1. Secret Image Sharing Based on Encrypted Pixels
Source:  IEEE Access. March, doi: /ACCESS
Authors: ZHILI ZHOU, CHING-NUNG YANG, (Senior Member, IEEE), YI
CAO AND XINGMING SUN AND XINGMING SUN, (Senior Member)
Speaker: LiLin (李琳)
Date:

2. Outline Related Work The perfect secret sharing
The existing polynomial based secret image sharing
The problems of the existing SIS (SIS: Secret Image Sharing)
The proposed Scheme
A secure (k, n)-SIS scheme
A modified (k, n)-SIS scheme
Proof
Conclusions

3. Related Works -- The perfect secret sharing(1/3)
Shamir[1] and Blakley[2] independently proposed the first secret sharing scheme in 1979.
The embedding procedure:
[1]. Shamir A. How to share a secret. Commun ACM 1979, Volume. 22, no. 11, pp. 612–613. [2]. Blakley G.R. Safeguarding cryptographic keys. Managing Requirements Knowledge, International Workshop on(AFIPS) 1979, pp. 313–317.

4. The extraction procedure:
Related Works The perfect secret sharing(2/3)
The extraction procedure:
Using the Lagrange polynomial
interpolation method

5. Related Works -- The perfect secret sharing(3/3)
The perfect secret sharing is applied
to secret image sharing(SIS):
a0 = pix_value(i, j )
a0 = pix_value(i*, j* )
secret image
Shadow size: secret image size

6. …… The sharing phase Related works
--Polynomial based secret image sharing scheme(1/2)
r pixels
divided into section
(1≤𝑗≤M×N/r)
permuted
image ……
a permutation
sequence
(M×N/r)th
SH1
SH2
SHn
shadow size = 1/r×size of secret image
The sharing phase

7. apply inverse-permutation operation to all the M×N/r
Related works
--Polynomial based secret image sharing scheme(2/2)
coefficients a0-ar-1
r pixel values of the permuted image
Lagrange’s interpolation
block j
≥r shares
apply inverse-permutation operation to all the M×N/r
blocks ……
SHn
SH1
SH2
The revealing phase

8. The problem of the existing SIS(1/3)
Partial secret pixels can be reconstructed from less than k shadows the threshold properties of those (k, n)-SIS schemes.
Permutation only ciphers are insecure and correct permutation mapping can be recovered completely by a chosen-plaintext attack[3].
The permutation key for Thien and Lin’s (k, n)-SIS scheme can be easily obtain based on the fact that the permutation of pixels does not change histogram[4].
[3]. A. Jolfaei, X.-W. Wu, and V. Muthukkumarasamy, ‘‘On the security of permutation-only image encryption schemes,’’ IEEE Trans. Inf. Forensics Security, vol. 11, no. 2, pp. 235–246, Feb
[4]. C.-N. Yang, W.-J. Chang, S.-R. Cai, and C.-Y. Lin, “Secret image sharing without keeping permutation key.” in Proc. Int. Conf. Commun. Technol., 2014, pp. 410–416.

9. The problem of the existing SIS(2/3)

10. Example: The problem of the existing SIS(3/3)
(1). For (3, n)-SIS scheme:
Take three permutated secret pixels (a0, a1, a2)
(over finite field GF(251) )
(2). For (4, n)-SIS scheme:
All coefficients are used for embedding.
The permutation is not secure enough.
Finally, the partial pixels of a secret image will be reconstructed from
k-1 shadows, and this compromises the threshold properties of those
existing (k, n)-SIS scheme.

11. The proposed (k, n)-SIS scheme(1/5)
Based on encrypted pixels
Combines the perfect secret, the existing secret image and encryption
Shadow size is the 1/k size of a secret image plus a short piece of key

12. Notation and description
The proposed (k, n)-SIS scheme(2/5)
Notation and description
XTS-AES

13. Distribution: The proposed (k, n)-SIS scheme(3/5) K--> a0
every k encrypted pixels as
(128-bit key for
AES encryption) , F1 F2
Fn-1 Fn

14. …… Reconstruction: The proposed (k, n)-SIS scheme(4/5) S1 S2 Sk
𝐼 =𝐶 𝑆 𝑘,𝑛 −1 ( 𝐹 1 , 𝐹 2 ,..., 𝐹 𝑘

15. The proposed (k, n)-SIS scheme(5/5)

16. The modified (k, n)-SIS scheme(1/3)
128 super blocks
Change one bit in SBi to let
128 blocks
128 blocks S1 S2
Sn-1 Sn
128 super blocks

17. The modified (k, n)-SIS scheme(2/3)
for i = 1:128 {
if XOR( ) = ki;
continue;
else {
for j = 1: b
= Changed_ LSB(Bi,j);
if XOR( ) = ki;
break;
else undo_change; } }}
The modified (k, n)-SIS scheme(2/3)

18. Proof: The modified (k, n)-SIS scheme(3/3)
The probability of success is
1- (0.5)16*b , PSNR between I and :
When b = 128( for a 512*512 size image)
1 – (0.5)16*128 = 1 – (0.5)16*128 ≈ 100%
For small-size image, e.g. 64*32-pixel image
Also divide it into 128 super blocks, each of which is 16 blocks
For this case, b = 1
The probability is 1 – (0.5)16 = %
Also can change two LSBs in a block,
The probability is %
PSNR between I and : 78.2dB

19. Conclusion
Address the weakness that the threshold properties of existing (k, n)- SIS schemes are compromised.
Propose a (k, n)-SIS scheme based on encrypted pixels.
Propose a (k, n)-SIS with the same shadow size of Thien and Lin’s scheme.
Computationally secure.

20. Thanks for your listening!