Survey on Using Chaotic Maps in Image Encryption Techniques

Abstract

In this work, a direct experiment realization is proposed to encrypt 256×256 pixels grayscale image by using five different chaotic systems (Logistic, Tent, Henon, Lorenz, and a Logistic–Tent hybrid system). The permutation and diffusion process were executed with chaotic sequences derived from the same maps in order to quantitatively analyze the influence of each chaotic system on the statistical security metrics and the computation cost in a single unified execution environment. The results indicate that the quality of randomness was increased by increasing the complexity of the chaotic map as the entropy values were 7.91 for the Logistic map and 7.94 for the Tent map, 7.96 for the Henon map, 7.98 for the Lorenz system and a maximum of 7.99 for the hybrid model. This is a 0.08 better than worst model and it is closer to ideal entropy value 8. At the same time, the correlation coefficient of two adjacent pixels sharply reduced from 0.0043 to 0.0008, about 81% of decrease, which quantitatively verifying that the spatial dependencies in plain images is almost completely eliminated in the encrypted images.  Regarding differential diffusion, all schemes attained NPCR values above 99.5%; however, the Lorenz system and the hybrid model yielded the best values of 99.71% and 99.74%, accompanied by UACI of 33.42% and 33.45%. This means that on average the intensity of a plain-pixel change was magnitude 33 variation to the average among 99.7% cipher-pixels. This numerical behaviour is mirrored in key sensitivity tests where a change in the control parameter μ or the initial condition x₀ in the 6th decimal place causes total decryption breakdown which is quantitatively in line with the large values of NPCR and UACI and establishes the presence of an extremely sensitive and non-approximable effective key space. The run times were 0.38 s and 0.42 s for the Tent map and the Logistic map, respectively, and rose to 0.50 s for the Henon map, and 0.63 s for the Lorenz system, whereas the hybrid model realized a medium execution time of 0.56 s. There is thus a clear quantitative trade-off between the security and the computational cost, as the marginal entropy increase of 0.01–0.02 in the Lorenz system was reached at an extra cost of 0.07 s with respect to the hybrid scheme, for this reason the security-to-time ratio of the latter was bigger. Also, when numerically compared with traditional algorithms, the hybrid chaotic approach provided better performance than AES in entropy value (7.99 compared to 7.85), in diminishing pixel correlation by up to 95% (0.0008 compared to 0.015), and in reducing execution time by 0.16 seconds. These results clearly illustrate that hybrid chaotic encryption can be expected to provide much better statistical security along with faster computation, which suggests that it is suitable for real-time image encryption and for use in systems with limited resource.