• Journal for History of Mathematics
• /
• v.20 no.1
• /
• pp.103-111
• /
• 2007

1997년 Coppersmith는 소인수분해를 모르는 법 N에 대한 합동방정식(modular equation)의 '작은 해'를 찾는 방법을 제안한다. 동시에 두 변수 다항식의 제한된 크기의 해를 찾는 방법도 격자이론을 이용하여 제안한다. 이러한 Coppersmith의 정리는 이후 암호학에서 매우 유용하게 사용되는데 특별히 RSA 암호체계에서 비밀 키를 찾아내거나 일부 비밀 키가 노출되었을 때 전체키를 복원하는 데에 중요한 역할을 한다. 본 논문에서는 Coppersmith의 정리를 살펴보고 이것이 RSA의 안전성에 어떠한 영향을 주었는지를 살펴본다.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.12 no.5
• /
• pp.185-189
• /
• 2012

It is almost impossible to directly find the prime factor, p,q of a large semiprime, n=pq. So Most of the integer factorization algorithms uses a indirect method that find the prime factor of the p=GCD(a-b,n),q=GCD(a+b,n) after getting the congruence of squares of the $a^2{\equiv}b^2$(mod n). Many methods of getting the congruence of squares have proposed, but it is not easy to get with RSA number of greater than a 100-digit number. This paper proposes a fast algorithm to get the congruence of squares. The proposed algorithm succeeded in getting the congruence of squares to a 19-digit number.

• Journal of Educational Research in Mathematics
• /
• v.25 no.1
• /
• pp.1-19
• /
• 2015

This paper aims to explore what we can improve in the curriculum, teaching-learning, and evaluation on the bases of the analyses of multiple-choice items set in National Assessment of Educational Achievement. For this goal, by using the distribution curves of the responses percentages, we will grasp the features of educational achievement which appear to students through an in-depth analysis about not only item itself but also the contents included in particular distracters. These analyses provide more information than the descriptive statistical values such as the mean of correct answer percentage and the discrimination of whole group and the mean of responses percentages of replies of subgroups. Because the distribution curves of the responses percentages reveal the transition from the lowest to the highest educational achievement very well. From these analyses we acquire the implications about the concept of prime factor or prime factorization, ratio(proportion) such as velocity, linear function, volume of cone, properties of solid figure, and probabilities of empty event and total event.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.5 no.1
• /
• pp.37-50
• /
• 1995

The smart card with the cryptography and VLSI technologies makes it possible to implement the electronic cash easily. A number of electronic each schemes have been proposed by many cryptographic researchers. In this paper, we propose a practical electronic cash system, using blind digital signature scheme. Schnorr's authentication scheme based on the discrete logarithm problem, and the hierarchical cash tree based on two one-way hash functions for dividable payment. Thisf electronic cash scheme has such properties as privacy of the payment, off-line payment, non-reuseability of cash, transferability of cash to another customer, and dividable payment of cash. This electronic cash protocol is well suited for implementing in smart card.

• Journal for History of Mathematics
• /
• v.17 no.1
• /
• pp.33-42
• /
• 2004

In this paper, we identify the essential ideas of Fundamental Theorem of Arithmetic(FTA). Then, we compare these ideas with several theorems of Euclid's Elements to investigate whether the essential ideas of FTA are contained in Elements or not. From this, we have the following conclusion: Even though Elements doesn't contain FTA explicitly, it contains all of the essential ideas of FTA. Finally, we assert two reasons why Greeks couldn't mention FTA explicitly. First, they oriented geometrically, and so they understood the concept of 'divide' as 'metric'. So they might have difficulty to find the divisor of the given number and the divisor of the divisor continuously. Second, they have limit to use notation in Mathematics. So they couldn't represent the given composite number as multiplication of all of its prime divisors.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.7 no.3
• /
• pp.545-551
• /
• 2012

In this paper, we propose a new cryptosystem based on the IQC depended on the complexity of class number and intractibility of factoring integer, and introduce two algorithm which reduce encryption and decryption times. To recognize the security of the cryptosystem, we take a simple example to analyze the complexities of public key and secret key and then introduce the operating process of the cryptosystem.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.11
• /
• pp.102-109
• /
• 1997

A two-degree-of freedom (TDF) $H_{\infty}$controller for a seeker scan loop is presented for the purpose of improving scanning performances. The perturbed plant model is characterized via the normalized coprime factorization. The TDF $H_{\infty}$controller is designed based on the loop shaping design procedure and model matching approach, and its performances are evaluated and compared with those of a previous work. It is demonstrated that the proposed TDF $H_{\infty}$controller is more effective to the control of the seeker scan loop than the previous controller.oller.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.16 no.2
• /
• pp.191-197
• /
• 2006

This paper deals with a fault detection system design for nuclear steam generator water level control system. We expressed the nonlinear properties of the steam generator level system as a T-S fuzzy system with time varying uncertain parameters. We design a residual generator using a left coprime factorization of the T-S fuzzy model and a fault detection filter in order to improve the fault detection performance. We demonstrate the efficiency of the suggested design method via many computer simulations.

• Review of KIISC
• /
• v.33 no.2
• /
• pp.31-37
• /
• 2023

소인수분해와 같이 매우 큰 경우의 수를 탐색하고 연산하며 비교하는 작업에서 강점을 가지는 양자컴퓨터는현재 사용되는 암호체계를 붕괴시킬 수 있다는 점에서 위협이 될 수 있다. 하지만 화학, 머신러닝과 같은 분야에서는 대단히 큰 혁신을 가져올 차세대 컴퓨터로 주목받고 있으며, IBM, Google, Amazon과 같은 세계적인 IT 기업들이 이러한 양자컴퓨터 관련 연구개발에 적극적으로 투자하고 있다. 본 고에서는 양자컴퓨터의 최근 개발 현황과 양자컴퓨팅을 위한 플랫폼인 IBM Qiskit, Google Cirq, ProjectQ, Amazon Braket, Microsoft Azure Quantum, Intel Quantum SDK에 대해 알아보고자 한다.

• Review of KIISC
• /
• v.34 no.2
• /
• pp.21-27
• /
• 2024

양자컴퓨터는 매우 많은 경우의 수를 탐색하고 연산하는 데에 있어 이점을 가지며, 이는 소인수분해와 같은 작업에서 기존 컴퓨팅을 능가할 수 있다. 이러한 능력으로 인해 양자컴퓨터는 현재 사용되는 암호체계를 위협할 수 있다. 또한, 화학, 머신러닝 등 다양한 분야에서 혁신을 가져올 수 있는 차세대 컴퓨팅 환경으로 주목받고 있다. 현재 IBM, Google, Amazon 등의 세계적인 IT 기업들이 이 분야의 연구 및 개발에 적극적으로 투자하고 있으며 본고에서는 양자컴퓨터의 최근 개발현황과 양자컴퓨팅을 위한 플랫폼인 IBM Qiskit, Google Cirq, ProjectQ, Amazon Braket, Microsoft Azure Quantum, Intel Quantum SDK, Pennylane에 대해 알아보고자 한다.