Source-linked AI summary
A combination chaotic system and application in color image encryption
R. Parvaz, M. Zarebnia
TL;DR
The paper addresses image encryption by constructing a combination chaotic system from Logistic, Sine, and Tent maps. It applies the system to color, grayscale, and binary images and evaluates security through simulation analyses. The reported results indicate resistance to several attack types and practical encryption behavior.
Problem
Image security has become increasingly important for network-based image transfer, while individual Logistic, Sine, and Tent maps have disadvantages for encryption.
Method
The paper constructs a combination chaotic system and uses it with XOR and circular shifts to encrypt color, grayscale, and binary images.
Results
The proposed algorithm is reported to resist differential, statistical, noise, data-loss, and chosen-plaintext attacks.
Takeaways & Limitations
The proposed chaotic system supports an image-encryption algorithm applicable to color, grayscale, and binary images.
Abstract
from arXiv · showhide
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.
R. Parvaza∗, M. Zarebniaa†
The paper concerns encryption, color images, chaotic systems, and cyclic shifts.
- The paper addresses image encryption.
- Its scope includes color images.
- The approach involves chaotic systems and cyclic shifts.
1 Introduction
The paper motivates image security for network communication and introduces an encryption algorithm based on combination maps, XOR, and circular shifts. The algorithm partitions color images, encrypts the parts, recombines them, and repeats the combined-image encryption.
- 1 Introduction: Image security is increasingly important as network communication develops and image transfer expands.
- 1 Introduction: Logistic, Sine, and Tent maps are used because of their sensitivity to initial values and control parameters.
- 1 Introduction: The proposed encryption algorithm combines a combination map, XOR operation, and circular shift.
- 1 Introduction: The algorithm divides a color image into twelve parts and encrypts each part using the combination map.
- 1 Introduction: After recombining the encrypted parts, the algorithm repeats encryption on the combined image.
2 A combination chaotic system
The paper defines a Logistic-, Sine-, and Tent-based combination chaotic system and studies its chaotic behavior through Lyapunov exponents, bifurcation diagrams, cobweb plots, and output distributions.
- 2 A combination chaotic system: The Logistic-Tent system can remain nonchaotic for some parameters and has a non-flat output histogram, motivating weighted combinations.
- 2 A combination chaotic system: The proposed combination system incorporates a Logistic or Sine map with weighted functions and configurable real parameters.
- 2 A combination chaotic system: The Lyapunov exponent is defined as the long-run average of ln |G′_r(x_i)| along an orbit.
- 2 A combination chaotic system: A positive average Lyapunov exponent indicates chaos, whereas negative and zero values correspond to periodic or bifurcation behavior, respectively.
- 2 A combination chaotic system: Cases (ii) and (iii) have positive Lyapunov exponents across r ∈(0, 4] and more uniform output distributions than the Logistic-Tent comparison.
3 Proposed encryption and decryption process
The proposed algorithm encrypts color images by generating chaotic sequences, dividing each image into twelve parts, applying shifts and bitwise operations, and recombining the parts. It also specifies adaptations for grayscale or binary images and uses inverse operations for decryption.
- Encryption process: The encryption process assumes an m × n color image and begins by determining chaotic sequences from initial values and parameters.
- Encryption process: Cyclic shifts, generated matrices, and bitxor operations are applied to transform the image parts during encryption.
- Encryption process: Each color image is divided into twelve parts by separating red, green, and blue channels and splitting each channel into four equal parts.
- Decryption process: Decryption reverses the encryption process, using the inverse of Div(·) and corresponding inverse transformations to reconstruct the image.
- Encryption process: The joined encrypted image is further transformed with channel-specific and whole-image circshift operations before producing the final encrypted image.
4 Simulation results and security analysis
Simulations evaluate the encryption algorithm across color, grayscale, and binary images, while security analyses test key sensitivity, statistical properties, differential attacks, noise, data loss, and chosen-plaintext attacks.
- Simulation results: The experiments cover color, grayscale, and binary images, including a difficult binary case transformed into a noise-like encrypted image with a flat histogram.Test images include Sailboat on lake, Airplane, Lena, girl, and Horse; encryption and decryption times are also reported.
- Security key analysis: A change of 10^-15 in r0 prevents reconstruction of the original image during decryption, indicating high key sensitivity.The altered parameter is r0 = 2 + 10^-15, producing decrypted results that cannot reconstruct the original image.
- Statistical analysis: Original images have high pixel correlation, whereas encrypted images have very low correlation values, supporting the statistical analysis of encryption security.Correlation distributions for the original and encrypted Lena images are also shown in Fig. 11.
- Statistical analysis: Information-entropy results are close to the maximum value, and encrypted-image histograms are flat while plain-image histograms are not.The entropy test evaluates image randomness over the range [0, 8].
- Sensitivity analysis: After changing one plaintext pixel, NPCR and UACI results are close to their ideal values in the tested Lena, Sailboat on lake, and Airplane images.The modified pixels are A(200, 150, 1), A(100, 250, 2), and A(180, 334, 3), each changed to 0.
- Noise and data-loss attacks: Decryption retains most original visual information after removing a 200 × 200 encrypted region or adding zero-mean Gaussian noise with different variances.The reconstructed images remain recognizable in the reported data-loss and noise experiments.
- Chosen-plaintext attack: Random numbers in the first encryption step produce different ciphertexts for repeated encryption of the same image, supporting resistance to chosen-plaintext attacks.The comparison uses the pixel-to-pixel difference |C1 − C2| between two encrypted images.
5 Conclusion
The paper constructs a Logistic–Tent combination chaotic system and proposes an image-encryption algorithm that resists several attacks. Figure 14 illustrates differing encrypted outputs and their pixel-to-pixel difference when the same key is reused.
- The proposed system combines Logistic and Tent systems to produce a large number of chaotic maps.
- The associated encryption algorithm is reported to resist differential, statistical, noise, data loss, and chosen-plaintext attacks.
- Figure 14 compares the original image with first and second encrypted images, their histograms, and the pixel-to-pixel difference.