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Fig. 12. Images corresponding to the generation of the
combined fusion image in the DEsS.
Fig. 14. Scrambled image IDEnc.
Fig. 13. XOR operation fusion images with RGB chaotic
image.
B. Optical Encryption Results Fig. 15. Optical encryption results (Lena and Baboon). (a)
The simulation results of the OEsS are displayed in Fig. 15. scrambled image, (b) cipher image after optical mask1, (c)
The scrambled image (part (a) of this figure) is used as the cipher image after optical mask2, (d) final cipher image.
input of this OEsS. The cipher images after optical mask1,
after optical mask2, and the final result IEnc are presented in A. Information Entropy
parts (b) to (d) of this figure, respectively. The output of the The performance of the proposed HDOE scheme is tested
HDOE scheme describes the final cipher image, which will be through entropy measures. The entropy for the three-color
applied to the security evaluation tester later in this subsection. channels of the final optical encrypted color images IEnc are
presented in Table I. The values in this table are very close to
C. Decryption Results 8, which corresponds to the entropy of an ideal encryption;
The decryption algorithm is processed as done in the encryp- log2256 = 8.
tion algorithm but in reverse order. The decryption scheme
consists of an optical decryption subscheme (ODsS) followed B. Histogram Analysis
by a digital decryption subscheme (DDsS). Fig. 16 presents The histograms of the encrypted images corresponding to
the results related to the final stage of the decryption process, the images of Lena-baboon, Barbara-airplane, and sailboat-
namely the DDsS. Parts a-d of the figure shows the unscram- peppers are shown in Fig. 17. It can be seen that the histogram
bled, de-fusion, and decrypted images, respectively. of the encrypted image is quite uniform and significantly dis-
similar to the histogram of the plaintext image. This prevents
V. PERFORMANCE EVALUATION METRICS an attacker from learning anything about the plain image from
FOR THE HDOE SCHEME its encrypted version. Note that the histograms of the de-
crypted images match that of the original input images given
A security analysis is provided to evaluate the algorithm’s
performance. The test images used to assess the efficiency
and security level are given in Fig. 10.
