• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.27-44
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• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.23 no.3
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• pp.359-370
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• 2013

Lin and Chan proposed a reversible secret image sharing scheme in 2010. The advantages of their scheme are as follows: the low distortion ratio, high embedding capacity of shadow images and usage of the reversible. However, their scheme has some problems. First, the number of participants is limited because of modulus prime number m. Second, the overflow can be occurred by additional operations (quantized value and the result value of polynomial) in the secret sharing procedure. Finally, if the coefficient of (t-1)th degree polynomial become zero, (t-1) participants can access secret data. In this paper, an improved reversible secret image sharing scheme which solves the problems of Lin and Chan's scheme while provides the low distortion ratio and high embedding capacity is proposed. The proposed scheme solves the problems that are a limit of a total number of participants, and occurrence of overflow by new polynomial operation over GF($2^8$). Also, it solve problem that the coefficient of (t-1)th degree polynomial become zero by fixed MSB 4-bit constant. In the experimental results, PSNR of their scheme is decreased with the increase of embedding capacity. However, even if the embedding capacity increase, PSNR value of about 45dB or more is maintained uniformly in the proposed scheme.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.225-234
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• 1998

We compute genus distributions for bouquets of dipoles by using the method concerning the cycle structure of permutations in the symmetric group. From this, we can deduce that every bouquet of dipoles is upper embeddable. We find a foumula for computing the embedding polynomials for bouquets of dipoles.

• The Transactions of the Korea Information Processing Society
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• v.13 no.2
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• pp.34-40
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• 2024

Secret sharing is a cryptographic technique that involves dividing a secret or a piece of sensitive information into multiple shares or parts, which can significantly increase the confidentiality of a secret. There has been a lot of research on secret sharing for different contexts or situations. Tassa's conjunctive secret sharing method employs polynomial derivatives to facilitate hierarchical secret sharing. However, the use of derivatives introduces several limitations in hierarchical secret sharing. Firstly, only a single group of participants can be created at each level due to the shares being generated from a sole derivative. Secondly, the method can only reconstruct a secret through conjunction, thereby restricting the specification of arbitrary secret reconstruction conditions. Thirdly, Birkhoff interpolation is required, adding complexity compared to the more accessible Lagrange interpolation used in polynomial-based secret sharing. This paper introduces the multi-compartment secret sharing method as a generalization of the conjunctive hierarchical secret sharing. Our proposed method first encrypts a secret using external groups' shares and then generates internal shares for each group by embedding the encrypted secret value in a polynomial. While the polynomial can be reconstructed with the internal shares, the polynomial just provides the encrypted secret, requiring external shares for decryption. This approach enables the creation of multiple participant groups at a single level. It supports the implementation of arbitrary secret reconstruction conditions, as well as conjunction. Furthermore, the use of polynomials allows the application of Lagrange interpolation.

• Journal of Korea Multimedia Society
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• v.17 no.8
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• pp.953-960
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• 2014

In Shamir's (t,n)-threshold based secret image sharing schemes, there exists a problem that the secret image can be reconstructed when an arbitrary attacker becomes aware of t secret image pieces, or t participants are malicious collusion. It is because that utilizes linear combination polynomial arithmetic operation. In order to overcome the problem, we propose a secret image sharing scheme using matrix decomposition and adversary structure. In the proposed scheme, there is no reconstruction of the secret image even when an arbitrary attacker become aware of t secret image pieces. Also, we utilize a simple matrix decomposition operation in order to improve the security of the secret image. In experiments, we show that performances of embedding capacity and image distortion ratio of the proposed scheme are superior to previous schemes.

• Journal of Korea Multimedia Society
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• v.16 no.5
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• pp.577-590
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• 2013

Shamir's (k,n)-threshold secret sharing scheme is not secure against cheating by attacker because the signature of participants is omitted. To prevent cheating, many schemes have been proposed, and a proactive secret sharing is one of those. The proactive secret sharing is a method to update shares in the secret sharing scheme at irregular intervals. In this paper, a proactive image secret sharing scheme over $GF(2^8)$ is proposed for the first time. For the past 30 years, Galois field operation is widely used in order to perform the efficient and secure bit operation in cryptography, and the proposed scheme with update phase of shadow image over $GF(2^8)$) at irregular intervals provides the lossless and non-compromising of secret image. To evaluate security and efficiency of images (i.e. cover and shadow images) distortion between the proposed scheme and the previous schemes, embedding capacity and PSNR are compared in experiments. The experimental results show that the performances of the embedding capacity and image distortion ratio of the proposed scheme are superior to the previous schemes.

• Journal of Korea Multimedia Society
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• v.18 no.11
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• pp.1332-1341
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• 2015

This paper proposes a novel reversible secret sharing scheme using AES algorithm in encrypted images. In the proposed scheme, a role of the dealer is divided into an image provider and a data hider. The image provider encrypts the cover image with a shared secret key and sends it to the dealer. The dealer embeds the secret data into the encrypted image and transmits encrypted shadow images to the corresponding participants. We utilize Galois polynomial arithmetic operation over 2⁸ and the coefficient of the higher-order term is fixed to one in order to prevent the overflow. In experimental results, we demonstrate that the PSNR is sustained close to 44dB and the embedding capacity is 524,288 bits.

• Journal of Biomedical Engineering Research
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• v.26 no.4
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• pp.231-241
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• 2005

New methods to register multiple hemispheric slices of the postmortem brain to anatomically corresponding in-vivo MRI slices within a 3D volumetric MRI are presented. Gel-embedding and fiducial markers are used to reduce geometrical distortions in the postmortem brain volume. The registration algorithm relies on a recursive extraction of warped MRI slices from the reference MRI volume using a modified non-linear polynomial transformation until matching slices are found. Eight different voxel similarity measures are tested to get the best co-registration cost and the results show that combination of two different similarity measures shows the best performance. After validating the implementation and approach through simulation studies, the presented methods are applied to real data. The results demonstrate the feasibility and practicability of the presented co­registration methods, thus providing a means of MR signal analysis and histological examination of tissue lesions via co­registered images of postmortem brain slices and their corresponding MRI sections. With this approach, it is possible to investigate the pathology of a disease through both routinely acquired MRls and postmortem brain slices, thus improving the understanding of the pathological substrates and their progression.

• The KIPS Transactions:PartB
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• v.10B no.4
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• pp.373-380
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• 2003

Most of low cost digital cameras reveal relatively high lens distortion. The purpose of this research is to compensate the degradation of image quality due to the geometrical distortion of a lens system. The proposed method consists of two stages : calculation of a lens distortion coefficient by a simplified version of Tsai´s camera calibration and subsequent image warping of the original distorted image to remove geometrical distortion based on the calculated lens distortion coefficient. In the lens distortion coefficient calculation stage, a practical method for handling scale factor ratio and image center is proposed, after which its feasibility is shown by measuring the performance of distortion correction using a quantitative image quality measure. On the other hand, in order to apply image warping via inverse spatial mapping using the result of the lens distortion coefficient calculation stage, a cubic polynomial derived from an adopted radial distortion lens model must be solved. In this paper, for the purpose of real-time operation, which is essential for embedding into an information device, an approximated solution to the cubic polynomial is proposed in the form of a solution to a quadratic equation. In the experiment, potential for real-time implementation and equivalence in performance as compared with that from cubic polynomial solution are shown.