# A Content-Aware Pure Permutation with Intrinsic Avalanche Effect: Breaking the Diffusion-Permutation Dichotomy

arXiv: https://arxiv.org/abs/2608.09452 · HTML: https://mlsanity.com/paper/2608.09452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 40 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Built on by (most cited first, 1 of 1)

- [Bit-Level Triangular Content-Aware Permutation for Fragile Image Watermarking: Zero False Positive Rate, Single-Bit Sensitivity, and Arbitrary Dimension Support](https://mlsanity.com/paper/2608.14800/) (2026)

## Abstract (arXiv)

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.