• School Mathematics
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• v.13 no.2
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• pp.267-286
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• 2011

In this paper I investigated the historical developments of the algorithms for multiplication of natural numbers. Through this analysis I tried to describe more concretely what is to understand the common algorithm for multiplication of natural numbers. I found that decomposing dividends and divisors into small numbers and multiplying these numbers is the main strategy for carrying out multiplication of large numbers, and two decomposing and multiplying processes are very important in the algorithms for multiplication. Finally I proposed some implications based on these analysis.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.293-309
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• 2012

The algorithm of natural number multiplication is one of the basic topics of elementary school mathematics. Mastery of algorithm and understanding of the principles are important educational aims. In this paper we analyzed elementary school mathematics textbooks of South Korea, the United States, Singapore, Japan. As a result of analysis, we found out that there are much differences in the teaching of multiplication with three numbers, '${\times}10$', and '${\times}tens$'. We suggested some implication for the teaching of algorithm of natural number multiplication.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.505-525
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• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.6
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• pp.27-35
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• 2004

Finite or Galois fields have been used in numerous applications such as error correcting codes, digital signal processing and cryptography. These applications often require exponetiation on GF(2$^{m}$ ) which is a very computationally intensive operation. Most of the existing methods implemented the exponetiation by iterative methods using repeated multiplications, which leads to much computational load, or needed much hardware cost because of their structural complexity in implementing. In this paper, we present an effective VLSI architecture for exponentiation on GF(2$^{m}$ ). This circuit computes the exponentiation by multiplying product terms, each of which corresponds to an exponent bit. Until now use of this type algorithm has been confined to a primitive element but we generalize it to any elements in GF(2$^{m}$ ).

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.2
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• pp.115-123
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• 2007

In cryptographic devices like a smart-card whose computing ability and memory are limited, cryptographic algorithms should be performed efficiently. Scalar multiplication is very important operation in Elliptic Curve Cryptosystems, and so must be constructed in safety against side channel attack(SCA). But several countermeasures proposed against SCA are exposed weaknesses by new un-dreamed analysis. 'Double-and-add always scalar multiplication' algorithm adding dummy operation being known to secure against SPA is exposed weakness by Doubling Attack. But Doubling Attack cannot apply to sABS receding proposed by Hedabou, that is another countermeasure against SPA. Our paper proposes new strengthened Doubling Attacks that can break sABS receding SPA-countermeasure and a detailed method of our attacks through experimental result.

• Journal of Internet of Things and Convergence
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• v.6 no.2
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• pp.25-29
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• 2020

The elliptic curve crypto-algorithm is widely used in authentication for IoT environment, since it has small key size and low communication overhead compare to the RSA public key algorithm. If the scalar multiplication, a core operation of the elliptic curve crypto-algorithm, is not implemented securely, attackers can find the secret key to use simple power analysis or differential power analysis. In this paper, an elliptic curve scalar multiplication algorithm using a randomized scalar and an elliptic curve point blinding is suggested. It is resistant to power analysis but does not significantly reduce efficiency. Given a random r and an elliptic curve random point R, the elliptic scalar multiplication kP = u(P+R)-vR is calculated by using the regular variant Shamir's double ladder algorithm, where l+20-bit u≡rn+k(modn) and v≡rn-k(modn) using 2^lP=∓cP for the case of the order n=2^l±c.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.10 no.1
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• pp.3-11
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• 2000

AAL-1에서는 (128, 124) Reed-Solomon부호를 사용한 인터리버 및 디인터리버에 의해 ATM 셀에서 발생하는 오류를 정정하고 있다. Reed-Solomon부호의 복호법 중 직접복호법은 오류위치다항식의 계산없이 오류위치와 오류치를 알 수 있으며 유한체 GF(2m)의 표현에서 정규기저를 사용하면 곱셈과 나눗셈을 단순한게 비트 이동만으로 처리할 수 있다. 직접복호법과 정규기저를 사용하여 ATM 적응계층에 적용 가능한 (128, 124) Reed-Solomon부호의 복호기를 설계하고 VHDL로 시뮬레이션 하였으며 이 복호기는 동일한 복호회로에 의해 둘 또는 하나의 심벌에 발생한 오류를 정정할 수 있다.

• Journal of the Korean Society for Nondestructive Testing
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• v.26 no.2
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• pp.108-114
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• 2006

Transient and asymmetric density distributions of butane flow have been investigated from laser image signals by developed three-dimensional digital speckle tomography. Moved signals of speckles have been captured by multiple CCD images in three angles of view simultaneously because the flows were asymmetric and transient. The signals of speckle movements between no flow and downward butane flow from a circular half opening have been calculated by a cross-correlation tracking method so that those distances can be transferred to deflection angles of laser rays fur density gradients. The three-dimensional density fields have been reconstructed from the fringe shift signal which is integrated from the deflection angle by a real-time multiplicative algebraic reconstruction technique (MART).

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.10
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• pp.1093-1100
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• 2015

Since the security of RSA cryptosystem depends on the difficulty of factoring integers, it is the most important problem to factor large integers in RSA cryptosystem. The Lenstra elliptic curve factorization method(ECM) is considered a special purpose factoring algorithm as it is still the best algorithm for divisors not greatly exceeding 20 to 25 digits(64 to 83 bits or so). ECM, however, wastes most time to calculate $M{\cdot}P$ mod N and so Montgomery and Koyama both give fast methods for implementing $M{\cdot}P$ mod N. We, in this paper, further analyze Montgomery and Koyama's methods and propose an efficient algorithm which choose the optimal parameters and reduces the number of multiplications of Montgomery and Koyama's methods. Consequently, the run time of our algorithm is reduced by 20% or so than that of Montgomery and Koyama's methods.

• Korean Journal of Optics and Photonics
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• v.9 no.4
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• pp.245-250
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• 1998

A new computational algorithm is presented for the peak point detection of white light interferograms. Assuming the visibility function of white light interferograms as a quadratic polynomial, the peak point is searched so as to minimize the error sum between the measured intensity data and the analytical intensity. As compared with other existing algorithms, this new algorithm requires less computation since the peak point is simply determined with a single step matrix multiplication. In addition, a good robustness is obtained against external random disturbances on measured intensities since the algorithm is based upon least squares principles.