Enhancing image security via chaotic maps, Fibonacci, Tribonacci transformations, and DWT diffusion: a robust data encryption approach

Abstract

Abstract In recent years, numerous image encryption schemes have been developed that demonstrate different levels of effectiveness in terms of robust security and real-time applications. While a few of them outperform in terms of robust security, others perform well for real-time applications where less processing time is required. Balancing these two aspects poses a challenge, aiming to achieve efficient encryption without compromising security. To address this challenge, the proposed research presents a robust data security approach for encrypting grayscale images, comprising five key phases. The first and second phases of the proposed encryption framework are dedicated to the generation of secret keys and the confusion stage, respectively. While the level-1, level-2, and level-2 diffusions are performed in phases 3, 4, and 5, respectively, The proposed approach begins with secret key generation using chaotic maps for the initial pixel scrambling in the plaintext image, followed by employing the Fibonacci Transformation (FT) for an additional layer of pixel shuffling. To enhance security, Tribonacci Transformation (TT) creates level-1 diffusion in the permuted image. Level-2 diffusion is introduced to further strengthen the diffusion within the plaintext image, which is achieved by decomposing the diffused image into eight-bit planes and implementing XOR operations with corresponding bit planes that are extracted from the key image. After that, the discrete wavelet transform (DWT) is employed to develop secondary keys. The DWT frequency sub-band (high-frequency sub-band) is substituted using the substitution box process. This creates further diffusion (level 3 diffusion) to make it difficult for an attacker to recover the plaintext image from an encrypted image. Several statistical tests, including mean square error analysis, histogram variance analysis, entropy assessment, peak signal-to-noise ratio evaluation, correlation analysis, key space evaluation, and key sensitivity analysis, demonstrate the effectiveness of the proposed work. The proposed encryption framework achieves significant statistical values, with entropy, correlation, energy, and histogram variance values standing at 7.999, 0.0001, 0.0156, and 6458, respectively. These results contribute to its robustness against cyberattacks. Moreover, the processing time of the proposed encryption framework is less than one second, which makes it more suitable for real-world applications. A detailed comparative analysis with the existing methods based on chaos, DWT, Tribonacci transformation (TT), and Fibonacci transformation (FT) reveals that the proposed encryption scheme outperforms the existing ones.