• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.3
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• pp.65-76
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• 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 Chungcheong Mathematical Society
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• v.14 no.1
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• pp.85-103
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• 2001

Suppose that Hand K are paired Hopf algebras and that A is an H - K - bicomodule algebra with multiplication which is a left H-comodule map and is a right K-comodule map. We define a new twisted algebra, $A^{\tau}$ and define $M^{\tau}$ for $M{\in}M_A^K$. We find an equivalent condition for $M^{\tau}{\in}M_{A^{\tau}}^K$. We show that the above defined twisted multiplication is the special case of Beattie's twist multiplication. We show that if K is commutative, then A is an H-module algebra and show that if $H^*$ is cocommutative then the construction of smash product appears as a special case of the new twist product.

• ETRI Journal
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• v.21 no.1
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• pp.28-39
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• 1999

Koblitz has suggested to use "anomalous" elliptic curves defined over ${\mathbb{F}}_2$, which are non-supersingular and allow or efficient multiplication of a point by and integer, For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. in this paper, we propose an algorithm to speed up scalar multiplication on an elliptic curve defined over a small field. The proposed algorithm uses the same field. The proposed algorithm uses the same technique as Muller's to get an expansion by the Frobenius map, but its expansion length is half of Muller's due to the reduction step (Algorithm 1). Also, it uses a more efficient algorithm (Algorithm 3) to perform multiplication using the Frobenius expansion. Consequently, the proposed algorithm is two times faster than Muller's. Moreover, it can be applied to an elliptic curve defined over a finite field with odd characteristic and does not require any precomputation or additional memory.

• Proceedings of the Korean Information Science Society Conference
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• 2010.06a
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• pp.166-170
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• 2010

센서네트워크는 유비쿼터스 환경을 실현할 수 있는 기술로서, 최근 무인 경비 시스템이나 에너지 관리, 환경 모니터링, 홈 자동화, 헬스케어 응용 등과 같은 다양한 응용 분야에 활용되고 있다. 하지만 자신의 정보가 무선통신상에 쉽게 노출됨으로써 도청과 전송 메시지에 대한 위변조, 서비스 거부 공격을 받을 위험이 있다. 더욱이 센서네트워크의 자원 제약성(적은 메모리, 컴퓨팅 성능의 제약)과 키분배 관리의 어려움으로 인해 기존의 공개키, 대칭키 기반의 면안프로토콜을 대체할 수 있는 프로토콜이 필요하다. 그러므로 키분배 관리에 장 접을 가지는 Bilinear map 기반 프로토콜은 적합한 대안이다. 하지만 프로토콜에 사용되는 Pairing연산은 높은 컴퓨팅 성능이 요구된다. 따라서 제한된 성능을 가진 센서상의 구현을 위해서는 Computation Cost를 줄이고 연산 수행 속도를 가속화 할 필요성이 있다. 본 논문에서는 프로토콜 구현에 필요한 Pairing의 핵심 연산인 Multiplication을 대표적인 센서노드 프로세서인 MSP430상에서 최적화 구현함으로써 성능을 개선한다.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.727-733
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• 2001

Let A be a commutative ring with nonzero identity and let M be an A-module. In this note we show that if $x = x_1, ..., x_n\; and\; y = y_1, ..., y_n$ both M-cosequence such that $Hx^T = y^T\; for\; some\; n\times n$ lower triangular matrix H over A, then the map $\beta_H : \;Ann_M(y_1,..., y_n)\;\rightarrow Ann_M(x_1,..., x_n)$ induced by multiplication by ｜H｜ is surjective.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.180-188
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• 1995

A modified Kohonen's self-organizing feature map (SOFM) algorithm which has binary reinforcement function and a constant learning rate is proposed. In contrast to the time-varing adaptaion gain of the original Kohonen's SOFM algorithm, the proposed algorithm uses a constant adaptation gain, and adds a binary reinforcement function in order to compensate for the lowered learning ability of SOFM due to the constant learning rate. Since the proposed algorithm does not have the complicated multiplication, it's digital hardware implementation is much easier than that of the original SOFM.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.277-280
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• 2000

In this paper, we designed a turbo decoder using VHDL. To maximize effective free distance of the turbo code, we implemented pseudo random interleaver. A MAP(Maximum a posteriori) decoder is used as a primimary decoder. We avoided multiplication by using lookup tables(ROM). We expect that this small-sized turbo decoder is suitable for mobile communication. We simulated turbo decoder with Altera MAX+PLUS II.

• Journal of Korea Multimedia Society
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• v.21 no.8
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• pp.821-828
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• 2018

Image Enhancement is used in various applications. Among them, unsharp masking methods can improve the contrast with a simple operation. However, it has problems of noise enhancement and halo effect caused by the use of a single filter. To solve this problems, adaptive processing using multi-scale and bilinear filters is being studied. These methods are effective for improving the halo effect, but it require a lot of calculation time. In this paper, we want to simplify adaptive filtering by generating a weight map based on local brightness. This weight map enables adaptive processing that eliminates the halo effect through a single multiplication operation. Through experiments, we confirmed the suppression of the halo effect through the result image of the proposed algorithm and existing algorithm.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.695-698
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• 2005

The finite-field multiplication can be applied to the wide range of applications, such as signal processing on communication, cryptography, etc. However, an efficient algorithm and the hardware design are required since the finite-field multiplication takes much time to compute. In this paper, we propose a radix-4 systolic multiplier on $GF(2^m)$ with comparative area and performance. The algorithm of the proposed standard-basis multiplier is mathematically developed to map on low-cost systolic cell, so that the proposed systolic architecture is suitable for VLSI design. Compared to the bit-serial and digit-serial multipliers, the proposed multiplier shows relatively better performance with low cost. We design and synthesis $GF(2^{193})$ finite-field multiplier using Hynix $0.35{\mu}m$ standard cell library and the maximum clock frequency is 400MHz.