• ETRI Journal
• /
• v.27 no.5
• /
• pp.617-627
• /
• 2005

This paper proposes an efficient scalar multiplication algorithm for hyperelliptic curves, which is based on the idea that efficient endomorphisms can be used to speed up scalar multiplication. We first present a new Frobenius expansion method for special hyperelliptic curves that have Gallant-Lambert-Vanstone (GLV) endomorphisms. To compute kD for an integer k and a divisor D, we expand the integer k by the Frobenius endomorphism and the GLV endomorphism. We also present improved scalar multiplication algorithms that use the new expansion method. By our new expansion method, the number of divisor doublings in a scalar multiplication is reduced to a quarter, while the number of divisor additions is almost the same. Our experiments show that the overall throughputs of scalar multiplications are increased by 15.6 to 28.3 % over the previous algorithms when the algorithms are implemented over finite fields of odd characteristics.

• International Journal of Aeronautical and Space Sciences
• /
• v.12 no.1
• /
• pp.37-42
• /
• 2011

An extended scalar adaptive filter for guided missiles using a global positioning system receiver is presented. A conventional scalar adaptive filter is adequate filter for eliminating sudden abnormal jumping measurements. However, if missile or vehicle velocities have variation, the conventional filter cannot eliminate abnormal measurements. The proposed filter utilizes an acceleration term, which is an improvement not used in previous conventional scalar adaptive filters. The proposed filter continuously estimates noise measurement variance, velocity error variance and acceleration error variance. For estimating the three variances, an innovation method was used in combination with the least square method for the three variances. Results from the simulations indicated that the proposed filter exhibited better position accuracy than the conventional scalar adaptive filter.

• 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.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.13 no.3
• /
• pp.65-70
• /
• 2003

In this paper, we propose a scalar multiplication method and its hardware architecture which is resistant to SPA while its computation speed is faster than Colon's. There were SPA-resistant scalar multiplication method which has performance problem. Due to this reason, the research about an efficient SPA-resistant scalar multiplication is one of important topics. The proposed architecture resists to SPA and is faster than Colon's method under the assumption that Colon's and the proposed method use same fmite field arithmetic units(multiplier and inverter). With n-bit scalar multiple, the computation cycle of the proposed is 2n·(Inversion cycle)+3(Aultiplication cycle).

• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.36 no.5
• /
• pp.455-461
• /
• 2008

In this paper, the performance of a scalar filter and a scalar adaptive filter are analyzed. In order to make indoor experimental environment similar to outdoor test, ultrasonic sensors are used instead of GPS. The scalar adaptive filter, which is continuously estimating velocity error covariance and measurement noise covariance by using adaptive method, is different from the scalar filter. Experimental results show that the scalar adaptive filter has better position estimating performance than the scalar filter by estimating above two parameters with an adaptive method.

• ETRI Journal
• /
• v.23 no.1
• /
• pp.16-22
• /
• 2001

Efficient quantization methods of the line spectrum pairs (LSP) which have good performances, low complexity and memory are proposed. The adaptive quantization range method utilizing the ordering property of LSP parameters is used in a scalar quantizer and a vector-scalar hybrid quantizer. As the maximum quantization range of each LSP parameter is varied adaptively on the quantized value of the previous order's LSP parameter, efficient quantization methods can be obtained. The proposed scalar quantization algorithm needs 31 bits/frame, which is 3 bits less per frame than in the conventional scalar quantization method with interframe prediction to maintain the transparent quality of speech. The improved vector-scalar quantizer achieves an average spectral distortion of 1 dB using 26 bits/frame. The performances of proposed quantization methods are also evaluated in the transmission errors.

• Journal of Institute of Control, Robotics and Systems
• /
• v.15 no.1
• /
• pp.31-36
• /
• 2009

This paper presents a novel scalar adaptive filter, which is reformulated by additional acceleration term. The filter continuously estimates three different kinds of covariance such as the measurement noise covariance, the velocity error covariance and the acceleration error covariance. For estimating three covariances, we use the innovation method for the measurement noise covariance and the least square method for other covariances. In order to verify the proposed filter performance compared with the conventional scalar adaptive filter, we make indoor experimental environment similar to outdoor test using the ultrasonic sensors instead of GPS. Experimental results show that the proposed filter has better position accuracy than the traditional scalar adaptive filter.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.12
• /
• pp.1211-1217
• /
• 1991

A three dimensional magnetostatic probodm is analyzed using the boundary element method and the magnetic scalar potential are employed in order to reduce the size of system matrix. Although the total magnetic scalar potential gives very accurate solutions at inner and outer regions of magnetic materal, the method has limitation on application because the magnetic scalar potential due to applied magnetic field sources is hard to be obtained. The reduced magnetic scalar potential gives more or less inaccurate solutions inside the magnetic material but very accurate solutions outside. Hence it can be concluded that the reduced magnetic scalar potential is very useful when the magnetic fields of outside of magnetic fields of outside of magnetic material are interested. It is also shown, from the numerical example, that the linear shape function gives more efficient solutions than the constant shape functions.

• Honam Mathematical Journal
• /
• v.28 no.3
• /
• pp.399-407
• /
• 2006

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