**3.5 Comparison with other encryption algorithms**

The performance of the proposed algorithm compared to similar and good standing ones in literature is shown in **Table 7**. From the table, we can observe that the proposed encryption algorithm has a large key space and can encrypt a large number of target images in a good time compared to others. As for UACI and NPCR, they are about the best values expected (respectively >33.3 for UACI and >99.6 for NPCR) as can be seen in the table. Finally, our cryptosystem exhibits the best correlation value and a reduced normalized Mean Square Error (MSE) after decryption step.


#### **Table 5.**

that by changing only one bit in any parameter of the key, it is not possible to

Multiplex encrypted image 1 NCPR 99.62

Multiplex encrypted image 2 NCPR 99.63

UACI 33.54

UACI 33.47

**Image Test**

An excellent encryption algorithm should have the desirable property of spreading the influence of slight change to the plain text over as much of the cipher text as possible. The sensitivity of a cryptosystem is evaluated through Number of Pixel Change Rate (NPCR), see Eq. (19), and Unified Average Change Intensity (UACI), see Eq. (20), criteria, which consist in testing the influence of one-pixel change of a plain image in the resulting cipher image.where *C*<sup>1</sup> and *C*<sup>2</sup> are two images with same size *W* � *H*. If *C*1(i, j) # *C*2(i, j) C1ð Þ i, j 6¼ C2ð Þ i, j then *D i*ð Þ¼ , *j* 1

**Table 4** gives the measurement of NCPR and UACI between two cipher images of cameraman, Lena and peppers, when a Least Significant Bit (LSB) changed on gray value in the last pixel's position. We can notice that the values obtained are around the mean of 99.61 for NCPR and 33.49 for UACI. This result shows that a slight change to the original images will result in a great change in all the encrypted images. The results also imply that the proposed algorithm has an excellent ability to

As the number of target images to encrypt increases, the quality of recovered images decreases. In order to reduce the NMSE between plain and decrypted images and enlarge the number of target images, we grouped them into two multiplexed images before encryption. To evaluate quantitatively the quality of decrypted image, we used the normalized mean square error (NMSE) between the original

<sup>j</sup>¼<sup>1</sup>½ � IDð Þ� i, j IEði, j<sup>Þ</sup> <sup>2</sup>

<sup>j</sup>¼<sup>1</sup>½ � IEð Þ i, j <sup>2</sup> (21)

recover the plain images.

*Multimedia Information Retrieval*

**Table 4.**

**3.3 Sensitivity analysis**

*3.3.1 Differential attack analysis*

*NCPR AND UACI measure after a LSB change.*

D i, j ð Þ¼ 1, otherwise, *D i*ð Þ¼ , *j* 0.

resist the differential attack.

**34**

*3.3.2 Quality of reconstructed images*

image and the decrypted image. The NMSE is defined as:

P<sup>N</sup> i¼1 P<sup>M</sup>

> P<sup>N</sup> i¼1 P<sup>M</sup>

where M � N are the size of the image, ID(i, j) and IE(i, j) are the values of the decrypted image and the original image at the pixel (i, j), respectively. **Table 5** presents the values of NMSE for a set of different target images of size 512 � 512. From this table, we can observe that for *N = 16* target images combined in one multiplex image, that is, 32 images to encrypt by the proposed cryptosystem,

NMSE ¼

*NMSE for a set of different target images.*


#### **Table 6.**

*Encryption time in seconds.*


#### **Table 7.**

*Comparison of the proposed cryptosystem with others.*
