• 충청수학회지
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• 제28권1호
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• pp.97-102
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• 2015

In this work, we study some arithmetic properties of an intermediate modular curve $X_{\Delta}(21)$.

• 충청수학회지
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• 제30권4호
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• pp.445-447
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• 2017

We investigate congruence properties of Fourier coefficients of modular forms for ${\Gamma}^+_0(2)$.

• 정보보호학회논문지
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• 제29권3호
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• pp.515-518
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• 2019

타원곡선 상수배 연산은 사영좌표계를 기반으로 대부분 모듈러 곱셈으로 계산되므로 모듈러 곱셈의 효율성은 타원곡선암호의 성능에 크게 영향을 미친다. 본 논문에서는 FIPS 186-4의 224비트 소수체에서 효율적인 모듈러 곱셈 방법을 제안한다. 제안하는 방법은 Karatsuba 곱셈과 새로운 모듈러 감산을 수행한다. 제안하는 모듈러 곱셈은 기존방법에 비하여 25%정도 빠르며, 모듈러 감산만 비교하면 기존 방법보다 50% 연산으로 계산이 가능하다.

• 대한수학회보
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• 제44권1호
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• pp.47-59
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• 2007

We find the uniformizers of modular curves $X_{1}(N)\;(N=2,3)$ and explore the relationship with Thompson series and number theoretic property.

• 디지털산업정보학회논문지
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• 제16권2호
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• pp.1-9
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• 2020

Many cryptographic and error control coding algorithms rely on finite field GF(2m) arithmetic. Hardware implementation of these algorithms needs an efficient realization of finite field arithmetic operations. Finite field multiplication is complicated among the basic operations, and it is employed in field exponentiation and division operations. Various algorithms and architectures are proposed in the literature for hardware implementation of finite field multiplication to achieve a reduction in area and delay. In this paper, a low area and delay efficient semi-systolic multiplier over finite fields GF(2m) using the modified Montgomery modular multiplication (MMM) is presented. The least significant bit (LSB)-first multiplication and two-level parallel computing scheme are considered to improve the cell delay, latency, and area-time (AT) complexity. The proposed method has the features of regularity, modularity, and unidirectional data flow and offers a considerable improvement in AT complexity compared with related multipliers. The proposed multiplier can be used as a kernel circuit for exponentiation/division and multiplication.

• 디지털산업정보학회논문지
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• 제18권1호
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• pp.1-9
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• 2022

Galois field arithmetic is important in error correcting codes and public-key cryptography schemes. Hardware realization of these schemes requires an efficient implementation of Galois field arithmetic operations. Multiplication is the main finite field operation and designing efficient multiplier can clearly affect the performance of compute-intensive applications. Diverse algorithms and hardware architectures are presented in the literature for hardware realization of Galois field multiplication to acquire a reduction in time and area. This paper presents a low complexity semi-systolic multiplier to facilitate parallel processing by partitioning Montgomery modular multiplication (MMM) into two independent and identical units and two-level systolic computation scheme. Analytical results indicate that the proposed multiplier achieves lower area-time (AT) complexity compared to related multipliers. Moreover, the proposed method has regularity, concurrency, and modularity, and thus is well suited for VLSI implementation. It can be applied as a core circuit for multiplication and division/exponentiation.

• 대한수학회논문집
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• 제23권4호
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• pp.479-485
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• 2008

In this note, we study arithmetic properties for the exponents of modular forms on ${\Gamma}_0(p)$ for primes p. Our aim is to refine the result of [4] by using the geometric property of the modular curve of ${\Gamma}_0(p)$.

• International Journal of Contents
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• 제3권2호
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• pp.40-43
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• 2007

This paper proposed a new modular inverse algorithm based on the right-shifting binary Euclidean algorithm. For an n-bit numbers, the number of operations for the proposed algorithm is reduced about 61.3% less than the classical binary extended Euclidean algorithm. The proposed algorithm implementation shows substantial reduction in computation time over Galois field GF(p).

• 정보보호학회논문지
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• 제29권3호
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• pp.511-514
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• 2019

타원곡선암호시스템(ECC)은 같은 보안강도일 때 상대적으로 작은 키 길이를 가지며, 암호시스템의 효율성은 기존의 공개키 암호시스템과 같이 유한체 연산에 의존한다. 타원곡선 암호시스템의 경우 주로 이진체 또는 소수체에서 고려되며 유한체 연산에서 모듈러 곱셈 연산이 효율성에 가장 큰 영향을 미친다. 본 논문은 NIST P256에서 효율적인 모듈러 감산 방법을 제안한다. 제안하는 방법을 소프트웨어로 구현하면 결과 기존 대비 대략 25% 빨라진다.

• 한국수학사학회지
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• 제12권2호
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• pp.47-54
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• 1999

We introduce some historical facts on number theory, especially prime numbers and modular arithmetic. And then, with the viewpoint of computer arithmetic, residue number systems are considered as an alternate to positional number systems so that high performance and high speed computation can be achieved in a specified domain such as cryptography and digital signal processing.