A Novel One-Dimensional Chaotic System for Image Encryption Through the Three-Strand Structure of DNA

Abstract

Digital images have been widely applied in fields such as mobile devices, the Internet of Things, and medical imaging. Although significant progress has been made in image encryption technology, it still faces many challenges, such as attackers using powerful computing resources and advanced algorithms to crack encryption systems. To address these challenges, this paper proposes a novel image encryption algorithm based on one-dimensional sawtooth wave chaotic system (1D-SAW) and the three-strand structure of DNA. Firstly, a new 1D-SAW chaotic system was designed. By introducing nonlinear terms and periodic disturbances, this system is capable of generating chaotic sequences with high randomness and initial value sensitivity. Secondly, a new diffusion rule based on the three-strand structure of DNA is proposed. Compared with the traditional DNA encoding and XOR operation, this rule further enhances the complexity and anti-attack ability of the encryption process. Finally, the security and randomness of the 1D-SAW and image encryption algorithms were verified through various tests. Results show that this method exhibits better performance in resisting statistical attacks and differential attacks.

Keywords: SHA-256 hash function; one-dimensional chaotic system; security analysis; three-stranded structure of DNA.

Figure 1

(A): A DNA three-stranded structure containing two triplet base pairs, C⁺-G-C and T-A-T, (B): A DNA three-stranded structure containing two triplet base pairs, G-G-C and A-A-T. (created in BioRender. Hisey, J. (2024). https://BioRender.com/f14l364, accessed on 26 November 2024).

Figure 2

The LE values of 1D-SAW, 1-DSP, 1D quadratic chaotic map, 1-DSCM, and 1D-SLCM.

Figure 3

The initial value and parameter perturbation of 1D-SAW.

Figure 4

Bifurcation diagram of 1D-SAW.

Figure 5

The SE values of 1D-SAW, 1-DSP, 1D quadratic chaotic map, 1-DSCM, and 1D-SLCM.

Figure 6

The 0-1 test results of 1D-SAW, 1-DSP, 1D quadratic chaotic map, 1-DSCM and 1D-SLCM.

Figure 7

The visual representation of the proposed method.

Figure 8

Original images and encrypted images.

Figure 9

Histogram analysis of baboon.

Figure 10

Correlation analysis of original and encrypted baboon image in four directions.

Figure 11

Encryption results for all-black and all-white images.

Figure 12

(a) 0.01 Gaussian noise attack, (b,d,f,h,j,l,n,p) the decrypted images, (c) 0.01 Salt & Pepper noise attack, (e) 0.01 speckle noise attack, (g) 0.05 speckle noise attack, (i,k) 10% unilateral cropping attack. (m,o) ≈20% multilateral cropping attack.