Main Ideas and Contributions of This Study

In this study, the secret sharing proposed by Shamir in 1979 is utilized to develop a series of image authentication methods with data recovery capabilities. The original aim of the secret sharing method is to deal with the issue of key management in cryptographic systems. This technique transforms the value of a key into many data pieces, called secret shares, which are then distributed to some participants. At a later time, the value of the key can be reconstructed using a sufficient number, but not necessarily all, of the shares. This results in a property of loss-tolerant capability, which inspires us to apply such a secret sharing technique to develop a data recovery capability for the image authentication method. Accordingly, the content of the image to be authenticated may be transformed into many secret shares; and can be recovered, even if tampered with, when a sufficient number of shares are collected.

However, a problem one may encounter here is how to find enough space in an image to accommodate the secret shares. The embedding spaces in the spatial or frequency domain provided by conventional methods seem insufficient to satisfy the requirement of large-volume spaces for embedding the shares. To deal with this issue, the PNG image with an alpha channel plane is explored in this study to solve the problem. Meanwhile, the transparency of the alpha channel is also utilized to provide a camouflage effect to the embedded secret shares, resulting in a nearly transparent image.

In addition to the previously-mentioned inspiration of using the secret sharing technique, in the following we state further more benefits of using the secret sharing method for data recovery in the image authentication methods to be proposed later in

this thesis. Moreover, some additional new ideas behind other methods proposed in this study are also described in this section. Finally, the main contributions made in this study are listed.

A. Why secret sharing

An intuitive strategy for image recovery in an image authentication method is data duplication, which means that multiple copies of image data are created and stored somewhere in the image itself. Accordingly, if the image is damaged to some extent, it may be recovered by utilizing the surviving copies. This strategy is reasonable but has two drawbacks. The first is that the data sequence in the stored image copies must be known, and the second is that if a part of the stored image data is destroyed, the image content will possibly not be recoverable even when other parts of the image data are retained.

In this study, we propose the use of the Shamir secret sharing method, also called the (k, n)-thresholding method, to overcome the two drawbacks mentioned above. By the method, the original data are transformed into n shares, and when k of the n shares are collected, the original data can be reconstructed without the prior knowledge of the data sequence. As a result, a higher capability of fault tolerance is yielded. This merit is not found in the approach of data duplication. An example for revealing this merit is shown in Fig. 1.2.

Specifically, in the upper rectangle shown in Fig. 1.2, the original data consisting of two parts, “10” and “20,” are duplicated into three copies to become six digits as shown in the figure. Then, if two digits, both “20,” survive attacks, the original data unfortunately cannot be reconstructed because both are the same value “20.” On the other hand, the rectangle shown below in the figure illustrates the case of (2, 6)-thresholding. The original data 10 and 20 are transformed into 6 shares, and even if only two shares survive, the original data can still be reconstructed without errors.

This reveals that in the same condition of collecting two surviving digits, the capability of fault tolerance provided by the (k, n)-thresholding method is better than that provided by the data duplication scheme.

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Fig. 1.2 Illustration of the better capability in fault tolerance of using secret sharing than using data duplication.

B. Other new ideas proposed in this study for enhancing multimedia security

In the field of steganography, the existing methods are mostly only concerned with statistical undetectability and none of them can promise the receiver that the message that he/she extracts from a stego-file is trusty and intact. To deal with this weakness, we propose in this study a new steganographic method with a self-authentication capability for secret data hiding in spreadsheets using the secret sharing technique. In the method, a scheme of (k, k+1)-threshold secret sharing is developed for the first time to provide a self-authentication capability by checking the value-consistency of k + 1 results coming from all k + 1 combinations to determine whether an extracted secret is intact or not.

Finally, in the field of reversible data hiding, histogram shifting is an efficient technique used in many related methods. However, an issue of how to share the information of the used peak points between the sender and the receiver remains to be solved. In this study, a new histogram-shifting-based blind reversible data hiding method composed of two-phase iterations for more effective data hiding is proposed.

With the cooperation of the two data hiding phases based on histogram shifting, the proposed method skillfully stores the value of the peak point yielded in phase 1 via the use of phase 2, solving the common problem of sharing the peak information between the two parties.

C. Main contributions of this study

The main contributions of this thesis study are summarized in the following.

1. A new blind image authentication method with a data repair capability for binary-like grayscale document images based on secret sharing is proposed.

The proposed method has higher possibility to survive image content attacks and provides pixel-level repairs of tampered image parts.

2. A new approach to binary image authentication based on the uses of PNG images and the secret sharing technique with a self-recovery capability for repairing tampered image data is proposed. The proposed method has the capabilities of tampering detection, tampering localization, and tampering recovery, and also has the capability of reversing the tampered image to its original content.

3. A new data hiding method via PNG images based on Shamir’s (k, n)-threshold secret sharing scheme is proposed and can be applied to color image authentication. The proposed image authentication method possesses the merits of losslessness during image authentication, high sensitivity to image alterations, good tampering localization capability, and very low false acceptance and rejection ratios.

4. A new blind pixel-level self-repairing grayscale image authentication method, which is optimal under a minimax criterion of image distortion reduction, is proposed. The proposed method develops the “bin code” for use both as an authentication signal for the image pixel and as an index for generating the data for repairing the image pixel when it is authenticated to have been tampered with.

5. A new covert communication method with a self-authentication capability for secret data hiding in spreadsheets using the information sharing technique is proposed. In the proposed method, the presence of the steganographic content is statistically undetectable and a receiver can confirm the correctness of the extracted secret message.

6. A blind two-phase reversible data hiding method based on histogram shifting is proposed. The proposed method has the advantageous property of blindness and significantly improves the data hiding capacity while keeping low degradations of the image quality when compared with other methods.

In addition, a summarized table listing applications for which the aforementioned proposed methods are developed is given in the following.

Table 1.1 Proper applications of proposed methods.

Image authentication

Covert Communication

Copyright protection

Data Association

1st method ^▲

2nd method ^▲

3rd method ^{▲ ▲}

4th method ^▲

5th method ▲

6th method ^{▲ ▲}