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Introduction to Visual Cryptography

電信所 碩一 R98942058 余芝融. Introduction to Visual Cryptography. Overview. What is Visual Cryptography How to share a secret Concept of Digital Halftoning G r a y s c a l e VC C o l o r VC Bit-level based secret sharing Conclusion. Visual Cryptography. Traditional cryptography :

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Introduction to Visual Cryptography

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  1. 電信所 碩一 R98942058 余芝融 Introduction to Visual Cryptography

  2. Overview • What is Visual Cryptography • How to share a secret • Concept of Digital Halftoning • GrayscaleVC • ColorVC • Bit-level based secret sharing • Conclusion

  3. 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 visionto decrypt encrypted images • Needs neither cryptography knowledge nor complex computation

  4. Visual Cryptography

  5. 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 ) =yifor all i • Assumeq(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

  6. Continuous-tone VS Halftone • Render the illusion of a continuous-tone image based on two-tone (half-tone) display • Black/whitegray-level image • Darker area denser black points per area • Whiter area sparser black points per area

  7. Continuous-tone VS Halftone

  8. Basic Theorem of VC

  9. VC For Binary Image Enlarged

  10. Grayscale VC

  11. Color Model RGB: TV’s and Monitors CMY: Color Printing Press Use Additive Color Use Subtractive Color

  12. Color Image Printing

  13. Color VC - Method(1)

  14. Color VC - Method(1)

  15. Color VC - Method(2)

  16. Color VC - Method(2)

  17. Color VC - Method(3)

  18. Color VC - Method(3)

  19. Bit plane b Bit plane 1 Bit-level based secret sharing • The drawback of visual sharing schemes • Cannot restore its original quality • Convert continuous-tone images into halftone images

  20. Bit-level based secret sharing • 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 27 26 25 24 23 22 21 20 (0 , 1) (1 , 1) (1 , 0) (0 , 0)

  21. 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

  22. 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

  23. 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”

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