Problem Description

Table of contents

• Introduction
• Algorithm
  • Encoding
  • Decoding
• Citations

Introduction

A fragile watermark is simply a mark likely to become undetectable after an original is modified in any way.

One fragile watermarking scheme will be described below. Because fragile marks are not our focus, we do not intend to have a full coverage on this topic. The scheme to be discussed was proposed by Wong (Wong 1998). The basic idea is to create a picture-dependent mark that is embedded in the least significant bits (LSB) of an image in the spatial domain. The author borrowed the public-key encryption technique to produce a mark so that it is hard to fabricate by an attacker. [1, p16]

Algorithm

The following scheme is a Least Significant Bit (LSB) replacement using RSA Encryption to encode the MD5 hash of an 32x32 pixel block which is then XORed with a watermark.

The encoding and decoding using an 8x8 pixel block will not work for the current RSA scheme today. RSA uses either 1024 bit (32 bytes) or 2048 bit (64 bytes) encryption. An 8x8 pixel block only allows 64 bits of encrypted bytes to be stored. Since we need to store 128 bits at the minimum, we will need a block size that is greater than or equal to 32x32.

Encoding

The encoding or embedding block diagram of this scheme is depicted in Figure 5. Let the original image X be 8 bits per pixel with image size M x N. X is first partitioned into blocks, for example, blocks with sizes 8 x 8. And then each block, X_r, is brought into the system from the lower left comer in Figure 5. The LSB’s of X_r are discarded. The seven most significant bits in X_r after discarding the LSB’s and the entire image X with size M x N are combined and mapped into a long bitstream, P_r, by a hash function. The Internet MD5 hash function is adopted in (Wong 1998). The length of P_r should be larger than the pixel number of an image block X_r, L. In case the length of P_r is longer than needed, only the first L bits are used, and the L-bit binary pattern is served as the watermark B_r. Next, performing the exclusive-or (XOR) operation with both the watermark to be embedded, B_r, and the hashed pattern, P_r. The result, W_r, is encrypted using the private key K‘ in a public key cryptography system, for instance, the RSA system (Rivest et al. 1978), and finally the output, C_r (an L-bit string), replaces the LSB’s of the original image block. [1, p18]

Decoding

The decoding or extracting procedure is pretty much the inverse operation of the encoding procedure step by step. The decoder diagram is shown in Figure 6. Note that the public-key decryption block uses the public key K. And it is reported in (Wong 1998) that this fragile mark has been tested for cropping, image size scaling, and pixel alternation. [1, p18]

Citations

1. J. Pan et al., "Fragile watermarks" in Intelligent Watermarking Techniques, River Edge, N.J.: World Scientific, 2004, ch. 5, sec. 5.2.2, pp. 18-19.