• ETRI Journal
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• v.26 no.3
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• pp.241-251
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• 2004

We propose two improved scalar multiplication methods on elliptic curves over $F_{{q}^{n}}$ $q= 2^{m}$ using Frobenius expansion. The scalar multiplication of elliptic curves defined over subfield $F_q$ can be sped up by Frobenius expansion. Previous methods are restricted to the case of a small m. However, when m is small, it is hard to find curves having good cryptographic properties. Our methods are suitable for curves defined over medium-sized fields, that is, $10{\leq}m{\leq}20$. These methods are variants of the conventional multiple-base binary (MBB) method combined with the window method. One of our methods is for a polynomial basis representation with software implementation, and the other is for a normal basis representation with hardware implementation. Our software experiment shows that it is about 10% faster than the MBB method, which also uses Frobenius expansion, and about 20% faster than the Montgomery method, which is the fastest general method in polynomial basis implementation.

• Proceedings of the IEEK Conference
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• 2002.06b
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• pp.345-348
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• 2002

This paper presents new fast scalar multiplier of elliptic curve cryptosystem that is regarded as next generation public-key crypto processor. For fast operation of scalar multiplication a finite field multiplier is designed with LFSR type of bit serial structure and a finite field inversion operator uses extended binary euclidean algorithm for reducing one multiplying operation on point operation. Also the use of the window non-adjacent form (WNAF) method can reduce addition operation of each other different points.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.309-322
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• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

• Current Optics and Photonics
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• v.5 no.5
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• pp.491-499
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• 2021

A scalar Fourier modal method for the numerical analysis of the scalar wave equation in inhomogeneous space with an arbitrary permittivity profile, is proposed as a novel theoretical embodiment of Fourier optics. The modeling of devices and systems using conventional Fourier optics is based on the thin-element approximation, but this approach becomes less accurate with high numerical aperture or thick optical elements. The proposed scalar Fourier modal method describes the wave optical characteristics of optical structures in terms of the generalized transmittance function, which can readily overcome a current limitation of Fourier optics.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.3
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• pp.587-601
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• 2016

In this paper we suggest method for scalar recoding which is both secure against SPA and DPA. Suggested method is countermeasure to power analysis attack through scalar recoding using negative expression. Suggested method ensures safety of SPA by recoding the operation to apply same pattern to each digit. Also, by generating the random recoding output according to random number, safety of DPA is ensured. We also implement precomputation table and modified scalar addition algorithm for addition to protect against SPA that targets digit's sign. Since suggested method itself can ensure safety to both SPA and DPA, it is more effective and efficient. Through suggested method, compared to previous scalar recoding that ensures safety to SPA and DPA, operation efficiency is increased by 11%.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.233-240
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• 2006

In this paper, we consider the problem of achieving a prescribed scalar curvature on warped product manifolds according to fiber manifolds with constant scalar curvature.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.56.3-56
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• 2001

This study describes the jump error smoothing scheme with fuzzy logic based on the scalar adaptive filter. The scalar adaptive filter is an useful algorithm for smoothing abrupt jump errors. However, the performances of scalar adaptive algorithm depend on the variance of real signal. So to design an effective algorithm, many informations of real and jump signal are required. In this paper, the fuzzy rules are designed by the analysis of scalar adaptive filter, and then the improved and simplified scheme is developed for smoothing the jump error. Simulations to INS/GPS integrated system show that the proposed method is effective.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.115-122
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• 1998

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on $M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$ with specific scalar curvatures.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.95-101
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• 1999

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future complete Lorentzian metrics on $M{\;}={\;}[\alpha,\infty){\times}_f{\;}N$ with specific scalar curvatures.

• The Journal of the Acoustical Society of Korea
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• v.17 no.4E
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• pp.35-40
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• 1998

In this paper, an efficient quantization method of line spectrum pairs(LSP) with cascaded structure of vector quantizer and scalar quantizer is proposed. First, input LSP parameters is vector-quantized using a codebook a with a moderate number of entries. In the second stage of quantization, the components of residual vector are individually quantized by the scalar quantizer. The utilization of ordering property of LSP parameters and the inclusion of interframe prediction improve the quantizer performance and remove the stability check routine after quantization procedure. The new vector-scalar hybrid quantizer using 26 bits/frame shows a transparent quality of speech that an average spectral distortion is 1 dB and the frame proportion with above 2 dB spectral distortion is less than 2%. The performances of proposed quantization method is evaluated in the transmission errors.