Novel 1-D enhanced Log-logistic chaotic map and asymmetric generalized Gaussian apertured FrFT for image encryption

This paper proposes a 1-D enhanced Log-logistic chaotic map (1-DELLCM) and an asymmetric generalized Gaussian apertured fractional Fourier transform (AGGAFrFT). The 1-DELLCM is a new chaotic map that introduces the nonlinear function log2(1 + x) into the traditional logistic map. This modification leads to a more intricate behavior and an expanded spectrum of chaos. On the other hand, the AGGAFrFT utilizes the asymmetric generalized Gaussian distribution with three shaping parameters as the soft aperture in the fractional Fourier optical system. This design choice enables the AGGAFrFT to exhibit a low-pass filtering performance, which helps to resist noise attacks to some extent. To bolster the sensitivity of the three shaping parameters, an iterative image encryption algorithm has been devised to create an apertured phase mask utilized for encrypting images. Based on the experimental outcomes, the sensitivities of the three shaping parameters, fractional order, and wavelength for AGGAFrFT are found to be at least up to 10−15. Additionally, experimental findings demonstrate that incorporating 1-DELLCM and AGGAFrFT into the proposed algorithm significantly bolsters the encryption process's security, rendering it resilient against diverse attacks, particularly noise attacks.