Index
A
ABPs, see Auxiliary black pixels
Additive color model, 34
average contrast, 301
basis matrices, 300
black pixel, ineffective, 306
block length, 300
darkness thresholds, 300
discussions, 325
misalignment deviation, 316
misalignment tolerant VCS, 319-325
decrypting algorithm, 321
encrypting algorithm, 320
misalignment with integer number of subpixels, 302-309
misalignment with less than one subpixel, 309-319
large subpixels have better misalignment tolerance, 316-319
shares with slightly misalignment can still recover secret image, 310-315
nonzero coordinates, 299
original secret image, 299
recovered secret image, 299
secret image
deterministically recovered, 315
regions of deviation, 313
shifted basis matrices, 302
shifted scheme, 302
shifted share matrices, 302
visible space, calculation of, 298
Almost ideal contrast, 265
AM, see Amplitude modulation
Amplitude modulation (AM), 105
banking information, 329, 330, 332
Cardano cryptography, 332, 334, 337, 346
compromise, 332
man-in-the-middle manipulation attack, 331
nested doll, 348
online money transfers, 329, 331
password, 334
redundancy of natural languages, 342
secret sharing, original purpose of, 332
security versus multiple use, 339-343
symbol-orientation, 332
technical problems concerning adjustment and parallaxes, 346-347
transaction number, 331
transaction server, 329
”transparency onto screen” idea, 333
trojan-secure authentication using PIN, 334-339
trojan-secure confirmation of transactions, 333-334
unknown plaintext attack, 341
voting with receipt based on visual cryptography, 347-349
Artificial image, 368
Attack
cipher-based, 404
color image sharing, 382
cover media and, 426
fake share offerings, 405
man-in-the-middle manipulation, 331
polynomial-based image sharing, 415
secret cheating, 294
secret image sharing, 427
trojan manipulation, 333
Authentication, image sharing with, 425-461
adopted techniques in proposed scheme, 434-445
edge lookup inverse halftoning technique, 441-443
error diffusion technique, 434-438
interpolation technique, 439-440
Shamir scheme for secret sharing, 443-445
Chinese Remainder Theorem, 427, 432
detection ratios of different schemes, 458
edge-based lookup table, 441
excursion skill, 437
Floyd and Steinberg error diffusion strategy, 434
Gaussian filter, 440
HyperText Markup Language, 426
least significant bits, 432
lookup table, 441
most significant bits, 452
pixels
binary representations of, 429
positions of, 436
reconstruction and verifying phase, 449-452
sharing and embedding phase, 445-449
Chang et al.’s scheme, 432-433
Lin and Tsai’s scheme, 428-430
visual secret sharing, 426
Authentication Based Cheating Prevention scheme, 287
Authentication-based steganography study, 404, see also Polynomial-based image sharing
Auxiliary black pixels (ABPs), 9
distribution, 13
predetermined, 15
B
BCB, see Borland C++ Builder
Binary error diffusion, 3
Binary secret sharing scheme (BSS), 266
Blue noise error diffusion, 3-5
Borland C++ Builder (BCB), 85
Bounds, see Contrast bounds
BSS, see Binary secret sharing scheme
C
Cardano cryptography, 332, 334, 337, 346
Characteristic parameters, 132
analysis of cheating prevention schemes, 294
Authentication Based Cheating Prevention scheme, 287
authentic conditions, 294
Boolean matrix, 282
cheating prevention schemes, 287-293
HCT1 and HCT2, 287
PS1 and PS2, 292
TCH, 290
contrast conditions, 283
Generic Algorithm, 290
cheating in VC, 285
prevention of shares against cheating, 294
security conditions, 283
Chinese Remainder Theorem (CRT), 427, 432
Chord-areas, 68
Cipher-based attacks, 404
Clark-Wilson security model, 382
Clustered-dot ordered dither, 104
CMY model, see Cyan, Magenta, and Yellow model
additive color model, 34
annihilator color, 39
color vision and color models, 32-37
darkening problem, 38
identity color, 39
formal models for colored VCS, 40-44
annihilator color, 42
annihilator presence, 43
base matrices, 44
distribution matrices, 41
models for B&W-VC, 40
safety property, 40
SC, ND, and General models, 43-44
secret palette, 41
security property, 42
shares palette, 41
strong contrast property, 42
weak contrast property, 42
light energy, 33
schemes for general model, 52-54
annihilator presence, 52
shares palette, 52
(2, 2)-threshold schemes, 52-53
(2, n)-threshold AS schemes, 54
annihilator presence, 51
concatenation of matrices, 50
upper bound, 52
BDD schemes, 47
CDD schemes and lower bound, 48-49
contrast property, 48
sharing passwords, 46
trick, 45
technically incorrect expressions, 33-34
Color visual cryptography, see also Color images
annihilator presence, 43
base matrices, 44
distribution matrices, 41
efficiency within, 386
models for B&W-VC, 40
progressive, 387
safety property, 40
SC, ND, and General models, 43-44
secret palette, 41
security property, 42
shares palette, 41
strong contrast property, 42
weak contrast property, 42
Commutative operation, 187
approximate inclusion exclusion, 227-232
asymptotic optimal k-out-of-n schemes, 241-243
black subpixels, 226
bound, sharp, 231
contrast, importance of, 224
contrast trade offs for extended visual cryptography schemes, 244-251
enhancing of contrast by nonstandard models, 251
Fisher’s inequality, 235
Hadamard matrix, 235
integer vector, 246
optimal contrast, 230
optimal 3-out-of-n schemes, 236-240
pairwise balanced design, 234
pixel expansion, 236
Plotkin bound, 232
visual cryptography scheme, formal definition of, 223
CRC, see Cyclic Redundant Code
CRT, see Chinese Remainder Theorem
Cyan, Magenta, and Yellow (CMY) model, 34, 35
Cyclic Redundant Code (CRC), 405, 415
D
Darkening problem, 38
Data hiding
authentication codes, 427
halftone images, 356
LSB scheme, 409
secret image sharing, 382
shares involved in, 396
Data Hiding by Conjugate Error Diffusion (DHCED), 359-363
Data Hiding by Stochastic Error Diffusion (DHSED), 356-359
DBS, see Direct binary search
Decoded image
composition of shares, 14
HVC expansion, 19
parallel error diffusion, 16
quality degradation, 387
Decomposing circle, 70
Decrypting algorithm, 321
Density pattern, 104
DHCED, see Data Hiding by Conjugate Error Diffusion
DHSED, see Data Hiding by Stochastic Error Diffusion
Digital rights management, 382
Direct binary search (DBS), 14, 19
Dispersed-dot ordered dither, 104, 105
Distribution matrices, 41
E
Edge-based lookup table (ELUT), 441
Effective block, 83
ELUT, see Edge-based lookup table
Encryption
histogram equalization before, 115
photograph visual cryptography, 107
process, photograph images, 119
progressive visual cryptography, 388
security of key used for, 382
segment code, 332
TiOISSS, 473
transparency of shadow, 117
visual cryptography scheme, 223
Error diffusion
binary, 3
constant, 15
constrained, 4
Floyd and Steinberg strategy, 434
halftone, see Halftone error diffusion
image sharing with steganography, 434-438
kernel, 352
multitone, 5
parallel, 16
photograph visual cryptography, 105
samples of error filters, 106
steganography in halftone images, 352-356
construction of VSS scheme, 8
notion and formal definitions, 5-8
EVC, see Extended visual cryptography
EVCS, see Extended Visual Cryptography Scheme
Excursion skill, 437
Extended block, 59
Extended visual cryptography (EVC), 19
Extended Visual Cryptography Scheme (EVCS), 96, 99
F
Floyd-Steinberg error filter, 4
FM, see Frequency modulation
Forbidden sets, 256
Frequency modulation (FM), 105
G
GAS, see General Access Structure
Gaussian filter, 440
General Access Structure (GAS), 99
H
Hadamard matrix, 235
Halftone error diffusion, 1-28
auxiliary black pixels, 9
binary error diffusion, 3
blue noise error diffusion, 3-5
blue noise halftoning algorithms, 4
Boolean matrix, 7
contrast condition, 8
contrast of decoded image, 8
diffused past errors, 4
comparison with other methods, 19
improvement of image quality, 19
error diffusion constant, 15
extended visual cryptography, 19
Floyd-Steinberg error filter, 4
halftone visual cryptography, 3, 4
halftone VSS construction using error diffusion, 9-16
distribution of SIPs and ABPs, 11-14
generation of halftone shares via error diffusion, 14-16
halftone VSS construction using parallel error diffusion, 16-17
Hamming weight, 7
human visual system model, 18
image quality
discrepancy, 18
improvement in, 19
uniform, 18
local geometric distortion, 26
multitone error diffusion, 6
parallel approach, 17
preset pixels, 16
quality of halftone shares, 17-18
quality index, 18
reconstructed image, 26
scheme robustness, 20
secret information pixels, 9
security condition, 8
share image quality, 21
thresholding block, 19
construction of VSS scheme, 8
notion and formal definitions, 5-8
Halftone images, steganography in, 351-380
artificial image, 368
Data Hiding by Conjugate Error Diffusion, 359-363
Data Hiding by Stochastic Error Diffusion, 356-359
data hiding techniques, 356
halftone pixel, probability distribution of, 353, 366
image halftoning, 351
intensity curves, 371
Jarvis kernel, 354, 355, 356, 370
least significant bit, 356
output halftone value, 353
review of error diffusion, 352-356
Steinberg kernel, 353, 355, 356
trial halftone value, 361
watermarking data, 352
Halftone visual cryptography (HVC), 4
constrained error diffusion, 4
expansion
image decoding, 19
SIP location, 11
visually pleasing halftone image, 18
Histogram linearization transformation, 115
HTML, see HyperText Markup Language
Human visual system (HVS), 18, 464
HVC, see Halftone visual cryptography
HVS, see Human visual system
HyperText Markup Language (HTML), 426
I
Identity color, 39
Image decoding, see Decoded image
Image halftoning, 351, see also Steganography in halftone images
Image secret sharing, 381-402, see also Steganography, image sharing with
approaches for image sharing, 389-396
color image sharing based on Lagrange interpolation, 389-392
color image sharing based on moving lines, 392-396
improved algorithm, 399
Shamir’s secret sharing scheme, 389
battlefield plans, 382
bichromatic construction, 384
Clark-Wilson security model, 382
color image reconstruction, 386, 395
color image sharing
compressed domain processing, 399
primitive example of, 385
color visual cryptography, efficiency within, 386
construction methods, 384
digital rights management, 382
experiment and evaluation, 397-399
fixed pixel expansion, 387
Galois field, 390
image halftoning, 387
Lagrange interpolation, 389, 391, 397, 399
loss of key, 382
lossless recovery scheme, 386
monochromatic construction, 384
Peak-Signal-to-Noise Ratio, 388
plurality of ways, 388
redundancy in protection, 382
secret key, backup mechanism to, 382
secret sharing system, 382
threshold cryptography scheme, 382
X-position parameter, 396
Image secret sharing scheme (ISSS), 463
Image sharing with steganography and authentication, 425-461
adopted techniques in proposed scheme, 434-445
edge lookup inverse halftoning technique, 441-443
error diffusion technique, 434-438
interpolation technique, 439-440
Shamir scheme for secret sharing, 443-445
Chinese Remainder Theorem, 427, 432
detection ratios of different schemes, 458
edge-based lookup table, 441
excursion skill, 437
Floyd and Steinberg error diffusion strategy, 434
Gaussian filter, 440
HyperText Markup Language, 426
least significant bits, 432
lookup table, 441
most significant bits, 452
pixels
binary representations of, 429
positions of, 436
reconstruction and verifying phase, 449-452
sharing and embedding phase, 445-449
Chang et al.’s scheme, 432-433
Lin and Tsai’s scheme, 428-430
visual secret sharing, 426
Ineffective block, 83
Inverted-Pattern-LSB information hiding algorithm (IPLA), 410
IPLA, see Inverted-Pattern-LSB information hiding algorithm
ISSS, see Image secret sharing scheme
J
Jarvis kernel, 354, 355, 356, 370
L
Lagrange interpolation, 389-392
Least significant bit (LSB), 356, 432
computed check bits and, 433, 448
data bits, 452
data hiding, 409
embedding technique, 356
image sharing, 432
modified, 432
scheme, inverted pattern, 409-410
LSB, see Least significant bit
LUT, see Lookup table
M
Mach-Zehnder interferometer, 155
Man-in-the-middle manipulation attack, 331
Maximal contrast schemes, 260
Maximum distance separable (MDS) codes, 163
MDS codes, see Maximum distance separable codes
Model(s)
additive color, 34
Clark-Wilson security, 382
annihilator color, 42
annihilator presence, 43
base matrices, 44
distribution matrices, 41
models for B&W-VC, 40
safety property, 40
SC, ND, and General models, 43-44
secret palette, 41
security property, 42
shares palette, 41
strong contrast property, 42
weak contrast property, 42
Cyan, Magenta, and Yellow, 34, 35
human visual system, 18
nonstandard, contrast bounds, 251
probabilistic, 131
Monochromatic-colored shares, 213
Most significant bits (MSBs), 452
MSBs, see Most significant bits
Multiple secrets, visual cryptography for, 57-93
absolute location of block, 73
black block, 83
Borland C++ Builder, 85
chord-areas, 68
decomposing circle, 70
decryption process, human visual ability to perform, 57
effective block, 83
encoding patterns, 59
extended block, 59
ineffective block, 83
Naor and Shamir’s basic visual secret sharing scheme, 59-61
new problems, 91
pixels
encoding set of, 73
reconstructed, 59
private key, 91
random shares, 58
secret binary images, 58
sector blocks, 66
transforming circle, 90
visual multiple-secret sharing schemes, 68-91
comparison and discussions, 87-91
encoding circle share A, 69-71
encoding circle share B, 71-80
visual secret-sharing schemes, 58
visual two-secret sharing schemes, 62-68
white block, 83
N
Nested doll, 348
Noise-encoding, 104
Nonzero coordinates, 299
O
Online money transfer, 329, 331
Optimal contrast, 230
Ordered dithering, 104, 351, 352
Output halftone value, 353
P
Passwords
sharing, 46
trojan-secure authentication, 334
Peak-Signal-to-Noise Ratio (PSNR), 388
Photograph images, extended visual cryptography for, 95-126
amplitude modulation, 105
basic visual cryptography schemes, 96-103
contrast condition, 100
extended condition, 100
extended visual cryptography scheme, 99-101
General Access Structure, 99
(k, n) visual secret sharing schemes, 96-99
reconstructed image, relative difference of, 100
relative difference of shadow images, 100
security condition, 100
shadow images, relative difference of, 100
uniform scheme, 98
basis matrices, 98
binary mage, encryption algorithm for, 102
clustered-dot ordered dither, 104
continuous-tone image, 108
dynamic ranges, 114
encryption, process of, 119
extended condition, 100
Extended Visual Cryptography Scheme, 96, 99
frequency modulation, 105
fundamentals of photograph visual cryptography, 103-108
clustered-dot ordered dither, 104
density pattern, 104
dispersed-dot ordered dither, 104, 105
error diffusion, 105
image quality and related parameters, 106-107
iterative and search-based methods, 105
noise-encoding, 104
ordered dither, 104
photograph visual cryptography with basic schemes, 107-108
pixel expansion, 106
pseudo-contours, 104
relative difference, 107
thresholding, 104
tone levels, 106
General Access Structure, 99
gray-scale value, 117
histogram linearization transformation, 115
misalignment tolerance, 116
misalignment-tolerant photograph visual cryptography, 116-120
results, 120
theory and implementation, 116-119
noise-encoding, 104
ordered dither, 104
pixel expansion, 97
progressive visual cryptography, 386
random dither, 104
relative difference, 97
secret image, 96
secret information pixels, 112
shares, 96
superimposition of random grids, 102
thresholding, 104
triplet, constraint values of, 114
uniform scheme, 98
variations of photograph visual cryptography, 109-115
approaches to photograph visual cryptography, 109
continuous-tone subpixel, 115
error and secret diffusion, 113-114
positive and negative shadow images, 112-113
random-dot shadow images, 111
secret information pixels, 112
similar shadow images, 111-112
simultaneous iterative search, 114
watermarking technique, 111
PISSS, see Polynomial-based ISSS
Pixel(s)
annihilated, 52
contrast bounds, 236
image secret sharing, 387
photograph visual cryptography, 106
probabilistic visual cryptography schemes, 128, 133, 138, 142
visual cryptography schemes with reversing, 256
visual secret sharing, 21, 111, 175
preset, 16
reconstructed, 59
reverse coding of, 148
Polynomial-based image sharing, 403-424
authentication-based steganography study, 404
cipher-based attacks, 404
Cyclic Redundant Code, 405, 415
evaluating authentication, 419-422
Inverted-Pattern-LSB information hiding algorithm, 410
pixel recovery, 406
polynomial-based sharing scheme, 405-407
Lagrange interpolation scheme, 406-407
Shamir’s secret sharing scheme, 405-406
preliminaries and related works, 407-412
inverted pattern LSB scheme, 409-410
scalable secret image sharing, 410-412
Thien-Lin scheme, 407
Yang et al.’s scheme, 409
random bit string, 408
Revised Algorithm of High-Capacity and Applications, 412
Secret Embedding and Detecting Algorithm, 416, 418
steganography, purpose of, 404
stego-image imperceptibility, 404
Target Secret Image Recovery Algorithm, 416, 417
set-up authentication, 414-415
Polynomial-based ISSS (PISSS), 464, 465
Private key, 91
Probabilistic visual cryptography schemes, 127-153
base matrices, 131
black subpixel, reconstructed, 141
canonical probabilistic schemes, 133-135
characteristic parameters of scheme, 132
constructing probabilistic schemes, 142-147
(2, n)-threshold probabilistic schemes with any pixel expansion, 144-147
(n, n)-threshold probabilistic schemes with any pixel expansion, 142-143
contrast thresholds, 130
cryptographic paradigm, 128
deterministic models, 128
distribution matrix, 129
novel probabilistic schemes, 142
open problems, 150
pixel expansion, 128, 133, 138
probabilistic schemes with Boolean operations, 147-150
(2, n) scheme for binary images (Wang), 147-149
(n, n) scheme for binary images (Wang), 149-150
probabilistic schemes with no pixel expansion, 135-138
reconstructed black pixel, 141
reconstruction phase, 148
reverse coding of pixel, 148
security property, 137
subpixels, 129
trading pixel expansion with probabilities, 138-141
cardinality of collections, 140
probabilistic schemes with given pixel expansion, 138-141
reconstructed black subpixel, 141
visual cryptography schemes, 129-133
Progressive visual cryptography, 388
PSNR, see Peak-Signal-to-Noise Ratio
Q
Qualified sets, 256
diffusion to grayscale pixels, 16, 17
excessive, 15
grayscale image, 4
SIP-caused, 11
R
RAHA, see Revised Algorithm of High-Capacity and Applications
Random dither, 104
Random grids, visual cryptography and, 185-221
binary image, 189, 198, 208, 213, 219
binary random pixel, 186
commutative operation, 187
generic procedure, 191
gray-level image, encryption, 206
light transmission, 202, 203, 204
mathematical induction, 199
monochromatic-colored shares, 213
random pixel, random grid, and average light transmission, 186-187
superimposition of random grids, 187-188
subtractive model, primitive colors in, 206
visual cryptograms of random grids, 189-219
algorithms of (n, n)-VCRG for binary images, 196-205
algorithms of (n, n)-VCRG for gray-level and color images, 206-207
definition of light contrast and performance evaluation, 194-196
experiments for (2, 2)-VCRG, 193-194
experiments for (n, n)-VCRG, 207-219
(2, 2)-VCRG algorithms for binary images, 190-193
Red, Green, and Blue (RGB) model, 34, 35
Reversing, visual cryptography schemes with, 255-279
almost ideal contrast VCS with reversing, 262-265
binary secret sharing scheme, 266
black pixels, perfect reconstruction of, 256, 260
concatenation of matrices, 261
efficiency of VCS, 276
forbidden sets, 256
ideal contrast VCS with reversing, 265-278
comparisons, 276
construction using binary secret sharing scheme, 266-268
construction using non-perfect black VCS, 276-278
construction using perfect black VCSs, 268-276
scheme by Cimato, De Santis, Ferrara, and Masucci, 269-271
scheme by Hu and Tzeng, 271-273
scheme by Yang, Wang, and Chen, 274-275
maximal contrast schemes, 260
no loss of resolution, 257, 266
pixel expansion, 256
qualified sets, 256
reversing, 262
shares, 255
stacking operations, 268
subtransparency, 272
VCS with reversing, 256
visual cryptography schemes, 258-262
(k, k)-threshold visual cryptography schemes, 259-260
perfect black visual cryptography schemes, 260-262
XOR, 271
Revised Algorithm of High-Capacity and Applications (RAHA), 412
RGB model, see Red, Green, and Blue model
S
Safety property, 40
Secret Embedding and Detecting Algorithm (SEDA), 416, 418
Secret information pixels (SIPs), 9, 15, 112
Secret key, backup mechanism to, 382
Secret palette, 41
Secret sharing (SS), 2, 382, see also Image secret sharing
Sector blocks, 66
Security property, 42
SEDA, see Secret Embedding and Detecting Algorithm
Shadow images
positive and negative, 112-113
random-dot, 111
relative difference of, 100
Shares palette, 41
Shifted scheme, 302
Shifted share matrices, 302, 306, 308
SIPs, see Secret information pixels
SS, see Secret sharing
Steganography, image sharing with, 425-461
adopted techniques in proposed scheme, 434-445
edge lookup inverse halftoning technique, 441-443
error diffusion technique, 434-438
interpolation technique, 439-440
Shamir scheme for secret sharing, 443-445
authentication codes, 427
Chinese Remainder Theorem, 427, 432
detection ratios of different schemes, 458
edge-based lookup table, 441
excursion skill, 437
Floyd and Steinberg error diffusion strategy, 434
Gaussian filter, 440
HyperText Markup Language, 426
least significant bits, 432
lookup table, 441
most significant bits, 452
pixels
binary representations of, 429
positions of, 436
ProbVSS scheme, 427
reconstruction and verifying phase, 449-452
sharing and embedding phase, 445-449
Chang et al.’s scheme, 432-433
Lin and Tsai’s scheme, 428-430
visual secret sharing, 426
Steganography in halftone images, 351-380
artificial image, 368
Data Hiding by Conjugate Error Diffusion, 359-363
Data Hiding by Stochastic Error Diffusion, 356-359
data hiding techniques, 356
halftone pixel, probability distribution of, 353, 366
image halftoning, 351
intensity curves, 371
Jarvis kernel, 354, 355, 356, 370
least significant bit, 356
output halftone value, 353
review of error diffusion, 352-356
Steinberg kernel, 353, 355, 356
trial halftone value, 361
watermarking data, 352
Steinberg kernel, 353, 355, 356
Symbol-orientation, 332
T
TAN, see Transaction number
Target Secret Image Recovery Algorithm (TSIRA), 416, 417
Threshold cryptography scheme, 382
TiOISSS, see Two-in-one ISSS
Transaction number (TAN), 331
Transforming circle, 90
TSIRA, see Target Secret Image Recovery Algorithm
Two-decoding-option image sharing method, 463-485
contrast condition, 466
experimental results and comparisons, 478-481
Galois Field, 466
gray-level secret image, 474
halftone secret image, 473
Hamming weight, 466
human visual system, 464
image secret sharing scheme, 463
perfect-reconstruction phase, 477
polynomial-based ISSS, 464
Jin et al.’s TiOISSS, 468
Lin and Lin's TiOISSS, 468-470
prime number, 465
secret image, no distortion in, 470
white pixels, 471
Two-in-one ISSS (TiOISSS), 464
U
Uniform scheme, 98
V
VCRG, see Visual cryptograms of random grids
Visual cryptograms of random grids (VCRG), 185, see also Random grids, visual cryptography and
Visual secret sharing (VSS), 426
applications to steganography, 2
basic properties, 107
block diagram, 15
comparison with other visual cryptography schemes, 108
definition, 2
example, 98
construction of VSS scheme, 8
notion and formal definitions, 5-8
innocent-looking images, 3
k-out-of-n, 2
multiple-secret sharing schemes, 68-91
principles, 426
ProbVSS scheme, 427
two-secret sharing schemes, 62-68
VSS, see Visual secret sharing
W
Watermark(ing)
active, 356
data, 352
state-of-the-art, 388
technique, 111
visibility, 363
White block, 83
X
XOR-based visual cryptography, 155-183
AND operation, 175
binary vector, 160
bitmap block truncation coding, 176
black image, change into white image, 156
Droste’s algorithm, 167
final shadows, 180
Hamming distance, 158
Mach-Zehnder interferometer, 155
maximum distance separable codes, 163
nonoverlapping blocks, 180
OR operation, 157
random mage, 180
scheme with contrast, 159
secret image, reconstruction of, 177
secret sharing scheme using Boolean operation, 174-181
security, 172
temporary shadows, 179
visual cryptography scheme using polarization of light, 158-168
(n, n) scheme, 159
visual cryptography scheme with reversing, 168-174
(k, n) VC scheme using cyclic-shift operation, 168-170
scheme for general access structure, 171-174
X-position parameter, 396