Adopting secret sharing for reversible data hiding in

Adopting secret sharing for reversible data hiding in encrypted images Source：Signal Processing Volume 143, February 2018, Pages 269 -281 Authors：Xiaotian Wu, Jian Weng, Wei. Qi Yan Speaker ：Lin Li Date ： 2019/08/22 1

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

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

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

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. 5 [2]. Blakley G. R. Safeguarding cryptographic keys. Managing Requirements Knowledge, International Workshop on(AFIPS) 1979, pp. 313– 317.

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

Related Works -- Shamir’s secret sharing method(3/3) a 0 = pix_value(i, j ) next a 0 = pix_value(i*, j* ) secret image • Shadow size: secret image size 7

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

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. ) 9

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

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

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

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

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

Proposed scheme (DHSM) (8/10) 15

Proposed scheme (DHSM) (9/10) 16

Proposed scheme (DHSM) (10/10) 17

Experimental results (1/7) 18

Experimental results (2/7) 19

Experimental results (3/7) 20

Experimental results (4/7) 21

Experimental results (5/7) 22

Experimental results (6/7) 23

Experimental results (7/7) 24

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

Thanks for your listening! 26