• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.435-440
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• 2011

This paper propose the method of constructing the highly efficiency adder and multiplier systems over finite fields. The addition arithmetic operation over finite field is simple comparatively because that addition arithmetic operation is analyzed by each digit modP summation independently. But in case of multiplication arithmetic operation, we generate maximum k=2m-2 degree of ${\alpha}^k$ terms, therefore we decrease k into m-1 degree using irreducible primitive polynomial. We propose two method of control signal generation for the purpose of performing 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 synthesizing ${\alpha}^k$ generation module and control signal CSt generation module with A-cell and M-cell. Next, we constructing the arithmetic operation unit over finite fields. Then, we propose the future research and prospects.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.27 no.1
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• pp.84-86
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• 1982

The experiment was conducted with three varieties (Hicks, Burley 21, and Sohyang) and cultivation type (Improved mulching, general mulching, and non mulching) of NC 2326 to model to curve of tabacco growth against time. The basic growth data were obtained by harvest method at intervals of ten days from transplanting at 7-8 times and analyzed by polynomial regression, orthogonal polynomial, and logarithmic transformation. It is shown that the C model of growth curve: T = A +$\sqrt{(1.4 AK + K)}$2K provides an excellent fit.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.8
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• pp.30-37
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• 2007

An exponentiation in $GF(2^m)$ is a basic operation for several algorithms used in cryptography, digital signal processing, error-correction code and so on. Existing hardware implementations for the exponentiation operation organize by Right-to-Left method since a merit of parallel circuit. Our paper proposes a polynomial exponentiation structure with a trinomial that is organized by Left-to-Right method and that utilizes a weakly dual basis. The basic idea of our method is to decrease time delay using precomputation tables because one of two inputs in the Left-to-Right method is fixed. Since $T_{sqr}$ (squarer time delay) + $T_{mul}$(multiplier time delay) of ow method is smaller than $T_{mul}$ of existing methods, our method reduces time delays of existing Left-to-Right and Right-to-Left methods by each 17%, 10% for $x^m+x+1$ (irreducible polynomial), by each 21%, 9% $x^m+x^k+1(1, by each 15%, 1% for $x^m+x^{m/2}+1$.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.45-52
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• 2002

In this contributions, we propose a new MSB(most significant bit) algorithm based on AOP(All One Polynomial) and two parallel semi-systolic architectures to computes $AB^2$over finite field $GF(2^m)$. The proposed architectures are based on standard basis and use the property of irreducible AOP(All One Polynomial) which is all coefficients of 1. The proposed parallel semi-systolic architecture(PSM) has the critical path of $D_{AND2^+}D_{XOR2}$ per cell and the latency of m+1. The modified parallel semi-systolic architecture(WPSM) has the critical path of $D_{XOR2}$ per cell and has the same latency with PSM. The proposed two architectures, PSM and MPSM, have a low latency and a small hardware complexity compared to the previous architectures. They can be used as a basic architecture for exponentiation, division, and inversion. Since the proposed architectures have regularity, modularity and concurrency, they are suitable for VLSI implementation. They can be used as a basic architecture for algorithms, such as the Diffie-Hellman key exchange scheme, the Digital Signature Algorithm(DSA), and the ElGamal encryption scheme which are needed exponentiation operation. The application of the algorithms can be used cryptosystem implementation based on elliptic curve.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.40.1-40.1
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• 2015

Off-axis reflective optical systems have attractive advantages relative to their on-axis or refractive counterparts, for example, zero chromatic aberration, no obstruction, and a wide field of view. For the efficient operation of off-axis reflective system, the surface accuracy of freeform mirrors should be higher than the order of wavelengths at which the reflective optical systems operate. Especially for applications in shorter wavelength regions, such as visible and ultraviolet, higher surface accuracy of freeform mirrors is required to minimize the light scattering. In this work, we propose the error compensation algorithm (ECA) for the correction of wavefront errors on freeform mirrors. The ECA converts a form error pattern into polynomial expression by fitting a least square method. The error pattern is measured by using an ultra-high accurate 3-D profilometer (UA3P, Panasonic Corp.). The measured data are fitted by two fitting models: Sag (Delta Z) data model and form (Z) data model. To evaluate fitting accuracy of these models, we compared the fitted error patterns with the measured error pattern.

• Journal of Ship and Ocean Technology
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• v.4 no.2
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• pp.38-57
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• 2000

This paper deals with reliability analysis of specially orthotropic plates subjected to transverse lateral pressure loads by using Monte Carlo simulation method. The plates are simply supported around their all edges and have a low short span to plate depth ratio with rectangular plate shapes. Various levels of reliability analyses of the plates are performed within the context of First-Ply-Failure(FPF) analysis such as ply-/laminate-level reliability analyse, failure tree analysis and sensitivity analysis of basic design variables to estimated plate reliabilities. In performing all these levels of reliability analyses, the followings are considered within the Monte Carlo simulation method: (1) input parameters to the strengths of the plates such as applied transverse lateral pressure loads, elastic moduli, geometric including plate thickness and ultimate strength values of the plates are treated as basic design variables following a normal probability distribution; (2) the mechanical responses of the plates are calculated by using simplified higher-order shear deformation theory which can predict the mechanical responses of thick laminated plates accurately; and (3) the limit state equations are derived from polynomial failure criteria for composite materials such as maximum stress, maximum strain, Tsai-Hill, Tsai-Wu and Hoffman.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2552-2557
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• 2007

Shape optimization of an internal cooling passage with staggered dimples on single surface is performed and performances of surrogates are evaluated in this paper. Optimizations are performed so that turbulent heat transfer can be enhanced compromising with pressure loss due to friction. The three-dimensional governing differential equations have been solved to find the overall Nusselt number and friction factor which are related to the objective functions of this problem. Three design variables were selected among the dimensionless geometric variables. Basic surrogate models such as second order polynomial response surface approximation (RSA), Kriging meta-modeling technique, radial basis neural network (RBNN), and derived press based averaged (PBA) surrogate model are constructed. The optimal points are searched from the above constructed surrogates by sequential quadratic programming (SQP). It is shown that use of multiple surrogates can increase the robustness in prediction of better design with minimum computational cost.

• Journal of Information Processing Systems
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• v.12 no.2
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• pp.214-225
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• 2016

Global value numbering (GVN) is a method for detecting equivalent expressions in programs. Most of the GVN algorithms concentrate on detecting equalities among variables and hence, are limited in their ability to identify value-based redundancies. In this paper, we suggest improvements by which the efficient GVN algorithm by Gulwani and Necula (2007) can be made to detect expression equivalences that are required for identifying value based redundancies. The basic idea for doing so is to use an anticipability-based Join algorithm to compute more precise equivalence information at join points. We provide a proof of correctness of the improved algorithm and show that its running time is a polynomial in the number of expressions in the program.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.390-396
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• 1982

The onset of longitudinal vortices in horizontal Blasius flow isothermally heated from below is studied analytically. The assumption that at the onset of thermal instability the thermal disturbances are confined within the thermal boundary layer is employed for the limiting case of large Prandtl number. Polynomial representations for the basic quantities obtained by the integral method of the boundary layer analysis have been used. Then the system of differential equations and boundary conditions for disturbance quantities is reformulated in a convenient form so that the solutions may be constructed as rapidly convergent power series. The critical buoyancy parameter G $r_{x}$ $^{*}$ /R $e^{*1.5}$ falls between 2 and 6, which is about one order of magnitude lower than the existing experimental values. It is also shown that the positions of the onset of instability can be closely predicted by the present theory.y.y.

• ETRI Journal
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• v.30 no.2
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• pp.326-334
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• 2008

This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field $F_{p^m}$ where p is characteristic. As a brute force method, when $p^m$ is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when $p^m$ is large, it becomes too difficult. The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when $mlog_2p$ = 160.