A Content-Aware Pure Permutation with Intrinsic Avalanche Effect: Breaking the Diffusion-Permutation Dichotomy
2026-08-10 • Computer Vision and Pattern Recognition
Computer Vision and Pattern RecognitionCryptography and Security
AI summaryⓘ
The authors show that simply rearranging pixels in an image (called permutation) can actually make the image very sensitive to tiny changes, which was previously thought impossible. They created a new method called Triangular Content-Aware Permutation (TCA) that uses edges and triangles in the image to decide how to shuffle pixels. When one pixel changes, the whole pattern changes a lot, creating a strong 'avalanche' effect without altering pixel values. Their tests show that TCA outperforms traditional methods in detecting small changes, making it useful for secure image applications like watermarking and encryption.
Pixel permutationNPCRUACICanny edge detectionDelaunay triangulationDifferential sensitivityImage encryptionWatermarkingSteganographyPSNR
Authors
Zahra Ghoraeian, Mohammad-Reza Sadeghi, Samaneh Mashhadi
Abstract
Pixel permutation is a fundamental tool in image processing, image encryption, and data hiding (including watermarking and steganography) that rearranges pixels without changing their values. A common assumption in the literature is that permutation alone cannot create differential sensitivity; changing one pixel merely relocates that pixel in the output, producing no avalanche effect. This paper challenges this by introducing the Triangular Content-Aware Permutation (TCA) algorithm. The method extracts edge points using Canny and applies Delaunay Triangulation to edges and corners, creating a unique partition. Since triangulation is highly sensitive to image geometry, changing a single pixel alters the edge map, resulting in a completely different triangulation and global permutation pattern. Unlike classical dimension-based permutations and advanced content-aware methods (2025-2026), which lack differential sensitivity, TCA increases NPCR from near-zero to 97.10% solely through pixel relocation. Experiments on 50 images show that TCA, with an average of 14.81 iterations, achieves NPCR = 97.10% and UACI = 20.06%, proving pure permutation can create significant differential sensitivity. Conventional methods maintain near-zero NPCR. The iteration threshold varies from 6.4 to 30.7 based on content complexity. Low PSNR (11.93 dB) and near-zero correlation (~10^-3) confirm superior statistical performance. Although slower than classical methods due to triangulation, this is a deliberate trade-off for stronger security. Given the non-analytic, content-dependent nature of the pattern, TCA is ideal for reference-based encryption, fragile watermarking, and non-blind steganography.