Figure 1.
Performance evaluation of the logistic map: (a) bifurcation diagram and (b) Lyapunov exponent.
Figure 1.
Performance evaluation of the logistic map: (a) bifurcation diagram and (b) Lyapunov exponent.
Figure 2.
Joseph traversal.
Figure 2.
Joseph traversal.
Figure 3.
Flow chart of the IEA-DIJT.
Figure 3.
Flow chart of the IEA-DIJT.
Figure 4.
Experimental results: (a,d,g,j) are the plain images “Lena”, “Cameraman”, “Elaine”, and “Airport”, (b,e,h,k) are the corresponding cipher images of (a,d,g,j), and (c,f,i,l) are the corresponding decrypted images of (b,e,h,k).
Figure 4.
Experimental results: (a,d,g,j) are the plain images “Lena”, “Cameraman”, “Elaine”, and “Airport”, (b,e,h,k) are the corresponding cipher images of (a,d,g,j), and (c,f,i,l) are the corresponding decrypted images of (b,e,h,k).
Figure 5.
Key sensitivity. The cipher image of the plain image “Lena” using (a) and (b) , (c) the difference between (a,b,d) the decoded image using , (e) the cipher image after a tiny change, and (f) the difference between (a,e).
Figure 5.
Key sensitivity. The cipher image of the plain image “Lena” using (a) and (b) , (c) the difference between (a,b,d) the decoded image using , (e) the cipher image after a tiny change, and (f) the difference between (a,e).
Figure 6.
Histograms of the IEA-DIJT: (a,c,e) are the histograms of the plain images “Lena”, “Peppers”, and “Cameraman”, respectively; and (b,d,f) are the histograms of the cipher images “Lena”, “Peppers”, and “Cameraman”, respectively.
Figure 6.
Histograms of the IEA-DIJT: (a,c,e) are the histograms of the plain images “Lena”, “Peppers”, and “Cameraman”, respectively; and (b,d,f) are the histograms of the cipher images “Lena”, “Peppers”, and “Cameraman”, respectively.
Figure 7.
Correlation: the correlation of (
a)
Figure 4a and (
b)
Figure 4b in three directions.
Figure 7.
Correlation: the correlation of (
a)
Figure 4a and (
b)
Figure 4b in three directions.
Figure 8.
Known-plaintext and chosen-plaintext attacks: (a,b) are two cipher images with only a one-bit difference in the original image “Lena”, and (c) the difference between (a,b,d–f) are the histograms of (a–c), respectively.
Figure 8.
Known-plaintext and chosen-plaintext attacks: (a,b) are two cipher images with only a one-bit difference in the original image “Lena”, and (c) the difference between (a,b,d–f) are the histograms of (a–c), respectively.
Figure 9.
Experimental results of the pure white and black: (a) the pure white image, (b) the cipher image of (a,c) the histograms of (b,d) pure black image, and (e) the cipher-image of (e,f) the histograms of (e).
Figure 9.
Experimental results of the pure white and black: (a) the pure white image, (b) the cipher image of (a,c) the histograms of (b,d) pure black image, and (e) the cipher-image of (e,f) the histograms of (e).
Figure 10.
Noise attack. The cipher-image “Lena” with noise intensity (a) , (b) , and (c) , and the decoded images of (a–f).
Figure 10.
Noise attack. The cipher-image “Lena” with noise intensity (a) , (b) , and (c) , and the decoded images of (a–f).
Figure 11.
Data loss attack. The cipher-image “Lena” with data loss proportions (a) , (b) , (c) , and (d) , and the decoded image of (a–h).
Figure 11.
Data loss attack. The cipher-image “Lena” with data loss proportions (a) , (b) , (c) , and (d) , and the decoded image of (a–h).
Table 1.
The obtained results.
Table 1.
The obtained results.
Size | Image | Value | H (0 or 1) | Decision |
---|
| Cameraman | 250.6172 | 0 | Accept |
Clock | 261.7734 | 0 | Accept |
House | 258.7813 | 0 | Accept |
Lena | 291.2969 | 0 | Accept |
Moonface | 287.2578 | 0 | Accept |
Peppers | 233.2734 | 0 | Accept |
| Baboon | 283.5293 | 0 | Accept |
Boat | 246.8066 | 0 | Accept |
Couple | 247.3340 | 0 | Accept |
Elaine | 263.0449 | 0 | Accept |
Lena | 262.1440 | 0 | Accept |
Peppers | 243.7363 | 0 | Accept |
Table 2.
Correlation of neighboring pixels of the IEA-DIJT.
Table 2.
Correlation of neighboring pixels of the IEA-DIJT.
Size | Image | Direction | IEA-DIJT | Size | Image | Direction | IEA-DIJT |
---|
| | | |
---|
| Cameraman | H | 0.8950 | −0.0017 | | Baboon | H | 0.7267 | 0.0010 |
V | 0.8987 | 0.0022 | V | 0.7328 | −0.0019 |
D | 0.9311 | 0.0011 | D | 0.6838 | 0.0011 |
Clock | H | 0.9340 | 0.000 | Lena | H | 0.9719 | −0.0004 |
V | 0.9431 | −0.0013 | V | 0.9850 | −0.0004 |
D | 0.9469 | 0.0007 | D | 0.9593 | 0.0002 |
Lena | H | 0.9143 | 0.0013 | Peppers | H | 0.9573 | 0.0008 |
V | 0.9039 | 0.0009 | V | 0.9667 | 0.0018 |
D | 0.9098 | 0.0007 | D | 0.9684 | 0.0007 |
Peppers | H | 0.9337 | −0.0031 | | | | |
V | 0.9464 | −0.0017 | | | | |
D | 0.9329 | −0.0028 | | | | |
Table 3.
Comparison results with other IEAs for the cipher image “Lena”.
Table 3.
Comparison results with other IEAs for the cipher image “Lena”.
Schemes | Directions |
---|
H | V | D |
---|
IEA-DIJT | 0.0009 | 0.0007 | −0.0031 |
Ref. [38] | −0.015595 | 0.028436 | −0.007102 |
Ref. [39] | 0.016720 | 0.006996 | 0.011698 |
Ref. [40] | −0.040583 | −0.027371 | −0.014449 |
Ref. [41] | 0.004555 | −0.015623 | −0.005112 |
Ref. [42] | 0.009998 | 0.001372 | −0.006567 |
Ref. [43] | −0.001885 | −0.012793 | 0.007396 |
Table 4.
Information entropy values of the IEA-DIJT.
Table 4.
Information entropy values of the IEA-DIJT.
Size | Image | IEA-DIJT | Size | Image | IEA-DIJT |
---|
| | | |
---|
| Cameraman | 6.9719 | 7.9973 | | Baboon | 7.3585 | 7.9992 |
Clock | 6.7057 | 7.9972 | Boat | 7.1914 | 7.9993 |
House | 6.4971 | 7.9971 | Couple | 7.2010 | 7.9994 |
Lena | 7.5534 | 7.9968 | Elaine | 7.5060 | 7.9993 |
Moonface | 6.7093 | 7.9968 | Lena | 7.4474 | 7.9995 |
Peppers | 7.5819 | 7.9974 | Peppers | 7.5925 | 7.9993 |
Table 5.
Comparison results of the information entropy.
Table 5.
Comparison results of the information entropy.
Size | Image | IEA-DIJT | Ref. [38] | Ref. [39] | Ref. [40] | Ref. [41] | Ref. [42] | Ref. [43] |
---|
| |
---|
| Baboon | 7.5534 | 7.9973 | 7.9302 | 7.9973 | 7.9970 | 7.9973 | 7.9787 | 7.9967 |
Lena | 7.5819 | 7.9974 | 7.9144 | 7.9970 | 7.9969 | 7.9973 | 7.9950 | 7.9971 |
| Baboon | 7.3585 | 7.9992 | 7.9866 | 7.9985 | 7.9992 | 7.9993 | 7.9791 | 7.9993 |
Lena | 7.4474 | 7.9995 | 7.9729 | 7.9986 | 7.9992 | 7.9992 | 7.9788 | 7.9993 |
Table 6.
LSE values for different cipher images.
Table 6.
LSE values for different cipher images.
Size | Image | LSE | Size | Image | LSE |
---|
| Cameraman | 7.902814 | | Baboon | 7.9032934 |
Clock | 7.9018914 | Boat | 7.9020965 |
House | 7.9036226 | Couple | 7.9013717 |
Lena | 7.9033111 | Elaine | 7.9025729 |
Moonface | 7.9025067 | Lena | 7.902469 |
Peppers | 7.9026073 | Peppers | 7.9019517 |
PASS/ALL | 11/12 |
Table 7.
and (%) scores of the IEA-DIJT.
Table 7.
and (%) scores of the IEA-DIJT.
Size | Image | | | Size | Image | | |
---|
|
| |
|
---|
| Cameraman | 99.6096 | 33.5167 | | Baboon | 99.6131 | 33.5181 |
Clock | 99.6118 | 33.4908 | Boat | 99.6265 | 33.5226 |
House | 99.6107 | 33.5008 | Couple | 99.6128 | 33.5269 |
Lena | 99.6098 | 33.4754 | Elaine | 99.6208 | 33.5054 |
Moonface | 99.6126 | 33.4708 | Lena | 99.6085 | 33.5172 |
Peppers | 99.6170 | 33.5672 | Peppers | 99.6143 | 33.5188 |
Table 8.
Comparison results of the (%).
Table 8.
Comparison results of the (%).
Size | Image | IEA-DIJT | Ref. [38] | Ref. [39] | Ref. [40] | Ref. [41] | Ref. [42] | Ref. [43] |
---|
| Baboon | 99.6096 | 99.1073 | 99.6216 | 99.5911 | 99.6231 | 99.5941 | 99.6307 |
Lena | 99.6098 | 98.9807 | 99.6346 | 99.6323 | 99.6154 | 99.6307 | 99.6506 |
| Baboon | 99.6131 | 99.4785 | 99.6268 | 99.6627 | 99.6299 | 99.5979 | 99.6147 |
Lena | 99.6085 | 99.5033 | 99.6436 | 99.6093 | 99.5845 | 99.6082 | 99.6059 |
Table 9.
Comparison results of the (%).
Table 9.
Comparison results of the (%).
Size | Image | IEA-DIJT | Ref. [38] | Ref. [39] | Ref. [40] | Ref. [41] | Ref. [42] | Ref. [43] |
---|
| Baboon | 33.4804 | 33.7694 | 33.2025 | 33.5648 | 33.4941 | 33.1112 | 33.1598 |
Lena | 33.5172 | 33.0815 | 33.1984 | 33.2378 | 33.3377 | 33.0881 | 33.4858 |
| Baboon | 33.5181 | 33.7609 | 33.1173 | 33.4588 | 33.4316 | 33.0019 | 33.4921 |
Lena | 33.5172 | 33.2334 | 33.6028 | 33.4873 | 33.5262 | 33.0228 | 33.4209 |
Table 10.
Encryption time (s) results.
Table 10.
Encryption time (s) results.
Size | Image | Time | Size | Image | Time |
---|
| Cameraman | 1.005048 | | Baboon | 5.208273 |
Clock | 0.974152 | Boat | 5.439504 |
House | 0.98626 | Couple | 5.362937 |
Lena | 1.006378 | Elaine | 5.394718 |
Moonface | 0.976231 | Lena | 5.522115 |
Peppers | 0.987105 | Peppers | 5.487128 |