• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2016.05a
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• pp.762-763
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• 2016

In realizing a homomorphic encryption system, the operations of encrypt, decypt, and recrypt constitute major portions. The most important common operation for each back-bone operations include a polynomial modulo multiplication for over million-bit integers, which can be obtained by performing integer Fourier transform, also known as number theoretic transform. In this paper, we adopt and modify an algorithm for calculating big integer multiplications introduced by Schonhage-Strassen to propose an efficient algorithm which can save memory. The proposed architecture of number theoretic transform has been implemented on an FPGA and evaluated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.8C
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• pp.729-737
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• 2007

The H.264/AVC video coding standard provides higher coding efficiency compared to the conventional MPEG-2 standard. Since a lot of videos have been encoded using MPEG-2, the format conversion from MPEG-2 to H.264 is essential. In this paper, we propose an efficient method for the conversion of DCT coefficients to H.264/AVC transform coefficients. This conversion is essential, since $8{\times}8$ DCT and $4{\times}4$ integer transform are used in MPEG-2 and H.264/AVC, respectively. The mathematical analysis and computer simulation show that the computational complexity of the proposed algorithm is reduced compared to the conventional algorithm, while the loss caused by the conversion is negligible.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.827-832
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• 2013

In this paper we apply the Catalan transform to the ${\kappa}$-Fibonacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the ${\kappa}$-Fibonacci sequence and obtain an unusual property.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.731-735
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• 2001

In this paper, we propose the new audio watermarking method and can be used on line processing. Instead of the wavelet transform, we use the integer wavelet transform for the reduction of the computational load. The watermark associated with the chi-square distribution is inserted into the signal on the integer wavelet domain. When extracting the watermark, the spread spectrum methods are used with the coefficients associated with the covariance sequence. We show that the chi-square distribution is a good tool for the spread spectrum method on the wavelet domain. This watermarking technique may be sued for the control of the electrical product which can be controlled with the hidden signals and can be moved according to the audible signals simultaneously.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.12C
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• pp.1039-1045
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• 2008

The H.264/AVC video coding standard shows extremely higher coding efficiency, but it causes high computational complexity. Especially, the intra mode decision using the rate-distortion method requires many computations. Thus, the efficient intra mode decision methods have been proposed by decreasing the encoding complexity. In this paper, we propose an efficient intra mode decision algorithm using $4{\times}4$ integer transform coefficients in the conversion of MPEG-2 to H.264 standard. It is shown that the proposed algorithm reduces encoding time and complexity compared to the conventional algorithm, while showing similar PSNR performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.8
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• pp.2816-2830
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• 2022

Number Theoretic Transform (NTT) is a method to design efficient multiplier for large integer multiplication, which is widely used in cryptography and scientific computation. On top of that, it has also received wide attention from the research community to design efficient hardware architecture for large size RSA, fully homomorphic encryption, and lattice-based cryptography. Existing NTT hardware architecture reported in the literature are mainly designed based on radix-2 NTT, due to its small area consumption. However, NTT with larger radix (e.g., radix-4) may achieve faster speed performance in the expense of larger hardware resources. In this paper, we present the performance evaluation on NTT architecture in terms of hardware resource consumption and the latency, based on the proposed radix-2 and radix-4 technique. Our experimental results show that the 16-point radix-4 architecture is 2× faster than radix-2 architecture in expense of approximately 4× additional hardware. The proposed architecture can be extended to support the large integer multiplication in cryptography applications (e.g., RSA). The experimental results show that the proposed 3072-bit multiplier outperformed the best 3k-multiplier from Chen et al. [16] by 3.06%, but it also costs about 40% more LUTs and 77.8% more DSPs resources.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.2
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• pp.352-358
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• 2004

This paper is studied the improvement of performance for moving picture encoder using H.263. This is used the new motion vector search algorithm using a relation with neighborhood search point and is applied the integer DCT for the encoder. The integer DCT behaves DCT by the addition operation of the integer using WHT and a integer lifting than conventional DCT that needs the multiplication operation of a floating point number. Therefore, the integer Dn can reduce the operation amount than basis DCT with having an equal PSNR. The new motion vector search algorithm is showed almost similar PSNR as reducing the operation amount than the conventional motion vector search algorithm. To experiment a compatibility of the integer DCT and the conventional DCT, according to result compare case that uses a method only and case that uses the alternate two methods of the integer DCT or the conventional DCT to H.263 encoder and decoder, case that uses the alternate two methods is showed doing not deteriorate PSNR-and being each other compatible visually than case that uses an equal method only.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.4 no.3
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• pp.263-269
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• 2003

This paper focuses on lossy medical image compression methods for medical images that operate on three-dimensional(3D) irreversible integer wavelet transform. We offer an application of the Set Partitioning in Hierarchical Trees(SPIHT) algorithm〔l-3〕to medical images, using a 3-D wavelet decomposition and a 3-D spatial dependence tree. The wavelet decomposition is accomplished with integer wavelet filters implemented with the lifting method, where careful scaling and truncations keep the integer precision small and the transform unitary. As the compression rate increases, the boundaries between adjacent coding units become increasingly visible. Unlike video, the volume image is examined under static condition, and must not exhibit such boundary artifacts. In order to eliminate them, we utilize overlapping at axial boundaries between adjacent coding units. We have tested our encoder on medical images using different integer filters. Results show that our algorithm with certain filters performs as well. The improvement is visibly manifested as fewer ringing artifacts and noticeably better reconstruction of low contrast.

• Proceedings of the IEEK Conference
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• summer
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• pp.114-117
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• 2004

This paper proposes a novel algorithm for hybrid lossless audio coding, which employs integer discrete cosine transform. The proposed algorithm divides the input signal into frames of a proper length, decorrelates the framed data using the integer DCT and finally entropy-codes the frame data. In particular, the adaptive Golomb-Rice coding method used for the entropy coding selects an optimal option which gives the best compression efficiency. Since the proposed algorithm uses integer operations, it significantly improves the computation speed in comparison with an algorithm using real or floating-point operations. When the coding algorithm is implemented in hardware, the system complexity as well as the power consumption is remarkably reduced. Finally, because each frame is independently coded and is byte-aligned with respect to the frame header, it is convenient to move, search, and edit the coded data.

• Journal of the Institute of Convergence Signal Processing
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• v.1 no.1
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• pp.82-88
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• 2000

In this paper, We compare the Harr wavelet of the S+P transform with various integer coefficient filter banks and apply 9/7 ICFB to the wavelet transform. In addition, we propose a entropy-coding method that exploits the multiresolution structure and the feedback of the prediction error, and can efficiently compress the transformed image for progressive transmission. Simulation results are included to compare to the compression ratio using the S+P transform with different types of images.