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1

An Image Authentication Based on Discrete Fourier Transform

Kieu T.D., Chang C-C.

Fundamenta Informaticae

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2009

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Vol. 97, nr 4

369-379

EN

The advances of network technologies and digital devices facilitate users to exchange multimedia data over the public networks. However, this also raises significant concerns about how to protect sensitive multimedia data from being illegally copied and unauthorized modifications. Thus, this paper proposes a fragile watermarking method to detect illegitimate alterations of the watermarked data. The proposed method embeds a grayscale watermark image into a grayscale cover image in a block-by-block manner by using discrete Fourier transform. Experimental results show that the proposedmethod can successfully and exactly detect and localize any tampered regions of the watermarked image.

2

High Capacity Data Hiding for Grayscale Images

Chang C-C., Chou Y-C., Kieu T.D.

Fundamenta Informaticae

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2008

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Vol. 86, nr 4

435-446

EN

High embedding capacity and low image distortion factors are main concerns of information hiding researchers. No scheme can achieve these two factors simultaneously. The purpose of achieving either high embedding capacity or low image distortion varies from application to application. This paper presents a high embedding capacity information hiding method for grayscale images. The proposed method converts binary secret data into secret digits in the base-5 numeral system first. Next, one secret digit in the base-5 numeral system is embedded into one cover pixel. The experimental results show that the proposed method can be used to embed two secret bits into one cover pixel with the imperceptible image distortion. Comparing with some other works, we found that our method indeed outperforms all others in terms of embedding capacity.

3

On the existence of a new family of Diophantine equations for Omega

Ord T., Kieu T.D.

Fundamenta Informaticae

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2003

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Vol. 56, nr 3

273-284

EN

We show how to determine the k-th bit of Chaitin's algorithmically random real number W by solving k instances of the halting problem. From this we then reduce the problem of determining the k-th bit of W to determining whether a certain Diophantine equation with two parameters, k and N, has solutions for an odd or an even number of values of N. We also demonstrate two further examples of W in number theory: an exponential Diophantine equation with a parameter k which has an odd number of solutions iff the k-th bit of W is 1, and a polynomial of positive integer variables and a parameter k that takes on an odd number of positive values iff the k-th bit of W is 1.