authenticatable VSS Scheme for Binary Secret Grayscale image Lena Grayscale image Baboon Binary main secret Halftone image of Lena Halftone image of Baboon Binary extra confidential image

Revealed extra confidential image Authenticatable VSS Scheme for Binary Secret Share image A Share image B Stacking result Revealed extra confidential image

Authenticatable VSS Scheme for Color Secret Color image Lena Color image Baboon Color main secret Color halftone image of Lena Color halftone image of Baboon Color halftone extra confidential image

Revealed extra confidential image Authenticatable VSS Scheme for Color Secret Share image A Share image B Stacking result Revealed extra confidential image

Visual cryptography (Cont.) Rotating 40o Stacking Stacking Share 1 Share 2 Secret 1 “VISUAL” Secret 2 “SECRET”

Steganography (Cont.) Text Video Sound 壞的毛病 壞毛病 山東的蘋果 山東蘋果 我的媽媽 我媽媽 壞的毛病 壞毛病 山東的蘋果 山東蘋果 我的媽媽 我媽媽 主要的問題 主要問題 另外的一件事 另外一件事 其他的問題 其他問題 北京的大學 北京大學 Video Sound

Conclusions An alternative for hiding visual secret Less secret Low computation cost

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