1. Adopting secret sharing for reversible data hiding in encrypted images
Source：Signal Processing Volume 143, February 2018, Pages
Authors：Xiaotian Wu, Jian Weng, WeiQi Yan
Speaker ：Lin Li
Date ：2019/08/22

2. Outline Research background Related work Proposed scheme
Shamir’s secret sharing method
Proposed scheme
Experimental results
Conclusions

3. Research background (1/2)
embedding
a bit
Research background (1/2)
an AES encrypted image
reducing data extraction errors
separability
increasing capacity
encrypted compressed images
homomorphic encryption
(computational complexity, seriously expanded)

4. Research background (2/2)
Encryption algorithm is simple.
The computational complexity is low.

5. Related Work --Shamir’s secret sharing method (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.

6. The extraction procedure:
Related Works -- Shamir’s secret sharing method (2/3)
The extraction procedure:
Using the Lagrange polynomial
interpolation method

7. Related Works -- Shamir’s secret sharing method(3/3)
a0 = pix_value(i, j )
next
a0 = pix_value(i*, j* )
secret image
Shadow size: secret image size

8. Proposed scheme (1/10) (Pair-wise image encryption by secret sharing)
: pixel pair
: generated by a pseudo-random number generator
: random integers

9. Proposed scheme (2/10)
Preserving the difference of two adjacent pixels (give an example: )
(The difference is 3.)
167, 15 , 42.
164, 12 , 39.
(167, 164), (15, 12), (42, 39).
(The difference 3 is kept.)

10. Proposed scheme (DEM) (3/10)
A difference expansion based method (DEM)
A difference histogram shifting based method(DHSM)

11. Proposed scheme (DEM) (4/10)
Reversible Integer Transform
m = mean of ( x , y )
d = difference of ( x , y ) pair

12. Proposed scheme (DEM) (5/10)
Reversibly embed a bit in the difference number

13. Proposed scheme (DEM) (6/10)
Example of Difference Expansion Embed

14. Proposed scheme (DEM) (7/10)
Example of Difference Expansion Extract
X = [ (6+1)/2 ] = 206
Y = 203 – [ 6/2 ] =200

15. Proposed scheme (DHSM) (8/10)

16. Proposed scheme (DHSM) (9/10)

17. Proposed scheme (DHSM) (10/10)

18. Experimental results (1/7)

19. Experimental results (2/7)

20. Experimental results (3/7)

21. Experimental results (4/7)

22. Experimental results (5/7)

23. Experimental results (6/7)

24. Experimental results (7/7)

25. Conclusions Secret sharing for RDH in encrypted images is adopted.
Reasonable image expansion is achieved (Two shares).
High embedding capacity is obtained.

26. Thanks for your listening!