# Security analysis of a self-embedding fragile image watermark scheme

## TL;DR

This paper critically analyzes a self-embedding fragile image watermark scheme, revealing its vulnerabilities to collage and multiple stego-image attacks, and provides a detailed security assessment based on permutation complexity.

## Contribution

It identifies security flaws in the scheme, especially its block independence and key generation process, and quantifies the difficulty of key recovery through permutation analysis.

## Key findings

- Scheme is vulnerable to collage attack.
- Authentication bits are not key-dependent.
- Permutation complexity for key recovery is factorial in block size.

## Abstract

Recently, a self-embedding fragile watermark scheme based on reference-bits interleaving and adaptive selection of embedding mode was proposed. Reference bits are derived from the scrambled MSB bits of a cover image, and then are combined with authentication bits to form the watermark bits for LSB embedding. We find this algorithm has a feature of block independence of embedding watermark such that it is vulnerable to a collage attack. In addition, because the generation of authentication bits via hash function operations is not related to secret keys, we analyze this algorithm by a multiple stego-image attack. We find that the cost of obtaining all the permutation relations of $l\cdot b^2$ watermark bits of each block (i.e., equivalent permutation keys) is about $(l\cdot b^2)!$ for the embedding mode $(m, l)$, where $m$ MSB layers of a cover image are used for generating reference bits and $l$ LSB layers for embedding watermark, and $b\times b$ is the size of image block. The simulation results and the statistical results demonstrate our analysis is effective.