(Visual Secret Sharing Scheme) VSSS VSSS 3 i

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1 13 A Visual Secret Sharing Scheme for Continuous Color Images

2 (Visual Secret Sharing Scheme) VSSS VSSS 3 i

3 Abstract A Visual Secret Sharing Scheme for Continuous Color Images Tomoe Ogawa The Visual secret Sharing scheme (VSSS) is a technology of encrypting a secret black-white image into shares and decrypting from the shares without using any cryptographic computation. This paper proposes an extension of VSSS for color images. One of the goals makes color expression possible in the optional fineness even it uses descrete color rank. The other makes decrypted images lighten. This paper describes that the implementation and the evaluation of three methods of the proposal. The paper shows that these methods can express arbitrary colors. In theoretically speaking, you can have the same colors of decrypted images as the original ones in case of using infinite shares. key words Visual Secret Sharing Scheme, Color Images, Shares ii

4 1 1 (VSSS).1 VSSS VSSS VSSS VSSS VSSS RGB CMY iii

5 iv

6 41 A 4 A A.1.1 A.1. Cyan Magenta Cyan Magenata A A..1 A.. A v

7 A.1 Cyan Magenta A. Cyan Magenta A A A vi

8 vii

9 1 n n k (Visual Secret Sharing Scheme) 1

10 (VSSS) (Visual Secred Sharing Scheme) M. Naor A. Shamir [1][] VSSS VSSS.1 VSSS VSSS (k,n) n k k n m Naor Shamir VSSS VSSS [3] VSSS

11 . VSSS 1. VSSS VSSS [4]..1 1 m.. VSSS (3,3) 1 4 (m = 4) VSSS (3,3)

12 . VSSS 3 4 C 0 = C 1 = C C

13 .3 VSSS..3 VSSS VSSS [3].3.1 CMY Cyan, Magenta, Yellow CMY CMY CMY CMY.3 VSSS.3. VSSS VSSS 1 8 VSSS 1 5

14 .3 VSSS Black Red Cyan Green Magenta Blue Yellow White Cyan C Magenta M Yellow Y 1 8 {[ ] } 0 Y M C C 0 = Y M C 1 {[ Y 0 M C C Y = 0 Y 1 1 M C 1 1 {[ M 0 C Y C M = 0 M 1 1 C Y 1 1 {[ C 0 Y M C C = 0 C 1 1 Y M 1 1 {[ Y M C C R = M Y 1 1 C ] } ] } ] ] } } 6

15 .4 {[ C Y M C G = Y C 1 1 M {[ M C Y C B = C M 1 1 Y {[ Y M C C 1 = Y M C 0 ] ] ] } } } CMY.4 VSSS.3 VSSS CMY CMY VSSS VSSS

17 3 VSSS 9

18 4 VSSS VSSS VSSS Black, Cyan, Magenta, Yellow 4.1 CMY 10

19 4.1!! CMYK Black % 11

20 !" #$&% '() i i,.-0/ * +! % ' i RGB CMY RGB CMY 1 1 RGB RGB CMY Cyan(%) = Red(%) Magenta(%) = Green(%) Yellow(%) = Blue(%) 1 CMY 1

21 Black Cyan Black 70 Magenta Black 70 Yellow Black

22 π 3i i+1 Black i i+1 Cyan Black i+1 Magenta Black i+1 Yellow Black i Cyan Magenta Yellow /(i+1) /(i+1) CMY Black Black 1 CMY 1 CMY 4 (Cyan, Magenta, Yellow, Black) 4 14

23 4.1 1 π 1 π 1 π Black CMY c% m% y% Black Cyan : 1 π c = c 00 π Magenta : 1 π m = m 00 π Yellow : 1 π y = y 00 π Black θ c, θ m, θ y Cyan : π θ c 360 = c 00 π Magenta : π θ m 360 = m 00 π Yellow : π θ y 360 = y 00 π θ c = 9 5 c θ m = 9 5 m θ y = 9 5 y Black : Cyan : Magenta : Yellow : c c m m y c 15

24 4.1 Cyan% % Black π : i + 1 : π π i + 1 π π i+1 Black CMY c% m% y% Black Cyan : Magenta : Yellow : ( π ( π ( π π ) c i + 1 = π ) m i + 1 = π ) y i + 1 = ( ) π π i+1 c ( ) π π i+1 m ( ) π π i+1 y Black θ c, θ m, θ y ( ) Cyan : π θ π π c 360 = i+1 c Magenta : π θ m 360 = ( π π i+1 ) m 16

25 4. Yellow : π θ y 360 = θ c = 18 ( i + 1 ( 1 1 θ m = 18 5 θ y = 18 5 i + 1 ( 1 1 i + 1 ( ) π π i+1 y ) c ) m ) y Black : i + 1 Cyan : i + 1 i Magenta : i + 1 i Yellow : i + 1 i i + 1 ( 1 1 i + 1 ( 1 1 i + 1 ( 1 1 i + 1 ) c ) m ) y 4. OHP OHP 4 OHP 17

26 Java gif EPSON, MJ-6000C OHP OHP, MJOHPS1N Cyan Yellow Cyan Cyan & Magenta Yellow Cyan & Magenta Java

27 Black % 1 4 Black 5% Black 50% Black 19

28 4. 75% Black 75% 5 8 Black 1 CMY Black 0

29 5 VSSS Black Black Black 180 1

30 5.1 Black color color Black Cyan Black 40 Magenta Black 40 Yellow Black Cyan Magenta Yellow Black 3 3 CMY Black 1 CMY

31 5.1 Black 1 π 3 π 1 π Black CMY c% m% y% Black Cyan : 1 π c = c 00 π Magenta : 1 π m = m 00 π Yellow : 1 π y = y 00 π Black θ c,θ m,θ y Cyan : π θ c 360 = c 00 π Magenta : π θ m 360 = m 00 π Yellow : π θ y 360 = y 00 π θ c = 9 5 c θ m = 9 5 m θ y = 9 5 y 1 Black : Cyan : Magenta : c c m m 3

32 5. Yellow : y c 3 % Black Black Black % 1 3 Black 4

33 5. 5% Black 50% Black 75% 4 6 Black 75% 4 7 Black 1 CMY Black Cyan, Magenta, Yellow 5

34 A CMY RGB 1 CYM c %, m %, y % RGB r %, g %, b % 4 RGB % Cyan Cyan, Black 6

35 6.1 Cyan : c = c Black : 1 = 50 : c = c RGB% Cyan Red Green Blue Cyan RGB 0 %, c %, c % Black RGB 0 %, 0 %, 0 % c %, c %, c RGB % RGB Red : c = c % Green : c c = 50% Blue : c c = 50% Magenta Magenta, Black Magenta : m = m Black : 1 = 50 : m = m RGB% Magenta Green Red Blue Magenta RGB m %,0 %, m % Black RGB 0 %, 0 %, 0 % 7

36 6.1 m %, m %, m RGB % RGB Red : m m Green : m Blue : m m = 50% = m % = 50% Yellow Yellow, Black Yellow : y = y Black : 1 = 50 : y = y RGB% Yellow Blue Red Green Yellow RGB y %, y %, 0 %, Black RGB 0 %, 0 %, 0 % y %, y %, y RGB % RGB Red : y y Green : y y Blue : y = 50% = 50% = y % 3 RGB Red : c % 8

37 6.1 Green : m % Blue : y % RGB Red : ( r) = r % ( g) Green : = g % ( b) Blue : = b % (r, g, b ) (r, g, b) 6.1 r g b = 1 r g b % (6.1) % 6.1. A CMY RGB Cyan Cyan, Black Black : 1 i + 1 = i + 1 Cyan : ( i + 1 ) c 9

38 6.1 : ( i + 1 ) c RGB% Cyan Red Green Blue Cyan RGB 0 %, ( i+1 ) c %,( i+1 ) c % Black RGB 0 %, 0 %, 0 % RGB ( i+1 ) c %, ( i+1 ) c %, ( i+1 ) c % RGB Red : ( i + 1 ) c Green : ( i + 1 ) Blue : ( i + 1 ) = ( i + 1 ) c % c c ( i + 1 ) c ( i + 1 ) c Magenta = i + 1 % = i + 1 % Magenta, Black Black : 1 i + 1 = i + 1 Magenta : ( i + 1 ) m : ( i + 1 ) m RGB% Magenta Green Red Blue Magenta RGB ( i+1 ) m %,0 %, ( i+1 ) m % Black RGB 0 %, 0 %, 0 % RGB ( m ) %, ( i+1 ) m %, ( i+1 ) m % i+1 RGB Red : ( i + 1 ) m ( i + 1 ) m = i + 1 % 30

39 6.1 Green : ( i + 1 ) m Blue : ( i + 1 ) m ( i + 1 ) m = ( i + 1 ) m % = i + 1 % Yellow Yellow, Black Black : 1 i + 1 = i + 1 Yellow : ( i + 1 ) y : ( i + 1 ) y RGB% Yellow Blue Red Green Yellow RGB ( i+1 ) y %,( i+1 ) y, 0 %, Black RGB 0 %, 0 %, 0 % RGB ( i+1 ) y %, ( i+1 ) y %, ( i+1 ) y % RGB Red : ( i + 1 ) y ( i + 1 ) y = i + 1 % Green : ( i + 1 ) y ( i + 1 ) y Blue : ( i + 1 ) y = i + 1 % = ( i + 1 ) y % 3 RGB Red : ( i + 1 ) c % Green : ( i + 1 ) m % 31

40 6.1 Blue : ( i + 1 ) y % i Red : lim {( i i + 1 ) c } = c = r% Green : lim {( i i + 1 ) m } = m = g% Blue : lim {( i i + 1 ) y } = y = b% (r, g, b ) (r, g, b) 6. lim i r g b = r g b % (6.) 6. i A CMY RGB Cyan Cyan, Black Cyan : c = c Black : 1 3 = 3 : 3 c = 00 3 c 3

41 6.1 RGB% Cyan Red Green Blue Cyan RGB 0 %, c %, c % Black RGB 0 %, 0 %, 0 % 00 3 c 00 %, 3 c 00 %, RGB 3 c % RGB Red : c = 00 3 c Green : c c = 00 3 Blue : c c = 00 3 Magenta Magenta, Black Magenta : m = m Black : 1 3 = 3 : 3 m = 00 3 m RGB% Magenta Green Red Blue Magenta RGB m %,0 %, m % Black RGB 0 %, 0 %, 0 % 00 3 m 00 %, 3 m RGB %, 00 3 m % RGB Red : m m = 00 3 Green : m = 00 3 m Blue : m m =

42 6.1 Yellow Yellow, Black Yellow : y = y Black : 1 3 = 3 : 3 y = 00 3 y RGB% Yellow Blue Red Green Yellow RGB y %, y %, 0 %, Black RGB 0 %, 0 %, 0 % 00 RGB 3 y 3 y 3 y % %, 00 %, 00 RGB Red : y y = 00 3 % Green : y y = 00 3 % Blue : y = 00 3 y % 3 RGB Red : 00 3 c % Green : 00 3 m % Blue : 00 3 y % RGB Red : 00 3 r Green : 00 3 g = r + 6 % = g + 6 % 34

43 6. Blue : 00 3 b = b + 6 % (r, g, b ) (r, g, b) 6.3 r g b = 1 r g b + 6 % (6.3) % r : g = 1 r g % b b r r : lim i g = g b b r : g = 1 r g b b % + 6 % Black,Cyan,Magenta,Yellow 35

44 6.3 (r,b,g ) (r,b,g ) 1 (r,b,g ) 1/ / (r,b,g) (r,b,g) 1 (r,b,g) 6.1 Black 180 CMY CMY 5 15 VSSS

45 Black, Cyan, Magenta, Yellow 3 8 Black Black,Cyan,Magenta,Yellow Cyan, Magenta, Yellow

46 6.4 50% 4 % 00 3 % Black Cyan Magenta Yellow i+1 i+1 i+1 i+1 3i

47 7 3 Java 6 39

48 SSS VSSS OHP OHP VSSS 40

49 [1] M. Naor and A. Shamir. Visual cryptography. In EUROCRYPT 94, LNCS950, pp. 1 1, [] A. Shamir. How to share a secret. In Commun. fo the ACM, Vol., pp , [3] H. Koga and H. Yamamoto. Proposal of a lattice-based visual secret sharing scheme for color and gray-scale images. In IEICE Trans., pp , [4]..,

50 A 1 Cyan Magenta Yellow c, m, c RGB % A.1 1 VSSS 1 Cyan Magenta A.1.1 Cyan Magenta A.1 Cyan Magenta 4

51 A.1 1 Cyan Red Green Blue Cyan RGB 0 %, c %, c % Magenta Green Red Blue Magenta RGB m %, 0 %, m % RGB RGB c m %, c m %, c m % 1 RGB Red : 0 + m + ( c m) = c% Green : c ( c m) = m% Bluel : c + m + ( c m) = % r c g = m % b (A.1) A.1. Cyan Magenata A. Cyan Magenta Cyan Magenta t Cyan Red Green Blue Cyan RGB 0%, (c t) %, (c t) % 43

52 A. 1 3 Magenta Green Red Blue Magenta RGB (m t) %, 0 %, (m t) % Cyan Magenta Red Green Blue 0 %, 0 %, t % c m + t RGB RGB c m + t %, c m + t %, c m + t % 1 RGB Red : 0 + (m t) + ( c m + t) = c% Green : (c t) ( c m + t) = m% Bluel : (c t) + (m t) + t + ( c m + t) = % r c g = m % b (A.) A.1 A. 1 RGB % A. 1 3 VSSS A..1 3 Cyan Red Green Blue Cyan RGB 0 %, c %, c % Magenta Green Red Blue Magenta RGB m 44

53 A. 1 3 A.3 3 %, 0 %, m % Yellow Blue Red Green Yellow RGB y %, y %, 0 % RGB RGB c m y %, c m y %, c m y % 1 RGB Red : 0 + m + y + ( c m y) = c% Green : c y( c m y) = m% Bluel : c + m ( c m y) = y% r c g = m % b y (A.3) A.. Cyan Magenta Cyan Magenta t Cyan Red Green Blue Cyan RGB 0%, (c t) %, (c t) % Magenta Green Red Blue Magenta RGB (m t) %, 0 %, (m t) % 45

54 A. 1 3 A.4 Yellow Blue Red Green Yellow RGB y %, y %, 0 % Cyan Magenta Red Green Blue 0 %, 0 %, t % c m y + t RGB RGB c m y + t %, c m y + t %, c m y + t % 1 RGB Red : 0 + (m t) + y ( c m y + t) = c% Green : (c t) y ( c m y + t) = m% Bluel : (c t) + (m t) t + ( c m y + t) = y% r c g = m % b y (A.4) A..3 3 Cyan Magenta t Magent Yellow s Cyan Red Green Blue Cyan 46

55 A. 1 3 A.5 3 RGB 0%, (c t) %, (c t) % Magenta Green Red Blue Magenta RGB (m t s) %, 0 %, (m t s) % Yellow Blue Red Green Yellow RGB (y s) %, (y s) %, 0 % Cyan Magenta Red Green Blue 0 %, 0 %, t % Magenta Yellwo Green Blue Red s % 0 %, 0 %, c m y + u + s + t RGB RGB c m y + t + s %, c m y + t + s %, c m y + t + s % 1 RGB Red : (m t s) (y s) + s + ( c m y + t + s) = c% Green : (c t) + (y s) + u + ( c m y + t + s) = m% Bluel : (c t) + (m t s) + t + ( c m y + t + s) = y% 47

56 A. 1 3 r c g = m % b y (A.5) A.3 A.4 A RGB % 48

paper.dvi

paper.dvi 28 Confined Decoding System for Medical Data Distributed by Secret Sharing Scheme and Its Security Evaluation 1195046 2017 3 6 DMAT i Abstract Confined Decoding System for Medical Data Distributed by Secret