• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.7
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• pp.327-331
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• 2008

Optimal Extension Fields (OEFs) are finite fields of a special form which are very useful for software implementation of elliptic curve cryptosystems. Bailey and Paar introduced efficient OEF arithmetic algorithms including the $p^ith$ powering operation, and an efficient algorithm to construct OEFs for cryptographic use. In this paper, we give a counterexample where their $p^ith$ powering algorithm does not work, and show that their OEF construction algorithm is faulty, i.e., it may produce some non-OEFs as output. We present improved algorithms which correct these problems, and give improved statistics for the number of OEFs.

• ETRI Journal
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• v.29 no.6
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• pp.769-778
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• 2007

This paper proposes a multiplication algorithm for $F_{p^m}$, which can be efficiently applied to many pairs of characteristic p and extension degree m except for the case that 8p divides m(p-1). It uses a special class of type- Gauss period normal bases. This algorithm has several advantages: it is easily parallelized; Frobenius mapping is easily carried out since its basis is a normal basis; its calculation cost is clearly given; and it is sufficiently practical and useful when parameters k and m are small.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.593-595
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• 2000

본 논문에서는 최적확장체(Optimal Extension Field; OEF)에서 정의되는 타원곡선 상에서 효율적인 스칼라 곱셈 알고리즘을 제안한다. 이 스칼라 곱셈 알고리즘은 프로비니어스 사상(Frobenius map)을 이용하여 스칼라 값을 Horner의 방법으로 Base-Ф 전개하고, 이 전개된 수식을 일괄처리 기법(batch-processing technique)을 사용하여 연산한다. 이 알고리즘을 적용할 경우, Kobayashi 등이 제안한 스칼라 곱셈 알고리즘보다 40% 정도의 성능향상을 보인다.

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.3
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• pp.197-203
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• 2009

Finite field arithmetic is very important in the area of cryptographic applications and coding theory, and it is efficient to use normal bases in hardware implementation. Using the fact that $GF(2^{mk})$ having a type-I optimal normal basis becomes the extension field of $GF(2^m)$, we, in this paper, propose a new serial multiplier which reduce the critical XOR path delay of the best known Reyhani-Masoleh and Hasan's serial multiplier by 25% and the number of XOR gates of Kwon et al.'s multiplier by 2 based on the Reyhani-Masoleh and Hasan's serial multiplier for type-I optimal normal basis.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1799-1809
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• 1995

The applicability of the field-consistency paradigm, which was originally employed for analysis of locking due to constrained energy having the second power of a strain, is extended to the constrained energy having a quadratic form of strain. For the extension, nearly-incompressible plane strain problem is considered by introducing the concept of reduced minimization. The field-consistent analysis of the plane strain problem leads to a clear and systematic understanding on the relation amongst constraints imposed on element, spurious constraint -free optimal points, and integration order used.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.531-538
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• 1997

In this paper, we show how to construct an optimal normal basis over finite field of high degree and compare two methods for fast operations in some finite field $GF(2^n)$. The first method is to use an optimal normal basis of $GF(2^n)$ over $GF(2)$. In case of n = st where s and t are relatively primes, the second method which regards the finite field $GF(2^n)$ as an extension field of $GF(2^s)$ and $GF(2^t)$ is to use an optimal normal basis of $GF(2^t)$ over $GF(2)$. In section 4, we tabulate implementation result of two methods.

• Journal of Environmental Policy
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• v.2 no.1
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• pp.51-75
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• 2003

The objective of this study is to analyze the problems of disposal and collection, including administrative management of agricultural PE waste and suggest effective management measurements. Information regarding problems of agricultural PE waste management were collected from field survey of farmers, regional governments and officials. On the national level, the low ratio of collection for optimal treatment of agricultural PE waste is a critical problem. , the negative discharging behavior of farmers, an illegal incineration and landfill of farmers and a lack of education and extension etc. An ambiguity of the management principle to agricultural PE waste, the differences in management among the regional governments, a lack of will of the regional governments and officials to realize SARD and lack of education and extension etc. are some of the problems in administrative management of agricultural PE waste collection. The major suggestions of this study are as follows : (1) to strengthen education and extension, (2) to adopt an improved economic incentive system and strong, lawful regulation simultaneously, (3) to use temporang collection and permanent collection site, and (4) to organize "OTC(Optimal Treatment Conference)" composed of farmers, regional cooperative, PE producers etc. for operating an effective management system.

• Proceedings of the Korea Multimedia Society Conference
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• 2003.11a
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• pp.158-161
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• 2003

1985년 N. Koblitz와 V. Miller가 각각 독립적으로 제안한 타원곡선 암호시스템(ECC : Elliptic Curve Cryptosystems)은 유한체 위에서 정의된 타원곡선 군에서의 이산대수 어려움에 기초한다. 타원곡선 암호시스템은 다른 공개키 시스템에 비해 보다 짧은 길이의 키만으로도 동일한 수준의 안전도를 유지할 수 있다는 장점으로 인하여, 스마트카드나 모바일 시스템 등에서와 같이 메모리와 처리능력이 제한된 하드웨어에도 이식 가능한 장점이 있다. 본 논문에서는 타원곡선 암호시스템에 필요한 유한체 연산을 이진체(Binary Finite Field)인 GF(2$^{193}$ )과 OEF(Oprimal Extension Field) 상에서 VHDL 언어를 사용하여 구현을 하였고 각 연산의 성능을 비교하였다.

• Korean Journal of Soil Science and Fertilizer
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• v.49 no.5
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• pp.548-554
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• 2016

Optimal range of soil physical quality to enhance crop productivity or to improve environmental health is still in dispute for the upland soil. We hypothesized that the optimal range might be established by comparing soil physical parameters and their interactions inhibiting crop growth. The parameter identifying optimal range covered favorable conditions of aeration, permeability and root extension. To establish soil physical standard two experiments were conducted as follows; 1) investigating interactions of bulk density and aeration porosity in the laboratory test and 2) determining effects of soil compaction and deep & conventional tillage on physical properties and crop growth in the field test. The crops were Perilla frutescens, Zea mays L., Solanum tuberosum L. and Secale cereael. The saturated hydraulic conductivity, bulk density from the root depth, root growth and stem length were obtained. Higher bulk density showed lower aeration porosity and hydraulic conductivity, and finer texture had lower threshold bulk density at 10% aeration bulk density. Reduced crop growth by subsoil compaction was higher in silt clay loam compared to other textures. Loam soil had better physical improvement in deep rotary tillage plot. Combined with results of the present studies, the soil physical quality was possibly assessed by bulk density index. Threshold subsoil bulk density as the upper value were $1.55Mg\;m^{-3}$ in sandy loam, $1.50Mg\;m^{-3}$ in loam and $1.45Mg\;m^{-3}$ in silty clay loam for optimal soil physical quality in upland.