Fig. 1. Bifurcation diagram and sequence distribution diagram of Logistic chaotic system and L-F chaotic system
Fig. 2. Multiple-image recombination process
Fig. 3. 3D binary matrix
Fig. 4. High plane bit scrambling
Fig. 5. Low plane bit scrambling
Fig. 6. Encryption process
Fig. 7. Effect of encryption and decryption
Fig. 8. The decrypted image after changing the key during decryption
Fig. 9. Decrypted image with arbitrary pixel value plus 1
Fig. 10. Histogram of plaintext and ciphertext
Fig. 11. Correlation diagram of adjacent horizontal pixels
Fig. 12. Robustness analysis
Any position pixel plus 1 | Swap positions of two different pixel values | NPCR | UACI | NPCR | UACI | 0.996 1 | 0.334 8 | 0.996 0 | 0.335 1 |
|
Table 1. Analysis of clear text sensitivity
Δx0, 1′=10-14 | ΔintF0, 1′=10-14 | Δu1′=10-14 | Δk=1 | Δx0, 2′=10-14 | ΔintF0, 2′=10-14 | Δu2′=10-14 | 0.007 8 | 0.005 9 | 0.008 9 | 0.006 3 | -0.002 0 | -0.001 0 | 0.000 1 |
|
Table 2. Correlation coefficient of ciphertext before and after key changes in encryption process
Lena | Gril | Lena | Monkey | Dragon | Ciphertext1 | Ciphertext 2 | Ciphertext 3 | Ciphertext 4 | Ciphertext 5 | 7.460 3 | 7.524 3 | 7.724 2 | 7.659 2 | 0.768 2 | 7.999 2 | 7.999 3 | 7.999 3 | 7.999 3 | 7.999 3 |
|
Table 3. Image information entropy
| Lena | Gril | Lena | Monkey | Dragon | Cipher-text1 | Cipher-text 2 | Cipher-text 3 | Cipher-text 4 | Cipher-text 5 | Level | 0.968 4 | 0.916 8 | 0.960 3 | 0.876 9 | 0.936 0 | 0.001 7 | 0.001 6 | 0.001 9 | -0.002 2 | 0.000 3 | Vertical | 0.935 2 | 0.917 3 | 0.919 6 | 0.916 9 | 0.922 4 | 0.002 3 | 0.000 1 | -0.000 6 | -0.000 1 | -0.001 2 | Diagonal | 0.908 3 | 0.870 0 | 0.891 2 | 0.845 9 | 0.894 9 | -0.002 5 | 0.000 1 | 0.000 3 | -0.000 2 | -0.003 3 |
|
Table 4. Correlation of adjacent pixels
| NPCR | UACI | Information entropy | Correlation coefficient(horizontal, vertical, diagonal) | Times | Ref.[16] | 0 | 0 | 7.997 9 | -0.078 1 | 0.066 5 | 0.060 7 | 9.656 | Ref.[17] | 0 | 0 | 7.614 8 | -0.007 1 | -0.001 4 | -0.002 6 | - | Ref.[18] | 0.996 2 | 0.334 3 | 7.999 3 | -0.002 2 | -0.003 1 | 0.001 6 | 0.710 3 | This paper | 0.996 1 | 0.334 8 | 7.999 2 | 0.001 7 | 0.002 3 | -0.002 5 | 0.502 3 |
|
Table 5. Comparative analysis