# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 1441-1455. doi: 10.3934/dcdss.2019099

## An algorithm for reversible information hiding of encrypted medical images in homomorphic encrypted domain

 School of Management, Guangdong University of Technology, Guangzhou 510520, China

* Corresponding author: Xueyan Wu

Received  June 2017 Revised  November 2017 Published  November 2018

At present, in reversible information hiding algorithm of image, the difference expansion idea is used. After the carrier image encryption, in encrypted image, information bits are embedded in the low value, resulting in the fact that in the image embedded with watermarking information, a part of the boundary pixel value has flipped. After being extracted, the carrier image cannot be recovered completely that is not only a large quantity of calculation, and the image quality has also been some damage. A algorithm for reversible information hiding of encrypted the medical image in the homomorphic encryption domain is proposed. Combining wavelet and fast fuzzy algorithm, the image edge is extracted from the high frequency and low frequency parts of medical image, and the medical image is reconstructed in the compressed boundary part. Combined with the thought of block compressed sensing and block edge pixels, the reconstructed medical image is divided to multiple non-overlapping blocks. The pixel in the right lower edge of the block is made homomorphic encryption operation, the remaining pixels are made compressed sensing operation, and the two parts are combined to a ciphertext to be sent to the owner of the channel According to the information hiding key the secret information is embedded into the ciphertext by the channel owners. The receiver can extract the information and restore the original image based on the encryption key and the information hiding key. The experimental results show that the proposed algorithm has high embedding capacity, the image quality after recovery is high, and the computational complexity is low.

Citation: Xueyan Wu. An algorithm for reversible information hiding of encrypted medical images in homomorphic encrypted domain. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1441-1455. doi: 10.3934/dcdss.2019099
##### References:

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##### References:
coefficient of medical images after block compression perception processing
grouping rules of medical image
standard test medical images
average computing time for LE in medical images
the number of inlay pixels for eight test images
 LE AI BA BN BO HI PE LA b/($\uparrow$) 0 3 514 285 26 0 2 1
 LE AI BA BN BO HI PE LA b/($\uparrow$) 0 3 514 285 26 0 2 1
maximum embedding rate and maximum pure embedding rate of eight test images
 LE AI BA BN BO HI PE LA Maximum embedding rate/bpp 0.4855 0.4855 0.4802 0.4812 0.4855 0.4855 0.4932 0.4932 Maximum embedding rate/bpp 0..4854 0.4852 0.4525 0.4758 0.4825 0.4821 0.4921 0.4924
 LE AI BA BN BO HI PE LA Maximum embedding rate/bpp 0.4855 0.4855 0.4802 0.4812 0.4855 0.4855 0.4932 0.4932 Maximum embedding rate/bpp 0..4854 0.4852 0.4525 0.4758 0.4825 0.4821 0.4921 0.4924
Comparison of the results of different algorithms performed on LE
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 1.425 38.1 54.25 14.25 36.58 45.8 ZF 0.074 38.1 68.47 2.58 36.58 51.41 LO 0.185 38.27 61.58 3.68 36.74 48.52 The proposed algorithm 0 26.85-42.1 $\uparrow$ 0 22.14-49.55 $\uparrow$
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 1.425 38.1 54.25 14.25 36.58 45.8 ZF 0.074 38.1 68.47 2.58 36.58 51.41 LO 0.185 38.27 61.58 3.68 36.74 48.52 The proposed algorithm 0 26.85-42.1 $\uparrow$ 0 22.14-49.55 $\uparrow$
Comparison of the results of different algorithms performed on AI
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 4.362 37.58 50.25 16.25 37.58 42.58 ZF 0.124 37.58 65.25 4.584 36.58 48.47 LO 0.685 36.78 48.25 5.147 36.14 48.62 The proposed algorithm 0 26.85-41.8 $\uparrow$ 0 22.14-52.41 $\uparrow$
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 4.362 37.58 50.25 16.25 37.58 42.58 ZF 0.124 37.58 65.25 4.584 36.58 48.47 LO 0.685 36.78 48.25 5.147 36.14 48.62 The proposed algorithm 0 26.85-41.8 $\uparrow$ 0 22.14-52.41 $\uparrow$
Comparison of the results of different algorithms performed on BA
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 33.25 36.25 38.58 25.25 36.25 39.58 ZF 20.54 36.25 40.25 9.25 36.25 43.25 LO 22.14 36.84 41.05 12.54 36.87 40.14 The proposed algorithm 0 22.14-32.14 $\uparrow$ 0 21.15-50.15 $\uparrow$
 Algorithm Embedding rate = 0.0145 Embedding rate = 0.0524 Error rate/% Direct decryption image restore image Error/% rate/% Direct decryption image restore image KF 33.25 36.25 38.58 25.25 36.25 39.58 ZF 20.54 36.25 40.25 9.25 36.25 43.25 LO 22.14 36.84 41.05 12.54 36.87 40.14 The proposed algorithm 0 22.14-32.14 $\uparrow$ 0 21.15-50.15 $\uparrow$
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