• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.1191-1194
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• 1987

This paper presents a method for computing the powers and inverse of an element in GF($2^m$). This method is based on the squaring algorithm $A^2=\sum\limits_{i=0}^{2m-2}P_i$, where $Pi={\alpha}_{i/2}$ if i is even, Pi=0 otherwise, derived from the multiplication algorithm for two elements in GF($2^m$). The powers and inverses in GF($2^m$) for m=2, 3, 4,5 were obtained using computer program, and used in circuit realization of Galois switching function. The squaring and inverse generating circuits are also shown.

• Journal of KIISE:Computing Practices and Letters
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• v.15 no.6
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• pp.425-429
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• 2009

Recently, Chen et al.'s proposed mutual authentication scheme based on the quadratic resiidue, finding the squaring root problem, for avoiding exhaustive search on the server. But, if a malicious reader sends same random value, the tag is traced by an adversary. Moreover, there is realization problem because of its limited ability to compute squaring and hash function. In this paper, we analyze Chen et al.'s scheme and its weakness. Furthermore we present an improved mutual authentication scheme based on the quadratic residue which solves the tracing problem by generating random value on the tag and uses only squaring. We also make the scheme satisfy to forward secrecy without updating and synchronizing and avoid exhaustive search.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.7
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• pp.1420-1428
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• 2017

It is difficult to guarantee the reliability of the algorithm due to the difference of the sampling frequency among the various ECG databases used for the R wave detection in case of applying to different environments. In this study, we propose an optimal threshold setting method for R wave detection according to the sampling frequency of ECG signals. For this purpose, preprocessing process was performed using moving average and the squaring function based the derivative. The optimal value for the peak threshold was then detected according to the sampling frequency by changing the threshold value according to the variation of the signal and the previously detected peak value. The performance of R wave detection is evaluated by using 48 record of MIT-BIH arrhythmia database. When the optimal values of the differential section, window size, and threshold coefficient for the MIT-BIH sampling frequency of 360 Hz were 7, 8, and 6.6, respectively, the R wave detection rate was 99.758%.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.6
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• pp.1083-1091
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• 2017

This paper describes a design of cryptographic processor supporting 224-bit elliptic curves over prime field defined by NIST. Scalar point multiplication that is a core arithmetic function in elliptic curve cryptography(ECC) was implemented by adopting the modified Montgomery ladder algorithm. In order to eliminate division operations that have high computational complexity, projective coordinate was used to implement point addition and point doubling operations, which uses addition, subtraction, multiplication and squaring operations over GF(p). The final result of the scalar point multiplication is converted to affine coordinate and the inverse operation is implemented using Fermat's little theorem. The ECC processor was verified by FPGA implementation using Virtex5 device. The ECC processor synthesized using a 0.18 um CMOS cell library occupies 2.7-Kbit RAM and 27,739 gate equivalents (GEs), and the estimated maximum clock frequency is 71 MHz. One scalar point multiplication takes 1,326,985 clock cycles resulting in the computation time of 18.7 msec at the maximum clock frequency.