An image encryption algorithm based on new generalized fusion fractal structure

Abstract

The design and utilization of suitable fractal structures is one of the prominent areas of security for the protection of digital data. This paper proposes a generalized fusion fractal structure by combining two one-dimensional fractals as seed functions from a larger spectrum of fractal functions. A fusion fractal termed as PLFF is formulated by combining traditional Phoenix and Lambda fractals. Improved randomized phase space, self-similar structure on various magnification scales, and fractional dimension are found in the resultant PLFF fractal. The capacity of PLFF to create a pseudo-random number (PRN) sequence in both integer and binary format is validated by its increased complexity and enhanced chaotic range. The generated PRN sequences feature a significant degree of uncorrelation and randomness. A novel image encryption algorithm based on the new PLFF fractal function is proposed which utilizes a generated PRN sequence as secret key. Standard security evaluations such as histogram variance, NPCR and UACI tests for plain-image sensitivity, key sensitivity, information entropy, pixel correlation, and noise and data loss, etc. are used to analyze the performance of the proposed encryption algorithm. The simulation results revealed performance indicators such as entropies > 7.997, NPCR > 96.6, UACI > 33.5, high throughput of ∼ 6MBps, and highly uncorrelated neighboring pixels in encrypted images. The findings are also compared with some current image encryption schemes, demonstrating that the proposed digital image encryption algorithm performs well.