• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2004.05b
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• pp.784-787
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• 2004

The most time-consuming back-bone operation in an elliptic curve cryptosystem is scalar multiplication. In this paper, we propose a method of inducing a GF operation named point quadruple operation to be used in the quad-and-add algorithm, whith was achieved by refining the traditional double-and-add algorithm. Induced expression of the algorithm was verified and proven by C program in a real model of calculation. The point quadruple operation can be used in fast and efficient implementation of scalar multiplication operation.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.581-583
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• 2017

Elliptic curve cyptography is relatively a current cryptography based on point arithmetic on elliptic curves and the Elliptic Curve Discrete Logarithm Problem (ECDLP). This discrete logarithm problems enables perfect forward secrecy which helps to easily generate key and almost impossible to revert the generation which is a great feature for privacy and protection. In this paper, we provide a lightweight Elliptic Curve Diffie-Hellman (ECDH) Key exchange generator that creates a 163 bit long shared key that can be used in an Elliptic Curve Integrated Encryption Scheme (ECIES) as well as for key agreement. The algorithm uses a fast multiplication algorithm that is small in size and also implements the extended euclidean algorithm. This proposed architecture was designed using verilog HDL, synthesized with the vivado ISE 2016.3 and was implemented on the virtex-7 FPGA board.

• Proceedings of the Korea Information Processing Society Conference
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• 2012.11a
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• pp.958-960
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• 2012

본 논문에서는 사용자에게 PHR(PHR : Personal Health Record) 서비스를 제공 할 때 발생 가능한 개인정보변조 및 유출에 대한 위협에 대응하기 위하여 PHR과 ECC(ECC : Elliptic Curve Cryptosystem)에 대한 연구 및 안전한 개인정보 전송을 위한 XML 형식의 PHR 서비스 메시지 구조설계와 ECC 알고리즘 기법을 이용한 PHR 암 복호화 시스템을 설계하였다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2018.05a
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• pp.163-165
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• 2018

GF(p)상 타원곡선 암호(ECC)와 RSA를 단일 하드웨어로 통합하여 구현한 공개키 암호 프로세서를 설계하였다. 설계된 EC-RSA 공개키 암호 프로세서는 NIST 표준에 정의된 소수체 상의 224-비트 타원 곡선 P-224와 2048-비트 키 길이의 RSA를 지원한다. ECC와 RSA가 갖는 연산의 공통점을 기반으로 워드기반 몽고메리 곱셈기와 메모리 블록을 효율적으로 결합하여 최적화된 데이터 패스 구조를 적용하였다. EC-RSA 공개키 암호 프로세서는 Modelsim을 이용한 기능검증을 통하여 정상동작을 확인하였으며, $0.18{\mu}m$ CMOS 셀 라이브러리로 합성한 결과 11,779 GEs와 14-Kbit RAM의 경량 하드웨어로 구현되었다. EC-RSA 공개키 암호 프로세서는 최대 동작주파수 133 MHz이며, ECC 연산에는 867,746 클록주기가 소요되며, RSA 복호화 연산에는 26,149,013 클록주기가 소요된다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.247-249
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• 2017

NIST에서 표준으로 정의된 P-192, P-224, P-256, P-384 타원곡선 상의 스칼라 곱셈(scalar multiplication) 연산을 지원하는 Scalable 타원곡선 암호(Elliptic Curve Cryptography; ECC) 프로세서의 설계에 대해 기술한다. 투영(projective) 좌표계를 이용하여 하드웨어 자원 소모가 큰 나눗셈 연산을 제거하였으며, GF(p) 상의 덧셈, 뺄셈, 곱셈 등의 유한체 연산을 지원한다. 워드 기반 몽고메리 곱셈기를 이용하여 다양한 크기의 필드(field)에서 고정된 하드웨어 자원을 통하여 곱셈 연산을 수행하도록 하였으며, 필드의 크기에 따라 연산 사이클이 증가하거나 감소한다. 설계된 Scalable ECC 프로세서는 Verilog HDL로 모델링 되었으며, Modelsim을 이용한 기능검증을 하였다. Xilinx Virtex5 FPGA 디바이스 합성결과 5,376-비트 RAM과 970 슬라이스로 구현되었으며, 최대 55 MHz의 동작 주파수를 갖는다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.25 no.8
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• pp.1095-1102
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• 2021

A scalable ECC architecture with high scalability and flexibility between performance and hardware complexity is proposed. For architectural scalability, a modular arithmetic unit based on a one-dimensional array of processing element (PE) that performs finite field operations on 32-bit words in parallel was implemented, and the number of PEs used can be determined in the range of 1 to 8 for circuit synthesis. A scalable algorithms for word-based Montgomery multiplication and Montgomery inversion were adopted. As a result of implementing scalable ECC processor (sECCP) using 180-nm CMOS technology, it was implemented with 100 kGEs and 8.8 kbits of RAM when N_PE=1, and with 203 kGEs and 12.8 kbits of RAM when N_PE=8. The performance of sECCP with N_PE=1 and N_PE=8 was analyzed to be 110 PSMs/sec and 610 PSMs/sec, respectively, on P256R elliptic curve when operating at 100 MHz clock.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.3
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• pp.1439-1444
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• 2013

Recently, as the use of the applications like online banking and stock trading is increasing by the rapid development of the network, security of data content is becoming more and more important. Accordingly, public key or symmetric key encryption algorithm is widely used in open networks such as the internet for the protection of data. Generally, public key cryptographic systems is based on two famous number theoretic problems namely factoring or discrete logarithm problem. So, public key cryptographic systems is relatively slow compared to symmetric key cryptography systems. Among public key cryptographic systems, the advantage of ECC compared to RSA is that it offers equal security for a far smaller key. For this reason, ECC is faster than RSA. In this paper, we propose a efficient key generation method for elliptic curve cryptography system based on the real number field.

• JSTS:Journal of Semiconductor Technology and Science
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• v.17 no.3
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• pp.425-437
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• 2017

For efficient hardware (HW) implementation of elliptic curve cryptography (ECC), various sub-modules for the underlying finite field operations should be implemented efficiently. Among these sub-modules, modular inversion (MI) requires the most computation; therefore, its performance might be a dominant factor of the overall performance of an ECC module. To determine the most efficient MI algorithm for an HW ECC module, we implement various classes of MI algorithms and analyze their performance. In contrast to the common belief in previous research, our results show that the right-shift binary inversion (RS) algorithm performs well when implemented in hardware. In addition, we present optimization methods to reduce the area overhead and improve the speed of the RS algorithm. By applying these methods, we propose a new RS-variant that is both fast and compact. The proposed MI module is more than twice as fast as the other two classes of MI: shifting Euclidean (SE) and left-shift binary inversion (LS) algorithms. It consumes only 15% more area and even 5% less area than SE and LS, respectively. Finally, we show that how our new method can be applied to optimize an HW ECC module.

• Proceedings of the Korea Information Processing Society Conference
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• 2003.11c
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• pp.1925-1928
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• 2003

컴퓨터와 네트워크의 보급이 일반화되면서 인터넷을 통한 정보전달이 일상 생활처럼 되고 있다. 기존에는 정보를 전달하기 위한 방법이 주로 전자메일에 한정되어 있던 것에 반해, 요즘은 좀 더 즉각적으로 메시지를 전달해주는 인스턴트 메신저를 많이 사용하고 있다. 인스턴트 메신저는 이러한 장점으로 인해 국내에서도 사용자가 급속하게 늘고 있다. 현재 사용하고 있는 대부분의 인스턴트 메신저는 서버에 로그 온 할 때 패스워드를 대칭키 암호기술로 암호화해서 보내지만 패스워드 크래킹 프로그램들이 많이 알려져 있어 전송되는 정보가 제 3자에 의한 암호 해독이 가능하게 된다. 또한 키 분배 및 관리에 있어서 어려움이 있다. 대칭키 암호기술의 어려움을 극복하는 방안으로 제안되었던 공개키 암호기준은 키 분배 및 관리는 편리해졌지만 알고리즘이 더 복잡하고 키의 길이가 상당히 길어 많은 제약이 따르며 처리속도가 오래 걸린다는 단점을 지닌다.[1] 이에 대안으로 제안된 타원곡선 암호체계(Elliptic Curve Cryptography, ECC)는 동일한 키 사이즈를 갖는 다른 암호체계보다 훨씬 강하다고 알려져 있다. 본 논문에서는 ECC를 이용하여 빠르고 효율적이며 높은 안전도를 나타내는 인스턴트 메신저에서의 패스워드 키 교환 방식을 설계한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.11
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• pp.5537-5555
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• 2017

Having the characteristics of unlinkability, anonymity, and unforgeability, blind signatures are widely used for privacy-related applications such as electronic cash, electronic voting and electronic auction systems where to maintain the anonymity of the participants. Among these applications, the blinded message is needed for a certain purpose by which users delegate signing operation and communicate with each other in a trusted manner. This application leads to the need of proxy blind signature schemes. Proxy blind signature is an important type of cryptographic primitive to realize the properties of both blind signature and proxy signature. Over the past years, many proxy blind signature algorithms have been adopted to fulfill such task based on the discrete logarithm problem (DLP) and the elliptic curve discrete log problem (ECDLP), and most of the existing studies mainly aim to provide effective models to satisfy the security requirements concerning a single blinded message. Unlike many previous works, the proposed scheme applies the signcryption paradigm to the proxy blind signature technology for handling multiple blinded messages at a time based on elliptic curve cryptography (ECC). This innovative method thus has a higher level of security to achieve the security goals of both blind signature and proxy signature. Moreover, the evaluation results show that this proposed protocol is more efficient, consuming low communication overhead while increasing the volume of digital messages compared to the performance from other solutions. Due to these features, this design is able to be implemented in small low-power intelligent devices and very suitable and easily adoptable for e-system applications in pervasive mobile computing environment.