1. 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

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

3. 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 .

4. 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 .

5. Proposed Method(1/2)

6. 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 − 𝑖𝑓 𝑏=0; 𝐸 𝑎 0𝑖 + 𝑎 1𝑖 𝑖𝑓 𝑏=1;
E 𝑎 1𝑖 ′ = 𝐸 𝑎 0𝑖 + 𝑎 1𝑖 𝑖𝑓 𝑏=0; 𝐸 𝑎 0𝑖 − 𝑎 1𝑖 − 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 ′ = −1 =97;
b= 0, 𝑖𝑓 𝑎 0𝑖 ′ <𝑎 1𝑖 ′ ; 1, 𝑖𝑓 𝑎 0𝑖 ′ >𝑎 1𝑖 ′ .
∵ 𝑎 0𝑖 ′ >𝑎 1𝑖 ′ ; ∴ 𝑏=1.

7. Experiment Results(1/5)7 7

8. Experiment Results(2/5)8 8

9. Experiment Results(3/5)9 9

10. Experiment Results(4/5)10 10

11. Experiment Results(5/5) -references
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Technol. 11 11

12. 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

13. Q&A 13 13