JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (3): 1-8,18.doi: 10.6040/j.issn.1671-9352.2.2019.021

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Reversible data hiding in homomorphic encrypted domain based on Paillier

Min-qing ZHANG(),Neng ZHOU*(),Meng-meng LIU,Han WANG,Yan KE   

  1. Key Laboratory of Network and Information Security under Chinese People Armed Police Force (PAP), College of Cryptography Engineering, Engineering University of PAP, Xi'an 710086, Shaanxi, China
  • Received:2019-09-05 Online:2020-03-20 Published:2020-03-27
  • Contact: Neng ZHOU E-mail:api_zmq@126.com;zn_2019@163.com

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Abstract:

Based on the homomorphism and probability characteristics of Paillier cryptosystem, a reversible data hiding in homomorphic encrypted domain based on Paillier is proposed. First, the original image is divided into blocks. The pixel groups randomly selected by the image owner have one reference pixel and eight target pixels. Least significant bits (LSBs) of reference pixel and all bits of target pixel are self-embedded into other parts of the image by a method of RDH. In order to avoid overflow when embedding data, LSBs of the reference pixel are reset to zero before encryption. The encrypted reference pixel replaces the target pixels surrounding it, thereby constructing mirror central ciphertext. In a set of mirroring central ciphertext, the data hider embeds data in the LSBs of the target pixels by homomorphic addition, while the reference pixel remains unchanged. The receiver can directly extract the extra information by modular multiplication inverse between the target pixels and the corresponding reference pixel or directly extract the secret information by plaintext subtraction and can restore the original image without loss. The experimental results show that the average embedding rate of the algorithm is 0.18 bpp (bit per pixel) under the premise of ensuring the quality of the directly decrypted image.

Key words: reversible data hiding, homomorphic encrypted domain, Paillier, mirroring central ciphertext

CLC Number: 

  • TP391

Fig.1

Overall framework of the proposed algorithm"

Fig.2

Image partition and self-reversible embedding"

Fig.3

n=3 is used as an example to illustrate the algorithm flow"

Fig.4

Test images used in the algorithm of this paper"

Table 1

Embedding capacity and PSNR values under different n"

图像 嵌入容量/bit 峰值信噪比/dB
n=1 n=2 n=3 n=4
5 460 45.77 46.49 48.54 47.31
10 920 40.67 41.37 46.41 42.10
16 380 37.62 38.26 45.01 39.07
21 840 35.51 36.09 42.56 36.99
Lena 32 760 32.55 33.19 40.16 34.26
43 680 30.60 31.30 34.75 32.57
65 520 28.14 29.04 33.36 30.73
76 440 27.35 28.37 33.00 30.23
5 460 46.47 47.70 52.48 49.77
10 920 43.13 44.35 49.41 46.49
16 380 40.97 42.27 47.44 44.41
21 840 39.32 40.73 46.12 42.82
F-16 32 760 37.03 38.52 41.23 40.81
43 680 35.52 37.14 39.88 38.50
65 520 33.41 34.99 38.92 37.30
76 440 32.57 34.16 37.12 36.57

Table 2

Embedding capacity and PSNR values under n=3"

嵌入容量/bit 峰值信噪比/dB
Lena F-16 Baboon Hill Lake Man
5 460 48.54 52.48 40.69 52.87 44.67 48.01
10 920 46.41 49.41 38.83 49.38 42.65 45.13
16 380 45.01 47.44 37.14 47.13 39.17 44.36
21 840 42.56 46.12 35.69 45.04 37.48 41.62
32 760 40.16 41.23 33.09 44.78 35.02 39.81
43 680 34.75 39.88 32.14 42.33 32.75 35.75
65 520 33.36 38.92 31.75 41.16 31.49 34.89
76 440 33.00 37.12 28.61 40.94 30.61 32.13

Table 3

Performance comparison of reversible data hiding in homomorphic encrypted domain"

算法 特征
生成和利用冗余 额外数据扩展 可分离 信息嵌入次数 信息嵌入过程计算复杂度 加密域中信息保护机制
文献[4] VRBE 是 否 1 O(k) Paillier同态和概率机制
文献[6] VRBE 是 否 1 O(k) Paillier同态和概率机制
文献[1] VRIE 否 是 1 O(k) R-LWE同态机制
文献[12] VRAE 否 是 2 O(k3) WPC编码机制
文献[8] VRBE 否 是 1 O(k) Paillier同态和概率机制
文献[7] VRBE 是 是 1 O(k) Paillier同态和概率机制
本文算法 VRBE 否 是 1 O(k) Paillier同态和概率机制

Fig.5

PSNR performance comparison on image of Lena"

Fig.6

PSNR performance comparison on image of F-16"

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