13 A Visual Secret Sharing Scheme for Continuous Color Images 10066 14 8
(Visual Secret Sharing Scheme) VSSS VSSS 3 i
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
1 1 (VSSS).1 VSSS................................. VSSS............................... 3..1............................ 3.. VSSS........................ 3.3 VSSS............................. 5.3.1............................ 5.3. VSSS........................ 5.4............................. 7 3 9 4 10 4.1...................................... 10 4.1.1................................ 10 4.1............................. 11 4.1.3............................ 11 4.1.4 RGB CMY....................... 1 4.1.5.............. 13 4.1.6.............. 14 4.1.7............. 14 4.1.8............. 16 iii
4....................................... 17 4..1................................ 18 4.............................. 18 4..3........................... 18 5 1 5.1...................................... 1 5.1.1................................ 1 5.1............... 5.1.3............. 5....................................... 4 5..1........................... 4 6 6 6.1.......................... 6 6.1.1........................... 6 6.1............................. 9 6.1.3............................ 3 6.1.4............................ 35 6........... 35 6.3................................. 36 6.3.1...................... 36 6.3............. 37 6.4................................. 37 7 39 40 iv
41 A 4 A.1 1...................... 4 A.1.1 A.1. Cyan Magenta................. 4 Cyan Magenata................... 43 A. 1 3...................... 44 A..1 A.. A..3 3..................... 44........................... 45 3........................... 46 v
.1............ 4............. 5.3....................... 6 4.1.................................... 11 4................................. 1 4.3............................. 13 4.4................. 13 4.5................. 14 4.6......................... 18 4.7 8 8.................. 19 5.1.............................. 5.................. 6.1....................... 36 A.1 Cyan Magenta..................... 4 A. Cyan Magenta........................ 43 A.3 3......................... 45 A.4............................... 46 A.5 3............................... 47 vi
6.1.................................... 38 6.......................... 38 vii
1 n n k (Visual Secret Sharing Scheme) 1
(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
. VSSS 1. VSSS VSSS [4]..1 1 m.. VSSS (3,3) 1 4 (m = 4) VSSS (3,3) 3 3 3 1 0 1 3 3
. VSSS 3 4 C 0 = C 1 = 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 3 C 0 1 0 0 1 1 1 0 0 1 1 0 1 0.1 3 C 1 1 1 0 1 0 0 0 1 1 0 1 1 0 4
.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
.3 VSSS Black Red Cyan Green Magenta Blue Yellow White.3 8 1 0 Cyan C Magenta M Yellow Y 1 8 {[ ] } 0 Y M C 1 1 1 1 C 0 = 0 1 1 1 Y M C 1 {[ Y 0 M C 1 1 1 1 C Y = 0 Y 1 1 M C 1 1 {[ M 0 C Y 1 1 1 1 C M = 0 M 1 1 C Y 1 1 {[ C 0 Y M 1 1 1 1 C C = 0 C 1 1 Y M 1 1 {[ Y M C 0 1 1 1 1 C R = M Y 1 1 C 0 1 1 ] } ] } ] ] } } 6
.4 {[ C Y M 0 1 1 1 1 C G = Y C 1 1 M 0 1 1 {[ M C Y 0 1 1 1 1 C B = C M 1 1 Y 0 1 1 {[ Y M C 0 1 1 1 1 C 1 = 1 1 1 1 Y M C 0 ] ] ] } } } CMY.4 VSSS.3 VSSS CMY CMY VSSS VSSS 1 8 3 4 7
.4 1 4 8
3 VSSS 9
4 VSSS VSSS VSSS 4.1 4.1.1 1 1 Black, Cyan, Magenta, Yellow 4.1 CMY 10
4.1!! 4.1 4.1. CMYK 180 1 180 Black 180 1 4.1.3 4. 1 % 11
4.1 34353!" #$&% '() 35343 i 34353 i,.-0/.1 34353 * +! % ' i 4. 4.1.4 RGB CMY RGB CMY 1 1 RGB RGB CMY Cyan(%) = Red(%) Magenta(%) = Green(%) Yellow(%) = Blue(%) 1 CMY 1
4.1 4.1.5 1 4 0 0 90 180 70 4.3 Black 90 70 Cyan Black 70 Magenta Black 70 Yellow Black 90 4.4 4.4 13
4.1 4.1.6 1 4 0 90 180 70 4.3 1 π 3i + 1 360 i+1 Black 180 180 180 i+1 180 + i+1 Cyan Black 180 + 180 i+1 Magenta Black 180 + 180 i+1 Yellow Black 180 180 i+1 4.5 Cyan Magenta Yellow 180+180/(i+1) 180-180/(i+1) 4.5 4.1.7 CMY Black Black 1 CMY 1 CMY 4 (Cyan, Magenta, Yellow, Black) 4 14
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 : 90 70 90+ 9 5 c 70+9 5 c 90+ 9 5 m 70+9 5 m 90 9 5 y 70 9 5 c 15
4.1 Cyan% 70 450 90 0% Black 90 70 1 4 4 4.1.8 1 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
4. Yellow : π θ y 360 = θ c = 18 ( 1 1 5 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 : 180 180 180 180 + i + 1 Cyan : 180 + 180 180 180 + i + 1 i + 1 + 18 5 Magenta : 180 + 180 180 180 + i + 1 i + 1 + 18 5 Yellow : 180 180 180 180 i + 1 i + 1 18 5 i + 1 ( 1 1 i + 1 ( 1 1 i + 1 ( 1 1 i + 1 ) c ) m ) y 4. OHP OHP 4 OHP 17
4. 4..1 Java gif EPSON, MJ-6000C OHP OHP, MJOHPS1N 4.. 1 4.7 Cyan Yellow Cyan Cyan & Magenta Yellow Cyan & Magenta 4.6 4..3 Java 1 1 1 8 8 1 4 18
4. 8 8 4 8 4 8 8 8 4 5 8 8 4.7 Black 1 4 1 3 4 5 6 7 8 4.7 8 8 10% 1 4 Black 5% 5 5 5 Black 50% 3 6 5 6 Black 19
4. 75% 4 7 5 7 Black 75% 5 8 Black 1 CMY 8 8 1 1 8 8 90 180 70 360 Black 0
5 VSSS 1 5.1 4 5.1.1 1 1 4 Black Black 10 10 180 10 Black 180 1
5.1 Black color color 5.1 5.1. 1 4 4 0 90 180 70 4.3 Black 10 40 Cyan Black 40 Magenta Black 40 Yellow Black 10 5. Cyan Magenta Yellow 5. 5.1.3 1 Black 3 3 CMY 10 180 Black 1 CMY
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 : 10 40 10+ 9 5 c 40+9 5 c 10+ 9 5 m 40+9 5 m 3
5. Yellow : 10 9 5 y 40 9 5 c 3 % 10 180 Black 1 4 4 5. 4.. 1 4.7 5..1 1 Black 3 1 3 9 9 1 4 9 9 4 1 Black 9 9 3 9 3 9 3 9 4 5 8 3 8 4 10% 1 3 Black 4
5. 5% 4 4 4 Black 50% 3 5 4 5 Black 75% 4 6 Black 75% 4 7 Black 1 CMY 1 1 9 9 90 180 70 360 Black Cyan, Magenta, Yellow 5
6 4 5 6.1 6.1.1 A CMY RGB 1 CYM c %, m %, y % RGB r %, g %, b % 4 RGB % Cyan Cyan, Black 6
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 : 0 + 0 + c = c % Green : c + 0 + c = 50% Blue : c + 0 + 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
6.1 m %, m %, m RGB % RGB Red : m + 0 + m Green : 0 + 0 + m Blue : m + 0 + 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 + 0 + y Green : y + 0 + y Blue : 0 + 0 + y = 50% = 50% = y % 3 RGB Red : c % 8
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 50 % 6.1. A CMY RGB Cyan Cyan, Black Black : 1 i + 1 = i + 1 Cyan : ( i + 1 ) c 9
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 : 0 + 0 + ( i + 1 ) c Green : ( i + 1 ) Blue : ( i + 1 ) = ( i + 1 ) c % c c + 0 + ( i + 1 ) c + 0 + ( 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 + 0 + ( i + 1 ) m = i + 1 % 30
6.1 Green : 0 + 0 + ( i + 1 ) m Blue : ( i + 1 ) m + 0 + ( 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 + 0 + ( i + 1 ) y = i + 1 % Green : ( i + 1 ) y + 0 + ( i + 1 ) y Blue : 0 + 0 + ( i + 1 ) y = i + 1 % = ( i + 1 ) y % 3 RGB Red : ( i + 1 ) c % Green : ( i + 1 ) m % 31
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 6.1.3 A CMY RGB Cyan Cyan, Black Cyan : c = c Black : 1 3 = 3 : 3 c = 00 3 c 3
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 : 0 + 0 + 00 3 c = 00 3 c Green : c + 0 + 00 3 c = 00 3 Blue : c + 0 + 00 3 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 + 0 + 00 3 m = 00 3 Green : 0 + 0 + 00 3 m = 00 3 m Blue : m + 0 + 00 3 m = 00 3 33
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 + 0 + 00 3 y = 00 3 % Green : y + 0 + 00 3 y = 00 3 % Blue : 0 + 0 + 00 3 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
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) 6.3 66 % 6.1.4 r : g = 1 r g % b b r r : lim i g = g b b r : g = 1 r g b b % + 6 % 6.1 6. 3 1 Black,Cyan,Magenta,Yellow 35
6.3 (r,b,g ) (r,b,g ) 1 (r,b,g ) 1/ /6 0 1 0 1 0 (r,b,g) (r,b,g) 1 (r,b,g) 6.1 Black 180 CMY 10 180 6.3 1 6.3.1 CMY 5 15 VSSS 1 9 9 8 8 36
6.4 6.3. 1 8 8 3 8 Black, Cyan, Magenta, Yellow 3 8 Black 90 180 70 1 9 9 3 8 4 8 Black,Cyan,Magenta,Yellow 3 8 4 8 Cyan, Magenta, Yellow 6.4 6.1 3 6. 37
6.4 50% 4 % 00 3 % 4 6.1 Black Cyan Magenta Yellow 1 1 1 1 4 i+1 i+1 i+1 i+1 3i+1 1 3 1 3 1 1 3 1 1 3 1 4 6. 38
7 3 Java 6 39
SSS VSSS OHP OHP VSSS 40
[1] M. Naor and A. Shamir. Visual cryptography. In EUROCRYPT 94, LNCS950, pp. 1 1, 1995. [] A. Shamir. How to share a secret. In Commun. fo the ACM, Vol., pp. 61 613, 1979. [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. 16 169, 1998. [4].., 000. 41
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
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 + 0 + ( 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
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) + 0 + ( 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 1 3 3 A..1 3 Cyan Red Green Blue Cyan RGB 0 %, c %, c % Magenta Green Red Blue Magenta RGB m 44
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 + 0 + y( c m y) = m% Bluel : c + m + 0 + ( 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
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 + 0 + ( c m y + t) = c% Green : (c t) + 0 + y + 0 + ( c m y + t) = m% Bluel : (c t) + (m t) + 0 + 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
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
A. 1 3 r c g = m % b y (A.5) A.3 A.4 A.5 3 1 RGB % 48