Overview of this dissertation

In this dissertation, several techniques to protect digital images are proposed for various applications. The proposed methods contain a flip VC method, a fast weighted image sharing method, a data hiding method, and a semi-fragile watermarking method. Fig. 1.2 shows the framework of the dissertation, and the brief overview of each proposed method is given in the subsections below.

Fig. 1.2. The framework of this dissertation.

1.3.1 Flip Visual Cryptography (FVC) with perfect security, conditionally optimal contrast, and no expansion

In Chapter 2, a flip visual cryptography (FVC) scheme is proposed. The proposed FVC scheme encodes two secret images into two dual-purpose transparencies. Sixteen basis matrices are designed to encode a pair of pixels of the two secret images, respectively. If the stacking result representing black pixels in the secret image is restricted (or not restricted, respectively) to be 100% opaque, we have two designs called opaque-oriented FVC and non-opaque-oriented FVC in the proposed scheme. We also prove that the contrast in our design here is conditionally optimal, no matter whether opaque-oriented FVC or non-opaque-oriented FVC is used.

Image security

To disperse secret images To protect content or accuracy of images

Flip Visual Cryptography

(Ch. 2)

Fast weighted secret image

sharing (Ch 3)

A hiding method based on a Weighted-sum

function (Ch. 4)

Semi-fragile watermarking with

recovery ability (Ch. 5)

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1.3.2 Fast weighted secret image sharing

Chapter 3 contains two topics. First, we bring up a weighted secret image sharing method. The method is based on polynomial division over a finite field. The size of each shadow depends on the weight choosen by the user. When an image has sufficient shadows where the sum of weights is larger than a pre-defined threshold, the secret image can be decoded by utilizing the extended Lagrange polynomial. When all weights are defined as 1, the proposed method is the same with Thien and Lin’s method [7]. Then, by observing characteristics of GF(2^k), a fast encoding algorithm under GF(2^k) is proposed. The encoding algorithm is a recursive function, and the running time depends only on the size of the secret image.

1.3.3 Weighted-sum function (WSF) − a gray-scale image hiding method with competitive PSNR over a wide range of embedding rates

In Chapter 4, a hiding method is proposed based on a weighted-sum function. With this method, m secret bits are embedded in z pixels, and the secret bits can be extracted by executing a weighted-sum function. To minimize distortion, two optimization patterns are proposed. First, to reduce the running time of obtaining the best values of stego-pixels, a table T is dynamically generated and the stego-pixels are calculated by looking up table T; second, to decide the weight values in weighted-sum functions with various embedding rates, some suggested weights based on exhaustive research are given in Table 3.2. The advantages of the proposed method include: (1) A wide range of embedding rates (such as 0.5 to 4 bits per pixel), (2) Competitive image quality over the whole wide range, (3) Once the embedding rate is given, our look-up table can predict the PSNR value, even before the actual embedding.

1.3.4 Authentication and recovery of an Image by using sharing and lattice-embedding In Chapter 5, we propose a semi-fragile watermarking method based on secret sharing and lattice-embedding. Using this method, a host image is transformed into an 8×8 DCT domain, and the coefficients in each DCT block are shared among many shadows by two-layer sharing[68]. Each shadow is then embedded in a DCT block by lattice-embedding.

Because the shadow is embedded in the DCT domain, shadow data that pass certain degree of JPEG compression remain intact. However, the repairing area is smaller than the fragile version, due to the smaller embedding capacity. As shown in experiments, the watermarked

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image can resist some content-preserving operations such as JPEG compression, Gaussian noise, or brightness adjustment.

1.4 Organization

The organization of the rest chapters of the dissertation is listed below. Flip Visual Cryptography is addressed in Chapter 2. Fast weighted secret image sharing is addressed in Chapter 3. A hiding method based on a weighted-sum function is addressed in Chapter 4. An image authentication method using semi-fragile watermarking with recovery ability is addressed in Chapter 5. Finally, the conclusion and the future works of this dissertation are given in Chapter 6.

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Chapter 2

Flip Visual Cryptography (FVC) with perfect security, conditionally optimal contrast, and no expansion

This chapter proposes a flip visual cryptography (FVC) scheme with perfect security, conditionally optimal contrast, and no expansion of size. The proposed FVC scheme encodes two secret images into two dual-purpose transparencies. Stacking the two transparencies can reveal one secret image. Flipping one of the two transparencies and then stacking with the other transparency can reveal the second secret image. The proposed scheme is proved to have conditionally optimal contrast: its contrast is optimal if the double-secrets non-expanded FVC scheme is required to have perfect security. The perfect security is also proved.

The remainder of this chapter is organized as follows: The proposed opaque-oriented FVC scheme and non-opaque-oriented FVC scheme are stated in Sec. 2.1, respectively.

Experimental results are shown in Sec. 2.2. Some discussions are shown in Sec. 2.3, and the conclusions are in Sec. 2.3. In Sec. 2.5, we prove that the contrast 1/6 (and 1/4, respectively) is conditionally optimal among the opaque-oriented FVC schemes (and non-opaque-oriented FVC schemes, respectively) that use basis-matrices design with perfect security.

Notations in this chapter:

ht The height of the secret image.

wh The width of the secret image.

S1, S2 Two binary secret images in which the size is ht×wh.

B, W Black and white.

T1, T2 Two generated transparencies.

S ′ ,1 S ′ ₂ Two stacking results which are similar to S1 and S2, respectively.

r The width of basis matrices.

b the minimal luminance transmission to represent B in stacking results.

w the minimal luminance transmission to represent W in stacking results.

α The contrast which is w – b.

⊗ Stacking operation.

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