(r, n)-Threshold Image Secret Sharing Methods with Small Shadow Images

Xiaofeng Wang, Zhen Li, Xiaoni Zhang, Shangping Wang

Xi'an University of Technology, Xi'an, Shaanxi, 710048, P.R.China

2

Outline

Introduction Proposed Scheme

Multi-Secret Sharing Mode Priority Sharing Mode

Experimental Results Conclusions

3

Introduction(1/1)

the characters of the proposed methods ： the sizes of generated shadow images are

smaller; provided a lossless secret image recovery

approach with smaller shadow images

4

Multi-Secret Sharing Mode( 1/3)

Original image IDividing I into four non-overlapping sub-image: I1, I2 , I3, I4

Dividing each sub-image into 8×8 non-overlapping blocks

Generating difference matrix of each 8×8 blockHuffman coding

Generating row vectors:D1, D2 , D3, D4

Pre-processing

5

Multi-Secret Sharing Mode( 2/3)

Generating sharing shareGenerating sub-shadow images si(1), si(2),si(3), si(4), si(5), si(6)

Combing the 24 sub-shadow images, generating four shadow images

Embedding these four shadow images to carrier images as watermark

Shadow generation

6

Multi-Secret Sharing Mode( 3/3)

Taking a pixel from each of the shadow images

Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial

Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the pixels of difference image

Inverse difference transformation

Recovered secret image

Recovery

7

Priority Sharing Mode(1/9)Pre-processing

Original image IDividing the secret image I into n bit-level images

0 1 1, , , nP P P

combing them to generate four combined bit-level images

1 2 3 4, , ,I I I I

1 7 6 2 5 4( ) , , ,B I b b B I b b

3 3 2 4 1 0( ) , , ,B I b b B I b b

Dividing into 2×2 image blocks, every minimum of blocks constructed matrix

1 2 3 4, , ,I I I I

iIM

ijkm

8

Priority Sharing Mode(2/9)

Defining matrix that would be used in recovery phase, the elements of are as follows:

iDiD

j, k=1,2,…,N/2 i=1,2,3,4

ijkkj

ijkkj

ijkkj

ijkkji

jkmbmb

mbmbd

2,212,2

2,1212,12

Pre-processing

9

Priority Sharing Mode(3/9)

( , ) 1, 1

, 1, 1, 1

, , 1

iui i

st u ui iu u

E s t s t

a E s t E s t s t

E s t E s t others

Dividing into 8×8 image blocks and computing the difference matrix

iIM iuE

ijkdiff

11 12 18

21 22 28

81 82 88

ijk

a a a

a a adiff

a a a

(i=1, 2, 3, 4)

Combining to generate matrix

ijkdiff

iDiff

u=1, ..., N/16×N/16 , )8,...,2,1,( ts

11 12 1, /16

21 22 2, /16

/16,1 /16,2 /16, /16

i i iN

i i iN

i

i i iN N N N

diff diff diff

diff diff diffDiff

diff diff diff

4,3,2,1i

Pre-processing

10

Priority Sharing Mode(4/9)

Re-arranging elements of by row to generate a row vector, and compressing it by Huffman coding, then converting the output into 0~255 decimal numbers, noted as

iDiff

1 2 3 4, , ( ), ( )C I C I C I C I

Pre-processing(4/4)

11

Priority Sharing Mode(5/9)Shadow generation

Taking every four pixels from as a sharing share, denoted as , then construct Lagrange polynomial for each sharing share

iC I 0 1 2 3, , ,a a a a

Generate six sub-shadow images , ks x 4,3,2,1k1,2,...,6x

Combining the 24 sub-shadow images, then generate four shadow images 1 2 3 4, , ,SH SH SH SH

12

Priority Sharing Mode(6/9)

The algorithm of generating shadow images 1 2 3 4, , ,SH SH SH SH

13

Priority Sharing Mode(7/9)Secret image reconstruction algorithm

Taking a pixel from each of the shadow images

Using r pixels and Lagrange’s interpolation to generate the coefficients of the Lagrange polynomial

Converting the coefficients into binary numbers, and then, Huffman decoding is used to obtain the difference bit-level images 1 2', ',..., 'rG G G

Using inverse difference transformation to obtain the bit-level images 1 2', ',..., 'rM M M

14

Priority Sharing Mode(8/9)

1

1

' , 1, 1

' , ' , 1, 1

' ,

i

j

i ij

k

ik

G j k j k

M j k G j k j k

G j k others

;,...,2,1 ri

2/,...,2,1, Nkj

15

Priority Sharing Mode(9/9)

' , ' , ,

' , 1 ' , ,

' 1, ' , 1,

' 1, 1 ' , 1, 1

ii i

ii i

ii i

ii i

I j k M j k D j k

I j k M j k D j k

I j k M j k D j k

I j k M j k D j k

Accumulating and the corresponding matrix to obtain , and obtain the recovered secret image

'iMiD 'iI

'I

;,...,2,1 ri 2/,...,2,1, Nkj

1 2' ' ' ... 'rI I I I

16

Experimental Results(1/4)

Fig. 1. Four shadow images generated by using the multi-secret sharing mode

(a) (b) (c) (d)

17

Experimental Results(2/4)

(e) (f) (g) (h)

(i) (j) (k)

Fig. 2. Reconstructed images by using different numbers of shadow images in multi-secret sharing mode, where (a)-(f) are recovered images by using two shadow images, (g)-(j) are recovered images by using three shadow images, and (k) is recovered image by using four shadow images.

18

Experimental Results(3/4)

Fig. 3. Shadow images generated by using the priority sharing mode.

(a) (b) (c) (d)

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Experimental Results(4/4)

(e) (f) (g) (h)

(i) (j) (k)

Fig. 4. The reconstructed images by using priority sharing mode. (a)-(f) are reconstructed images by using two shadow images, (g)-(j) are reconstructed images by using three shadow images, and (k) is reconstructed image by using four shadow images.

20

Conclusions

Smaller shadow images Saving storage space and transmission time