• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.15 no.3
• /
• pp.65-76
• /
• 2005

Speeding up scalar multiplication of an elliptic curve point has been a prime approach to efficient implementation of elliptic curve schemes such as EC-DSA and EC-ElGamal. Koblitz introduced a $base-{\phi}$ expansion method using the Frobenius map. Kobayashi et al. extended the $base-{\phi}$ scalar multiplication method to suit Optimal Extension Fields(OEF) by introducing the table reference method. In this paper we propose an efficient scalar multiplication algorithm on elliptic curve over OEF. The proposed $base-{\phi}$ scalar multiplication method uses an optimized batch technique after rearranging the computation sequence of $base-{\phi}$ expansion usually called Horner's rule. The simulation results show that the new method accelerates the scalar multiplication about $20\%{\sim}40\%$ over the Kobayashi et al. method and is about three times as fast as some conventional scalar multiplication methods.

• Honam Mathematical Journal
• /
• v.27 no.2
• /
• pp.273-285
• /
• 2005

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

• Honam Mathematical Journal
• /
• v.28 no.1
• /
• pp.141-164
• /
• 2006

Let $G=O(2){\times}O(2){\times}O(2)$ and let $M^4$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$. In this paper, we prove a property on $M^4$.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.259-268
• /
• 1998

In this paper the stochastic multiple objective programming problems where the right-hand-side of the constraints is stochastic are considered. We define the equivalent scalar-valued problem and study the stability of the equivalent scalar-valued problem with respect to the weight parameters and probability mesures under reasonable assumptions.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1037-1048
• /
• 1997

We show that an asymptotically Euclidean scalar-flat Kahler metric ona complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $C^2$ blown up at some points.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.543-550
• /
• 2000

We prove that every generalized Landsberg manifold of scalar curvature R is a Riemannian manifold of constant curvature, provided that $R\neq\ 0$.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.331-340
• /
• 2018

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.641-647
• /
• 2007

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

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

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.281-290
• /
• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.