Image encryption algorithm integrating multi-chaotic key fusion and bipolar fuzzy diffusion

The rapid growth of digital communication and cloud-based multimedia applications has significantly increased the demand for secure image encryption techniques capable of protecting visual information from unauthorized access and malicious attacks. In this study, a novel image encryption framework based on triple-chaotic key fusion and bipolar fuzzy based diffusion is proposed. The encryption scheme integrates three nonlinear chaotic systems, namely the Logistic map, Chebyshev map, and Circle map, to generate highly random pseudo-random sequences for key construction. The generated chaotic sequences are fused through modular arithmetic to enlarge the key space and enhance unpredictability. Furthermore, a bipolar fuzzy sets mechanism is introduced to construct an additional diffusion layer that strengthens encryption complexity and improves resistance against statistical and differential attacks. The proposed cryptosystem employs a permutation-diffusion architecture in which chaotic permutation destroys pixel correlations, while multi-stage XOR diffusion and bipolar fuzzy transformation provide strong confusion and diffusion properties. Experimental evaluations are conducted using benchmark grayscale images, including Flower and Leaves images. The encrypted images achieve entropy values of 7.999834 and 7.999990, respectively, which are extremely close to the theoretical maximum entropy value of 8. The correlation coefficients between adjacent pixels in the original uncoded images are around 0.998, whereas the correlation coefficient of adjacent pixels in the coded images are near zero; therefore, adjacent pixels are effectively decorrelated through this encrypting process. The histogram, entropy, correlation, NPCR, and UACI analysis results confirm the good security performance of our proposed method. The decrypted images accurately recover the original images with little or no distortion to support the claim of reversibility and reliability of the scheme. The results indicate that our proposed triple chaotic acoustic fuzzy image encryption framework has very high security, very strong randomness, and very strong resistance to statistical and differential attacks using cryptanalysis methods.