Minimizing Pixel Expansion of A (k, n)-VCS

innocentsickAI and Robotics

Nov 21, 2013 (3 years and 11 months ago)

75 views

1

Minimizing Pixel Expansion

of

A (
k
,
n
)
-
VCS

2

A (
k
,
n
)
-
VCS: Two multi
-
sets
C
0

and
C
1

of
n



m

matrices
B
0

and
B
1
.

m
: Pixel Expansion

m

1

m

n




















B
0

= ?




















B
1

= ?

m

n

Lower Bound

Upper Bound



m



3

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.

4

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.

2) ICS’96


T. Katoh and H. Imai,


Some Visual Secret Sharing Schemes
and Their Share Size,


Internal Computer Symposium
, 1996.

5

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.

2) ICS’96


T. Katoh and H. Imai,


Some Visual Secret Sharing Schemes
and Their Share Size,


Internal Computer Symposium
, 1996.

3) Droste


S. Droste,


New Results on Visual Cryptography,


CRYPTO’96
, 1996.

6

4) DCC2002


P. A. Eisen and D. R. Stinson,


Threshold Visual Cryptography
Schemes with Specified Whiteness
Levels of Reconstructed Pixels,


Designs, Codes and Cryptography
,
2002.

7

4) DCC2002


P. A. Eisen and D. R. Stinson,


Threshold Visual Cryptography
Schemes with Specified Whiteness
Levels of Reconstructed Pixels,


Designs, Codes and Cryptography
,
2002.

5) TCS2006


C. Blundo, S. Cimato and A. De Santis,



Visual Cryptography Schemes with
Optimal Pixel Expansion,


Theoretical Computer Science
, 2006.

8

5
-
1) Tzeng


W. G. Tzeng and C. M. Hu,



A New Approach for Visual
Cryptography,



Designs, Codes and Cryptography
,
2002.

9

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.

2) ICS’96


T. Katoh and H. Imai,


Some Visual Secret Sharing Schemes and Their Share Size,


Internal Computer Symposium
, 1996.

3) Droste


S. Droste,


New Results on Visual Cryptography,


CRYPTO’96
, 1996.

4) DCC2002


P. A. Eisen and D. R. Stinson,


Threshold Visual Cryptography Schemes with Specified Whiteness Levels
of Reconstructed Pixels,


Designs, Codes and Cryptography
, 2002.

5) TCS2006


C. Blundo, S. Cimato and A. De Santis,



Visual Cryptography Schemes with Optimal Pixel Expansion,


Theoretical Computer Science
, 2006.

5
-
1) Tzeng


W. G. Tzeng and C. M. Hu,



A New Approach for Visual Cryptography,



Designs, Codes and Cryptography
, 2002.

10

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.

11

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.


Proposed


(2,
n
)
-
VCS, (
k

= 2)



(
n
,
n
)
-
VCS, (
k

=
n
)



(
k
,
n
)
-
VCS

12

1) Naor and Shamir


M. Naor and A. Shamir,


Visual Cryptography,


EUROCRYPT
, 1994.


Proposed


(2,
n
)
-
VCS, (
k

= 2),



(
n
,
n
)
-
VCS, (
k

=
n
), 2
k
-
1



m



2
k
-
1



(
k
,
n
)
-
VCS,
m



n
k

2
k
-
1
,
m



汯l
n

2
O(
k
log
k
)

n
m
m









/2
13

2) ICS’96


T. Katoh and H. Imai,


Some Visual Secret Sharing Schemes
and Their Share Size,


Internal Computer Symposium
, 1996.

14

2) ICS’96


T. Katoh and H. Imai,


Some Visual Secret Sharing Schemes
and Their Share Size,


Internal Computer Symposium
, 1996.


Proposed


(2,
n
)
-
VCS, (
k

= 2)


(
n
,
n
)
-
VCS, (
k

=
n
)


(
k
,
n
)
-
VCS


Upper Bound

15

2) ICS’96

16

3) Droste


S. Droste,


New Results on Visual Cryptography,


CRYPTO’96
, 1996.

17

3) Droste


S. Droste,


New Results on Visual Cryptography,


CRYPTO’96
, 1996.


Proposed


(
k
,
n
)
-
VCS


Upper Bound


Lower Bound

18

3) Droste

19

4) DCC2002


P. A. Eisen and D. R. Stinson,


Threshold Visual Cryptography
Schemes with Specified Whiteness
Levels of Reconstructed Pixels,


Designs, Codes and Cryptography
,
2002.

20

4) DCC2002


P. A. Eisen and D. R. Stinson,


Threshold Visual Cryptography
Schemes with Specified Whiteness
Levels of Reconstructed Pixels,


Designs, Codes and Cryptography
,
2002.


Proposed


(2,
n
)
-
VCS, (
k

= 2)


Upper Bound

21

4) DCC2002

k

\

n

2

3

4

5

6

7

8

9

10

2

2

3

4

4

4

5

5





3



















4



















5



















6



















7



















8



















9



















10



















22

5) TCS2006


C. Blundo, S. Cimato and A. De Santis,



Visual Cryptography Schemes with
Optimal Pixel Expansion,


Theoretical Computer Science
, 2006.


The revealed images may be darker or
lighter than the backgrounds.



Proposed


(2,
n
)
-
VCS, (
k

= 2)

23

5
-
1) Tzeng


W. G. Tzeng and C. M. Hu,



A New Approach for Visual
Cryptography,


Designs, Codes and Cryptography
,
2002.


The revealed images may be darker or
lighter than the backgrounds.