A double scrambling-DNA row and column closed loop image encryption algorithm based on chaotic system

Abstract

In this paper, a dynamic update algorithm of double scrambling-DNA row and column closed loop based on chaotic system is proposed. The classical scrambling and diffusion structure are used in the whole process. In the scrambling stage, a new pixel reconstruction method is proposed by combining the Hilbert curve with Knuth-Durstenfeld shuffle algorithm to overcome the shortcoming of nearby storage of Hilbert curve. This method reconstructs the pixel matrix of one-dimensional vector according to the Hilbert curve coding method, and achieves good scrambling effect, while reducing its time complexity and space complexity. In the diffusion stage, combining the plaintext row, the ciphertext row and the key row, and taking advantage of the parallel computing power and high storage density of the DNA encoding, the existing block diffusion operation is improved, and the two-round diffusion of the DNA encoding is proposed. When the last line of ciphertext is generated, the first line of ciphertext is updated and the closed-loop dynamic update of the encryption system is realized. Finally, SHA-256 is used to give the secret key and calculate the initial value of the chaotic system. The simulation results show that the "double scrambling-DNA row and column closed loop dynamic" update algorithm proposed in this paper can effectively improve the efficiency of information transmission and have high security.

Fig 1. Attractors of 2D-LICM chaotic system with (a, k) = (0.6, 0.8).

Fig 2. Lyapunov spectrum of 2D-LICM chaotic system with a from 0.5 to 2.5.

Fig 3. Bifurcation diagram of the 2D-LICM chaotic system.

A: Bifurcation diagram of a ∈ [−50, 50] (k = 0.8). B: Bifurcation diagram of a ∈ [0.5, 2.5] (k = 0.8).

Fig 4. Hilbert curve of order 1, 2 and 3.

A: Hilbert curve of order 1. B: Hilbert curve of order 2. C: Hilbert curve of order 3.

Fig 5. Different curves.

A: Continuous raster method. B: Spiral method. C: Diagonal method.

Fig 6. The encryption flow diagram of the proposed scheme.

Fig 7. Numerical example of double scrambling method.

A: Original pixel matrix. B: Matrix with shuffling algorithm. C: The reconstructed matrix with Hilbert curve.

Fig 8. Flowchart of Peppers encryption step (size 256 x 256).

Fig 9. Histogram analysis of original and encrypted images.

A1-D1: Original images of Peppers, Baboon, House and Cameraman. A2-D2: The corresponding original image histograms. A3-D3: The encrypted images of Peppers, Baboon, House and Cameraman. A4-D4: The corresponding encrypted image histograms.

Fig 10. Pixel correlation analysis of plain image Peppers and corresponding encrypted image.

A: Horizontal pixel of plain image. B: Vertical pixel of plain image. C: Diagonal pixel of plain image. D:Horizontal pixel of cipher image. E:Vertical pixel of cipher image. F:Diagonal pixel of cipher image.

Fig 11. Analysis of encryption test results of all black images.

A: Original full black image. B: Encrypted full black image. C: Histogram of encrypted image. D: Horizontal pixel of original image. E: Vertical pixel of original image. F: Diagonal pixel of original image. G: Horizontal pixel of encrypted image. H: Vertical pixel of encrypted image. I: Diagonal pixel of encrypted image.

Fig 12. Analysis of encryption test results of all white images.

A: Original full white image. B: Encrypted full white image. C: Histogram pixel of encrypted image. D: Horizontal pixel of original image. E: Vertical pixel of original image. F: Diagonal pixel of original image. G: Horizontal pixel of encrypted image. H: Vertical pixel of encrypted image. I: Diagonal pixel of encrypted image.

Fig 13. Key sensitivity analysis.

A: Plain image of Peppers. B: Encrypted image C with correct key. C: Encrypted image C₁ with key S1 changed by one bit. D: |C₁ − C|. E: Encrypted image C₂ with key S2 changed by one bit. F: |C₂ − C|. G: Encrypted image C₃ with key S3 changed by one bit. H: |C₃ − C|. I: Encrypted image C₄ with key S4 changed by one bit. J: |C₄ − C|. K: Encrypted image C₅ with key x₀ changed by one bit. L: |C₅−C|. M: Encrypted image C₆ with key y₀ changed by one bit. N: |C₆ − C|.

Fig 14. Histogram analysis and entropy analysis of salt-and-pepper noise image and encrypted image.

Fig 15. Histogram analysis and entropy analysis of Gaussian noise image and encrypted image.