• Proceedings of the Korean Information Science Society Conference
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• 2004.04a
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• pp.370-372
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• 2004

본 논문에서는 162bits의 Key Size를 가지고서도 RSA 1024bits의 암호학적 강도를 지니는 스마트카드용으로 적합한 ECC Coprocessor의 구현하고자 한다. ECC의 하드웨어 구현시의 적합성을 위해 162bit Optimal Normal Basis를 선택하였으며, Multiplication은 23 클록 사이클에 수행이 되도록 구현하였으며. Inversion은 Multiplication을 11번 사용하는 알고리즘을 선택하였다. 이때 한번의 점간의 덧셈 연산을 마치는데 331(335) 클록 사이클이 소요되며 클록의 최소주기는 3ns 이다. 또한 Area는 37,111를 기록했다.

• 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 the Korea Institute of Information Security & Cryptology
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• v.16 no.4
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• pp.83-89
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• 2006

In H/W implementation for the finite field, the use of normal basis has several advantages, especially, the optimal normal basis is the most efficient to H/W implementation in GF($2^m$). In this paper, we propose a new, simpler, parallel multiplier over GF($2^m$) having a type II optimal normal basis, which performs multiplication over GF($2^m$) in the extension field GF($2^{2m}$). The time and area complexity of the proposed multiplier is same as the best of known type II optimal normal basis parallel multiplier.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.8
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• pp.1207-1212
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• 2013

Arithmetic operations over finite fields are widely used in coding theory and cryptography. In both of these applications, there is a need to design low complexity finite field arithmetic units. The complexity of such a unit largely depends on how the field elements are represented. Among them, representation of elements using a optimal normal basis is quite attractive. Using an algorithm minimizing the number of 1's of multiplication matrix, in this paper, we propose a multiplier which is time and area efficient over finite fields with optimal normal basis.

• 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.

• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.1 no.1
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• pp.79-86
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• 1975

The optimal time-sequential distribution of supporting fire against enemy ground units in combat against attacking friendly units is studied. Lanchester type models of warfare are combined with optimal control theory in this investigation. The optimal time-sequential fire-support policy is characterized for a specific problem. Although complete details for the determination of the optimal policy are not given, it is conjectured, on the basis of the theorems which were proved, that for this problem the optimal policy is to always concentrate all supporting fire on the same enemy unit until supporting fire must be lifted.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.517-527
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• 2014

In this paper, we study affine transformations of normal bases and give an explicit formulation of the multiplication table of an affine transformation of a normal basis. We then discuss constructions of self-dual normal bases using affine transformations of traces of a type I optimal normal basis and of a Gauss period normal basis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.6
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• pp.391-398
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• 2023

In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.75-84
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• 2002

Using good properties of an optimal normal basis of type I in a finite field ${\mathbb{F}}_{2^m}$, we present a design of a bit serial multiplier of Berlekamp type, which is very effective in computing $xy^2$. It is shown that our multiplier does not need a basis conversion process and a squaring operation is a simple permutation in our basis. Therefore our multiplier provides a fast and an efficient hardware architecture for a bit serial multiplication of two elements in ${\mathbb{F}}_{2^m}$.