• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2003.12a
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• pp.605-610
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• 2003

선거를 전자적으로 구성하기 위해서는 비밀성(privacy), 선거권(eligibility) 등과 함께 전체검증(universal verifiability)과 매표방지(receipt-freeness) 속성을 반드시 제공해야 한다. 지금까지 제안된 전자선거 기법은 매표방지와 전체검증을 제공하기 위해 도청 불가능한 채널이라는 물리적인 가정 하에 이루어지거나 하드웨어 장치를 이용하더라도 장치에 대한 신뢰가 가정되었다. 본 논문에서는 믹스 서버나 랜덤마이저의 역할을 스마트카드와 같은 안전한 하드웨어 장치가 하므로 물리적 가정 없이 효율적으로 구현한다. 제안한 시스템은 표를 섞는 과정에서 permutation matrix를 사용하여 증명하므로 증명의 회수가 적고 간단하여 효율적이다. 또한, 지금까지 제안된 대부분의 선거 기법은 ElGamal 암호시스템의 준동형 특성을 이용하여 모든 표를 결합한 다음 해독하여 집계를 계산하는데 이는 이산대수 문제를 효율적으로 해결할 수 있어야 가능했다. 이 논문에서는 ElGamal 암호시스템과 다차잉여 기반 암호알고리즘인 Naccacne 암호알고리즘을 결합하여 표를 인코딩 함으로써 유권자의 수가 많은 선거에 대해서도 다항 시간 내에 집계가 가능하다.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.371-384
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• 2022

Fix an integer n ≥ 1. Then the simplex Π_n, Birkhoff polytope Ω_n, and Latin square polytope Λ_n each yield projective geometries obtained by identifying antipodal points on a sphere bounding a ball centered at the barycenter of the polytope. We investigate conditions for homogeneous coordinates of points in the projective geometries to locate exact vertices of the respective polytopes, namely crisp distributions, permutation matrices, and quasigroups or Latin squares respectively. In the latter case, the homogeneous conditions form a crucial part of a recent projective-geometrical approach to the study of orthogonality of Latin squares. Coordinates based on the barycenter of Ω_n are also suited to the analysis of generalized doubly stochastic matrices, observing that orthogonal matrices of this type form a subgroup of the orthogonal group.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.387-395
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• 2010

It is important to identify the interaction of genes about human disease and characteristic value. Many studies as like logistic analysis, have associated being pursued, but, previous methods did not consider the sub-group of the genotypes. So, QTL interactions and the GMM (genotype matrix mapping) have been developed. In this study, we detect the superior genotype combination to have an impact on economic traits of Korean cattle based on the study over GMM method. Thus, we identified interaction effects of single nucleotide polymorphisms (SNPs) responsible for average daily gain(ADG), marbling score (MS), carcass cold weight (CWT), longissimus muscle dorsiarea (LMA) using GMM method. In addition, we examine significance of the major genotype combination selected by implementing permutation test of the F-measure which was not obtained by Sachiko et al.

• The KIPS Transactions:PartC
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• v.9C no.4
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• pp.445-452
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• 2002

In this paper, we suggest the design of 128bit block cipher which is provable security based on mathematics theory. We have derived the 16$\times$16 matrix(i.e.,linear transformation) which is numerous active S-box, and we proved for DC and LC which prove method about security of SPN structure cipher algorithm. Also, the minimum number of active S-box, the maximum differential probabilities and the maximum linear probabilities in round function of 128bit block cipher algorithm which has an effect to DC and LC are derived.

• Journal of Information Processing Systems
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• v.12 no.4
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• pp.765-778
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• 2016

In watermarking schemes, the discrete wavelet transform (DWT) is broadly used because its frequency component separation is very useful. Moreover, LU decomposition has little influence on the visual quality of the watermark. Hence, in this paper, a novel blind watermark algorithm is presented based on LU transform and DWT for the copyright protection of digital images. In this algorithm, the color host image is first performed with DWT. Then, the horizontal and vertical diagonal high frequency components are extracted from the wavelet domain, and the sub-images are divided into $4{\times}4$ non-overlapping image blocks. Next, each sub-block is performed with LU decomposition. Finally, the color image watermark is transformed by Arnold permutation, and then it is inserted into the upper triangular matrix. The experimental results imply that this algorithm has good features of invisibility and it is robust against different attacks to a certain degree, such as contrast adjustment, JPEG compression, salt and pepper noise, cropping, and Gaussian noise.

• Journal of Korea Society of Industrial Information Systems
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• v.15 no.2
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• pp.1-9
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• 2010

Feistel and SPN are the two main structures in a block cipher. Feistel is a symmetric structure which has the same structure in encryption and decryption, but SPN is not a symmetric structure. In this paper, we propose a SPN which has a symmetric structure in encryption and decryption. The whole operations of proposed algorithm are composed of the even numbers of N rounds where the first half of them, 1 to N/2 round, applies a right function and the last half of them, (N+1)/2 to N round, employs an inverse function. And a symmetry layer is located in between the right function layer and the inverse function layer. In this paper, AES encryption and decryption function are selected for the right function and the inverse function, respectively. The symmetric layer is composed with simple matrix and round key addition. Due to the simplicity of the symmetric SPN structure in hardware implementation, the proposed modified AES is believed to construct a safe and efficient cipher in Smart Card and RFID environments where electronic chips are built in.

• The KIPS Transactions:PartA
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• v.18A no.2
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• pp.39-44
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• 2011

This paper proposes the new high-performance circuit architecture of the transform and quantization for unified video CODEC. The proposed architecture can be applied to all kinds of transforms and quantizations for the video compression standards such as JPEG, MPEG-1/2/4, H.264 and VC-1. We defined the permutation matrices to reorder the transform matrix of the $8{\times}8$ DCT and partitioned the reordered $8{\times}8$ transform matrix into four $4{\times}4$ sub-matrices. The $8{\times}8$ DCT is performed by repeating the $4{\times}4$ DCT's based on the reordered and partitioned transform matrices. Since our circuit accepts the transform coefficients from the users, it can be extended very easily to cover any kind of DCT-based transforms for future standards. The multipliers in the DCT circuit are shared by the quantization circuit in order to minimize the circuit size. The quantization circuit is merged into the DCT circuit without any significant increase of circuit resources and processing time. We described the proposed DCT and quantization circuit at RTL, and verified its operation on FPGA board.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.123-136
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• 2004

In this paper, complexity and regularity of polynomial multiplication over $GF({2^n})$ are defined by using Hamming weight of rows and columns of the matrix ever GF(2) which represents polynomial multiplication. It is shown experimentally that in order to construct the block cipher robust against differential cryptanalysis, polynomial multiplication of substitution layer and the permutation layer should have high complexity and high regularity. With result of the experiment, a way of constituting S box and G function is suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with a nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over $GF({2^8})$ which has neither a fixed pout, whose input and output are the same except 0 and 1, nor an opposite fixed number, whose output is one`s complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes linear transform with 4 S-box outputs using the matrix of 4${\times}$4 over $GF({2^8})$. The components in the matrix of linear transformation have high complexity and high regularity. Furthermore, G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, and there can be no weak input where a fixed point an opposite fixed point, and output can be two`s complement of input. The primitive polynomials of nonlinear function affine transform and linear transformation are different each other. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.