• Proceedings of the Korean Information Science Society Conference
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• 2002.10e
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• pp.670-672
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• 2002

본 논문은 최소한의 정보량을 가지고 높은 안전성을 제공하는 타원곡선과 스마트 카드의 PIN을 동시에 이용하는 전자 지불 프로토콜을 제안한다. 타원 곡선 공개키 암호 알고리즘의 이용은 지불과정에서 필요한 계산 속도를 빠르게 함으로써 실제로 지불 시스템을 구현하였을 때 보다 효율적이고 편리한 이용환경을 제공할 수 있고 알고리즘과 스마트 카드의 고유 PIN을 이용하기 때문에 가지는 높은 안전성은 사용자들에게 지불시스템에 대한 신뢰성을 가지게 할 수 있다. 이와 같이 타원곡선 공개키 암호 알고리즘과 스마트 카드를 통하여 설계된 지불 시스템은 이동 컴퓨팅 환경에서도 효과적으로 사용될 수 있을 것이다.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.712-714
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• 2001

낮은 엔트로피의 패스워드를 이용하여 안전한 인증 및 키교환을 위해 Diffie-Hellman에 기반한 AMP(Authentication and key agreement via Memorable Password) 프로토콜이 제안되었다. 본 논문에서는 타원곡선 암호화가 가질수 있는 높은 보안성과 효율성을을 위해 타원곡선이산대수문제(Elliptic Curve Discrete Logarithm Problem)에 기반한 EC-AMP (Elliptic Curve-AMP)프로토콜을 제안한다. EC-AMP는 랜덤 오라클(random oracle) 모델에서 여러 가지 공격에 대해 안전하므로 인증 및 키교환이 필요한 네트워크 환경에 패스워드를 이용함으로 얻을수 있는 편의성과 타원곡선이산대수문제가 제공하는 안전성을 보장할 수 있다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.85-102
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• 1999

In this paper, we propose an EC-SRP(Elliptic Curve - Secure Remote Password) protocol that uses ECDLP(Elliptic Curve Discrete Logarithm Problem) instead SRP protocols’s DLP. Since EC-SRP uses ECDLP, it inherits the high performance and security those are the properties of elliptic curve. And we reduced the number of elliptic curve scalar multiplication to improve EC-SRP protocol’s performance. Also we have proved BC-SRP protocol is a secure AKC(Authenticated Key Agreement with Key Confirmation) protocol in a random oracle model.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.2 no.1
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• pp.45-48
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• 1992

제목에 주어진 타원 곡선들 $Y^{2}$=X$^{3}$+DX 은 허수 승법을 가진다. 이곡선을 소수 증명과 소인수 분해에 응용하는 방법을 이 논문에서 고찰해 본다.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2001.11a
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• pp.115-115
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• 2001

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.6 s.336
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• pp.67-74
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• 2005

Crypto-systems have difficulties in designing hardware due to the various standards. We propose a programmable and configurable architecture for cryptography coprocessors to accommodate various crypto-systems. The proposed architecture has a 32 bit I/O interface and internal bus width, and consists of a programmable finite field arithmetic unit, an input/output unit, a register file, and a control unit. The crypto-system is determined by the micro-codes in memory of the control unit, and is configured by programming the micro-codes. The coprocessor has a modular structure so that the arithmetic unit can be replaced if a substitute has an appropriate 32 bit I/O interface. It can be used in many crypto-systems by re-programming the micro-codes for corresponding crypto-system or by replacing operation units. We implement an elliptic curve crypto-processor using the proposed architecture and compare it with other crypto-processors

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.6
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• pp.1212-1217
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• 2004

The main back-bone operation in elliptic curve cryptosystems is scalar point multiplication. The most frequently used method implementing the scalar point multiplication, which is performed in the upper level of GF multiplication and GF division, has been the double-and-add algorithm, which is recently challenged by NAF(Non-Adjacent Format) algorithm. In this paper, we propose a more efficient and novel scalar multiplication method than existing double-and-add by applying redundant receding which originates from radix-4 Booth's algorithm. After deriving the novel quad-and-add algorithm, we created a new operation, named point quadruple, and verified with real application calculation to utilize it. Derived numerical expressions were verified using both C programs and HDL (Hardware Description Language) in real applications. Proposed method of elliptic curve scalar point multiplication can be utilized in many elliptic curve security applications for handling efficient and fast calculations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.3
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• pp.65-76
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• 2005

Speeding up scalar multiplication of an elliptic curve point has been a prime approach to efficient implementation of elliptic curve schemes such as EC-DSA and EC-ElGamal. Koblitz introduced a $base-{\phi}$ expansion method using the Frobenius map. Kobayashi et al. extended the $base-{\phi}$ scalar multiplication method to suit Optimal Extension Fields(OEF) by introducing the table reference method. In this paper we propose an efficient scalar multiplication algorithm on elliptic curve over OEF. The proposed $base-{\phi}$ scalar multiplication method uses an optimized batch technique after rearranging the computation sequence of $base-{\phi}$ expansion usually called Horner's rule. The simulation results show that the new method accelerates the scalar multiplication about $20\%{\sim}40\%$ over the Kobayashi et al. method and is about three times as fast as some conventional scalar multiplication methods.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.4
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• pp.548-555
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• 2022

This paper describes the hardware implementation of elliptic curve cryptography (ECC) used as a core operation in elliptic curve digital signature algorithm (ECDSA). The ECC processor supports eight operation modes (four point operations, four modular operations) on the NIST P-521 curve. In order to minimize computation complexity required for point scalar multiplication (PSM), the radix-4 Booth encoding scheme and modified Jacobian coordinate system were adopted, which was based on the complexity analysis for five PSM algorithms and four different coordinate systems. Modular multiplication was implemented using a modified 3-Way Toom-Cook multiplication and a modified fast reduction algorithm. The ECC processor was implemented on xczu7ev FPGA device to verify hardware operation. Hardware resources of 101,921 LUTs, 18,357 flip-flops and 101 DSP blocks were used, and it was evaluated that about 370 PSM operations per second were achieved at a maximum operation clock frequency of 45 MHz.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.111-119
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• 1997

본 논문에서는 Chaum이 처음으로 제안한 개념인 Blind signature를 타원곡선위에서 이산로그문제를 이용해 구현해보고 ECDSA와 Nyberg, Rueppel의 scheme을 Blind signature로 변형시킨 새로운 signature를 제시한다.