• Journal of IKEEE
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• v.25 no.1
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• pp.88-94
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• 2021

Public-key cryptographic algorithms such as RSA and ECC, which are currently in use, have used mathematical problems that would take a long time to calculate with current computers for encryption. But those algorithms can be easily broken by the Shor algorithm using the quantum computer. Lattice-based cryptography is proposed as new public-key encryption for the post-quantum era. This cryptographic algorithm is performed in the Polynomial Ring, and polynomial multiplication requires the most processing time. Therefore, a hardware model module is needed to calculate polynomial multiplication faster. Number Theoretic Transform, which called NTT, is the FFT performed in the finite field. The logic verification was performed using HDL, and the proposed design at the transistor level using Hspice was compared and analyzed to see how much improvement in delay time and power consumption was achieved. In the proposed design, the average delay was improved by 30% and the power consumption was reduced by more than 8%.

• Aerospace Engineering and Technology
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• v.4 no.1
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• pp.229-238
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• 2005

The main objective of this study is to develop RPC geometric correction module for the pre-processing systems of the satellite image. For this purpose, the Terrain-Independent Ⅰ, Terrain-Independent Ⅱ and Terrain-Dependent Ⅲ have been applied in tests with KOMPSAT-1 EOC and SPOT PAN images.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.469-474
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• 2011

The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1165-1176
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• 2020

Let M be a module over a commutative ring R. In this paper, we study Int(R, M), the module of integer-valued polynomials on M over R, and Int_M(R), the ring of integer-valued polynomials on R over M. We establish some properties of Krull dimensions of Int(R, M) and Int_M(R). We also determine when Int(R, M) and Int_M(R) are nontrivial. Among the other results, it is shown that Int(ℤ, M) is not Noetherian module over Int_M(ℤ) ∩ Int(ℤ), where M is a finitely generated ℤ-module.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.318-321
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• 2000

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fie2, degree of uk terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for perform above decrease process. One method is the combinational logic expression and the other method is universal signal generation. The proposed method of constructing the highly adder/multiplier systems is as following. First of all, we obtain algorithms for addition and multiplication arithmetic operation based on the mathematical properties over finite fields, next we construct basic cell of A-cell and M-cell using T-gate and modP cyclic gate. Finally we construct adder module and multiplier module over finite fields after synthesize ${\alpha}$$\^$k/ generation module and control signal CSt generation module with A-cell and M-cell. Then, we propose the future research and prospects.

• Journal of Electrical Engineering and Technology
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• v.9 no.5
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• pp.1471-1481
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• 2014

This paper presents the new power dissipation model of individual switching device in a high-level modular multilevel converter (MMC), which can be mostly used in voltage sourced converter (VSC) based high-voltage direct current (HVDC) system and flexible AC transmission system (FACTS). Also, the voltage balancing method based on sorting algorithm is newly proposed to advance the MMC functionalities by effectively adjusting switching variations of the sub-module (SM). The proposed power dissipation model does not fully calculate the average power dissipation for numerous switching devices in an arm module. Instead, it estimates the power dissipation of every switching element based on the inherent operational principle of SM in MMC. In other words, the power dissipation is computed in every single switching event by using the polynomial curve fitting model with minimum computational efforts and high accuracy, which are required to manage the large number of SMs. After estimating the value of power dissipation, the thermal condition of every switching element is considered in the case of external disturbance. Then, the arm modeling for high-level MMC and its control scheme is implemented with the electromagnetic transient simulation program. Finally, the case study for applying to the MMC based HVDC system is carried out to select the appropriate insulated-gate bipolar transistor (IGBT) module in a steady-state, as well as to estimate the proper thermal condition of every switching element in a transient state.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1905-1914
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• 2013

Let D be an integral domain with quotient field K, M a torsion-free D-module, X an indeterminate, and $N_v=\{f{\in}D[X]|c(f)_v=D\}$. Let $q(M)=M{\otimes}_D\;K$ and $M_{w_D}$={$x{\in}q(M)|xJ{\subseteq}M$ for a nonzero finitely generated ideal J of D with $J_v$ = D}. In this paper, we show that $M_{w_D}=M[X]_{N_v}{\cap}q(M)$ and $(M[X])_{w_{D[X]}}{\cap}q(M)[X]=M_{w_D}[X]=M[X]_{N_v}{\cap}q(M)[X]$. Using these results, we prove that M is a strong Mori D-module if and only if M[X] is a strong Mori D[X]-module if and only if $M[X]_{N_v}$ is a Noetherian $D[X]_{N_v}$-module. This is a generalization of the fact that D is a strong Mori domain if and only if D[X] is a strong Mori domain if and only if $D[X]_{N_v}$ is a Noetherian domain.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.2
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• pp.70-75
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• 2016

This paper proposes the constructing method of effective multiplier based on the finite fields in case of P=2. The proposed multiplier is constructed by polynomial arithmetic part, mod F(${\alpha}$) part and modular arithmetic part. Also, each arithmetic parts can extend according to m because of it have modular structure, and it is adopted VLSI because of use AND gate and XOR gate only. The proposed multiplier is more compact, regularity, normalization and extensibility compare with earlier multiplier. Also, it is able to apply several fields in recent hot issue IoT configuration.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.575-581
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• 1995

The simple modules and the simple comodules of the quantum group $X)q(2)$ defined by M. L. Ge, N. H. Jing and Y. S. Wu, are classified.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.4
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• pp.1-11
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• 2012

This paper is the study on the development of a torque precision measuring system using the curve fitting algorithm. This system can be divided into the hardware part and the software part. The hardware part consists of the main base board, the DAQ(Data Aquisition) board and Calibration parts. The software part consists of the software filter module and the curve fitting algorithm module. We have tested the torque transducer including the strain gauge for 200 Nm range and have analyzed the data acquired with the curve fitting algorithm by using this system. The DAQ board converts the electric signal induced by the transducer to the digital value precisely by using the shunt calibration procedure. The main board including the curve fitting algorithm calculates the exact digital torque value by using the digital value from the DAQ board. In this study, we confirmed that the result of the appropriate high-order power-series polynomial function is more accurate than the result of the low-order power-series polynomial through the system.