Reversible data hiding for encrypted signals by homomorphic encryption and signal energy transfer Source: J. Vis. Commun. Image R. 41 (2016) 58–64 Authors: Xiaotian Wu , Bing Chen , Jian Weng Speaker: Ran Tang Date: 06/08/2017 1 1

Outline Related Works Proposed Method Experiment Results Conclusions Paillier homomorphic encryption Signal energy transfer Proposed Method Experiment Results Conclusions 2 2

Related Works-Paillier homomorphic encryption p, q: two large primes, N =p*q; receiver 𝓡 computer: 𝝀=lcm(p−1,q−1); selects 𝐠∈ ℤ 𝑁 2 ∗ 𝑤𝑖𝑡ℎ gcd(L( 𝑔 𝜆 𝑚𝑜𝑑 𝑁 2 ),N)=1 where 𝐿 𝑥 = 𝑥−1 𝑁 , ℤ 𝑁 2 ∗ = 1,2,…, 𝑁 2 −1 . Public key:(N, g); Private key:(p, q, 𝝀). Plaintext: m∈ ℤ 𝑁 , 𝑟∈ ℤ 𝑁 ∗ 𝑖𝑠 𝑟𝑎𝑛𝑑𝑜𝑚𝑙𝑦 𝑠𝑒𝑙𝑒𝑐𝑡𝑑; Ciphertext: c= 𝑔 𝑚 𝑟 𝑁 𝑚𝑜𝑑 𝑁 2 . Decryption: m = 𝐿( 𝑐 𝝀 𝑚𝑜𝑑 𝑁 2 ) 𝐿( 𝑔 𝝀 𝑚𝑜𝑑 𝑁 2 ) . 𝐸(𝑚 1 + 𝑚 2 )=E( 𝑚 1 )𝐸 𝑚 2 ; 𝐸(𝑚) 𝑎 =𝐸 𝑎𝑚 .

Related Works-Signal energy transfer A signal can be represented by the sum of other signals. 𝑃 𝑖 = 𝑡 𝑖 + 𝑎 0𝑖 + 𝑎 1𝑖 ; 𝒙 𝒊 = 𝑃 𝑖 /2 . 𝒓 𝒊 𝑖𝑠 𝑟𝑎𝑛𝑑𝑜𝑚𝑙𝑦 𝑠𝑒𝑙𝑒𝑐𝑡𝑑 𝑓𝑟𝑜𝑚 0,1,2,…, 𝑥 𝑖 . 𝒂 𝟎𝒊 , 𝒂 𝟏𝒊 = 𝑟 𝑖 ; 𝒕 𝒊 = 𝑃 𝑖 −2 𝑟 𝑖 . 𝐸(𝑚 1 + 𝑚 2 )=E( 𝑚 1 )𝐸 𝑚 2 ; 𝐸(𝑚) 𝑎 =𝐸 𝑎𝑚 .

Proposed Method(1/2)

Proposed Method(2/2) Original pixel: 𝑃 𝑖 =97; 𝑠𝑒𝑐𝑟𝑒𝑡 𝑏𝑖𝑡:𝑏=1; Image encryption phase: 𝑥 𝑖 = 𝑃 𝑖 /2 = 97/2 =48; suppose that 𝑟 𝑖 =6 is randomly selectd from 0,1,2,…,48 ; 𝑎 0𝑖 = 𝑎 1𝑖 = 𝑟 𝑖 =6; 𝑡 𝑖 = 𝑃 𝑖 − 𝑎 0𝑖 − 𝑎 1𝑖 =97−12=85. When 𝑷 𝒊 is encrypted we get: 𝑬(𝒑 𝒊 )=E 85 E 6 E 6 . data embedding phase: E 𝑎 0𝑖 ′ = 𝐸 𝑎 0𝑖 − 𝑎 1𝑖 −1 𝑖𝑓 𝑏=0; 𝐸 𝑎 0𝑖 + 𝑎 1𝑖 +1 𝑖𝑓 𝑏=1; E 𝑎 1𝑖 ′ = 𝐸 𝑎 0𝑖 + 𝑎 1𝑖 +1 𝑖𝑓 𝑏=0; 𝐸 𝑎 0𝑖 − 𝑎 1𝑖 −1 𝑖𝑓 𝑏=1; ∵𝑏=1; ∴E 𝑎 0𝑖 ′ =𝐸 13 ;E 𝑎 1𝑖 ′ =𝐸 −1 . marked encrypted pixel: 𝑬(𝑷 𝒊 ′ )=𝐸 85 𝐸 13 𝐸 −1 ; data extraction and image recovery phase: directly decrypted: 𝐏 𝐢 ′ =85+13+ −1 =97; b= 0, 𝑖𝑓 𝑎 0𝑖 ′ <𝑎 1𝑖 ′ ; 1, 𝑖𝑓 𝑎 0𝑖 ′ >𝑎 1𝑖 ′ . ∵ 𝑎 0𝑖 ′ >𝑎 1𝑖 ′ ; ∴ 𝑏=1.

Experiment Results(1/5) 7 7

Experiment Results(2/5) 8 8

Experiment Results(3/5) 9 9

Experiment Results(4/5) 10 10

Experiment Results(5/5) -references [14] X. Zhang, Reversible data hiding in encrypted image, IEEE Signal Process.Lett.18 (4) (2011) 255–258. [15] W. Hong, T.-S. Chen, H.-Y. Wu, An improved reversible data hiding in encrypted images using side match, IEEE Signal Process. Lett. 19(4) (2012)199–202. [16] X. Zhang, Separable reversible data hiding in encrypted image, IEEE Trans. Inform. Forensics Secur. 7(2) (2012) 826–832. [20] W. Zhang, K. Ma, N. Yu, Reversibility improved data hiding in encrypted images, Sign. Process. 94 (2014) 118–127. [23] Y.-C. Chen, C.-W. Shiu, G. Horng, Encrypted signal-based reversible data hiding with public key cryptosystem, J. Vis. Commun. Image Represent. 25(5) (2014) 1164–1170. [24] C.W. Shiu, Y.C. Chen, W. Hong, Encrypted image-based reversible data hiding with public key cryptography from difference expansion, Sign. Process. Image Commun. 39 (PA) (2015) 226–233. [25] X. Zhang, J. Wang, Z. Wang, H. Cheng, Lossless and reversible data hiding in encrypted images with public key cryptography, IEEE Trans. Circ. Syst. Video Technol. http://dx.doi.org/10.1109/TCSVT.2015.2433194. 11 11

Conclusions Each unit in the original image is divided into three parts, and they are encrypted by Paillier homomorphic encryption. The proposed method have optimal visual quality and improved embedding rate. Moreover, the proposed method can be extended to deal with encoded multimedia. 12 12

Q&A 13 13