Novel Image Encryption Using a Pseudoset Generated by Chaotic Permutation Multicircular Shrinking with a Gradual Deletion of the Input Set

High-level security with a large keyspace and a short processing time is needed in digital image encryption. Generally, an encryption method that produces a large keyspace is characterized by a relatively slow encryption process. In this paper, we propose a new image encryption method that uses two chaotic pseudosets. A gradual deletion of the input set (GDIS) is introduced to enhance the process of chaotic permutation multicircular shrinking (CPMCS), herein referred to as GDIS CPMCS, to diffuse the image pixels and control the shift distance of the row and column rotations of an image. The proposed encryption scheme offers some advantages: it has a larger keyspace than the referenced image encryption schemes and a shorter processing time than CPMCS. The processing time of the proposed image encryption method with the GDIS CPMCS algorithm is 16.7 times faster for a gray image and 43 times faster for a color image than that in our previous work. Based on histogram and entropy analyses, the proposed scheme is also robust to statistical analysis. Moreover, the ciphered image has a very high degree of randomness according to the National Institute of Standards and Technology (NIST) randomness test results. In terms of differential analysis, a one-bit change in the original image leads to a substantial change in the ciphered image, as indicated by the unified average change intensity (UACI) and number of pixel change rate (NPCR) scores of 33.45% and 99.61%, respectively. Furthermore, GDIS CPMCS is robust to salt-and-pepper, Poisson, Gaussian, and speckle noise, with peak signal-to-noise ratios (PSNRs) higher than 14. The scheme is also robust to data loss since a reconstructed image with 50% data loss can be recognized, as indicated by a PSNR of 11.4.