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INTRODUCTION TO VISUAL CRYPTOGRAPHY

電信所 碩一 R98942058 余芝融

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Overview

What is Visual Cryptography How to share a secret Concept of Digital HalftoningGrayscale VCColor VC Bit-level based secret sharing Conclusion

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Visual Cryptography Traditional cryptography:

Both Encrypt & Decrypt Needs the knowledge of cryptography, keys and

possess high computational complexity

Visual Cryptography: Use the characteristic of human vision to decrypt

encrypted images Needs neither cryptography knowledge nor

complex computation

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Visual Cryptography

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How to Share a secret (k, n) Threshold Scheme k points in 2-D plane (x1 , y1) , … , (xk , yk) with

distinct xi ‘s, there’s one and only one polynomial q(x) of k -1 degree such that

q(xi ) = yi for all i Assume q(xi ) = a0+a1x+…+ak-1xk-1

Where D = a0 = q(0) evaluate D1 = q(1) ,..., Di = q(i) ,…. ,Dn = q(n) cannot solve with the knowledge of just k-1 values

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Continuous-tone VS Halftone Render the illusion of a continuous-tone image

based on two-tone (half-tone) display Black/white gray-level image Darker area denser black points per area Whiter area sparser black points per

area

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Continuous-tone VS Halftone

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Basic Theorem of VC

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VC For Binary Image

Enlarged

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Grayscale VC

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Color Model

RGB: TV’s and Monitors CMY: Color Printing Press

Use Additive Color Use Subtractive Color

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Color Image Printing

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Color VC - Method(1)

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Color VC - Method(1)

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Color VC - Method(2)

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Color VC - Method(2)

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Color VC - Method(3)

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Color VC - Method(3)

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Bit-level based secret sharing The drawback of visual sharing schemes

Cannot restore its original quality Convert continuous-tone images into

halftone images

Bit plane 1

Bit plane b

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Every pixel can be expressed as

We can obtain 8 shares(by size invariant VC) If white: If black:

Every share can decomposed into 2 sub-share Then combine the sub-share(with order of

MSB~LSB ) → 2 grayscale share images

Bit-level based secret sharing

27 26 25 24 23 22 21 20

(1 , 1)

(0 , 0)

(0 , 1)

(1 , 0)

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Conclusion Traditional VC only works on binary images Grayscale VC and Color VC→provide secure ways to

transfer images on the internet Advantages of VC: 1.exploit human eyes to decrypt secret images with no computation 2.easy to implement→no complex computation

Disadvantages of VC: 1. the image will become 4 times bigger 2. the quality of the restored image become worse

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Conclusion Utilizes bit-level decomposition and stacking

operations to both encrypt and decrypt B-bit image by computer

Bit-level based secret sharing allows for perfect reconstruction of the input B-bit image

Can encrypt binary, gray-scale and color images

Retain the size of the reconstructed image

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References [1] M. Noar and A. Shamir, “Visual Cryptography,” Advances in Cryptography Eurocrypt’94, Lecture Notes in Computer Science, Springer-Verlag, Vol. 950,

pp. 1-12, 1995. [2] AShamir, “ How To Share a Secret, ” Communications of the ACM, vol.22,no.

11, 1979,pp.612-613. [3] C.Y. Chang, Visual cryptography for color images, MS thesis, National Central

University, Taiwan, 2000. [4] Y.C. Hou, Visual cryptography for color images, Pattern Recognition 36 (2003)

1619–1629. [5]Chao-Yong Hsu, Chun-Shien Lu, and Soo-Chang Pei, "Joint Screening Halftoning

and Visual Cryptography for Image Protection," Int. Workshop on Digital

Watermarking (IWDW), Lecture Notes in Computer Science, 2006 [6]  陳尚寬 ,” A rapid-decoding secret sharing scheme based on visual cryptography”