• 한국정보보호학회:학술대회논문집
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• 한국정보보호학회 2006년도 하계학술대회
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• pp.356-360
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• 2006

Recently, many power analysis attacks have been proposed. Since the attacks are powerful, it is very important to implement cryptosystems securely against the attacks. We propose countermeasures against power analysis attacks for elliptic curve cryptosystems based on Koblitz curves (KCs), which are a special class of elliptic curves. That is, we make our countermeasures be secure against SPA, DPA, and new DPA attacks, specially RPA, ZPA, using a random point at each execution of elliptic curve scalar multiplication. And since our countermeasures are designed to use the Frobenius map of KC, those are very fast.

• 한국정보과학회논문지:시스템및이론
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• 제31권10호
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• pp.588-592
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• 2004

스칼라 곱셈은 정수 $textsc{k}$와 타원곡선 상의 한 점 P가 주어졌을 때 $textsc{k}$P를 계산하는 연산이다. 스칼라 곱셈을 빠르게 하기 위한 일반적인 방법으로 Agnew Mullin, Vanstone은 고정된 값의 해밍 웨이트를 갖는 스칼라 $textsc{k}$를 이용하는 방법을 제안하였다. 본 논문에서는 고정된 값의 부호화 해밍 웨이트를 갖는 $textsc{k}$를 이용하는 방법을 제안하고, 이 방법이 더 안전함을 보인다.

• JSTS:Journal of Semiconductor Technology and Science
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• 제16권1호
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• pp.118-125
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• 2016

This paper presents a new high-efficient algorithm and architecture for an elliptic curve cryptographic processor. To reduce the computational complexity, novel modified Lopez-Dahab scalar point multiplication and left-to-right algorithms are proposed for point multiplication operation. Moreover, bit-serial Galois-field multiplication is used in order to decrease hardware complexity. The field multiplication operations are performed in parallel to improve system latency. As a result, our approach can reduce hardware costs, while the total time required for point multiplication is kept to a reasonable amount. The results on a Xilinx Virtex-5, Virtex-7 FPGAs and VLSI implementation show that the proposed architecture has less hardware complexity, number of clock cycles and higher efficiency than the previous works.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 II
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• pp.1027-1030
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• 2003

In this paper, we designed GF(2$^{m}$ ) inversion and division processor for Elliptic Curve Cryptographic system. The processor that has 191 by m value designed using Modified Euclid Algorithm. The processor is designed using 0.35 ${\mu}{\textrm}{m}$ CMOS technology and consists of about 14,000 gates and consumes 370 mW. From timing simulation results, it is verified that the processor can operate under 367 Mhz clock frequency due to 2.72 ns critical path delay. Therefore, the designed processor can be applied to Elliptic Curve Cryptographic system.

• 한국멀티미디어학회논문지
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• 제20권2호
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• pp.289-297
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• 2017

When implementing a hardware elliptic curve cryptosystem (ECC) module, the efficient design of Modular Inverse (MI) algorithm is especially important since it requires much more computation than other finite field operations in ECC. Among the MI algorithms, binary Right-Shift modular inverse (RS) algorithm has good performance when implemented in hardware, but Montgomery Modular Inverse (MMI) algorithm is not considered in [1, 2]. Since MMI has a similar structure to that of RS, we show that the area-improvement idea that is applied to RS is applicable to MMI, and that we can improve the speed of MMI. We designed area- and speed-improved MMI variants as hardware modules and analyzed their performance.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2004년도 춘계종합학술대회
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• pp.784-787
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• 2004

타원곡선 암호시스템에서의 가장 줄기가 되는 연산은 스칼라 곱셈 연산이다. 본 논문에서는 기존의 두배점-덧셈 (double-and-add) 알고리즘으로 처리하였던 스칼라 곱셈 연산을 개선하여 네배점-덧셈(fund-and-add) 알고리즘을 사용하기 위하여 네배점 (point quadruple) 연산을 유도한다. 유도된 식은 C 프로그램을 사용하여 실제 계산에 응용하여 증명하였다. 네배점 스칼라 연산은 타원곡선 암호시스템의 효율적이고 빠른 연산을 처리하는데 응용될 수 있다.

• Journal of information and communication convergence engineering
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• 제2권3호
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• pp.182-186
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• 2004

When most of existing instant messengers log on server, they transmit to sever in encoding password to RC5. but RC5 don't be secured because it has been known many of password cracking tools. Also, messengers don't have any protection on the transmitted information with communicating two hosts since loging on, endangering the privacy of the user. As a counter measure, messengers need to provide security service including message encryption. In this paper, we designed a key exchange method of password representing fast, effective and high security degree, using ECC(Elliptic Curve Cryptography) that being known the very stronger than another public key cryptography with same key size. To effectively improve data transmission and its security using IPSec protocol between users, tunnel mode is introduced. Tunnel mode transmits Host-to-Host data through virtual pipelines on the Internet.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 B
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• pp.1014-1017
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• 2003

In this paper, after the crypto acceleration board of the server-termination type is designed, we implement the Elliptic Curve Digital Signature Algorithm on the board that serves data integrity and user authentication. For implementing ECDSA, we use crypto co-processor, MPC180, to reduce the computation burden of main Processor (MPC860) on the board. By using crypto co-processor, the computation efficiency in case prime field is improved more between 90 and 100 times than the software library and between 20 and 90 times in case binary field. Our result is expect to apply for SSL acceleration board.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2001년도 가을 학술발표논문집 Vol.28 No.2 (1)
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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.

• 대한수학회논문집
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• 제36권3호
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• pp.401-411
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• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.