• Journal of the Korea Institute of Information Security & Cryptology
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• v.21 no.6
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• pp.3-12
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• 2011

A hashing function that maps arbitrary messages directly onto curve points (MapToPoint) has non-negligible complexity in pairing-based cryptosystems. Unlike elliptic curve cryptosystems, pairing-based cryptosystems require the hashing function in ternary fields. Barreto et al. observed that it is more advantageous to hash the message to an ordinate instead of an abscissa. So, they significantly improved the hashing function by using a matrix with coefficients of the abscissa. In this paper, we improve the method of Barreto et al. by reducing the matrix. Our method requires only 44% memory of the previous result. Moreover we can hash a message onto a curve point 2~3 times faster than Barreto's Method.

• 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.11 no.2
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• pp.37-44
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• 2001

In this paper, an efficient architecture for the ECC multiplier in GF(2") is proposed. We give a design example for the irreducible trinomials $x_{193}\;+\;x_{15}\;+\;1$. In hardware implementations, it is often desirable to use the irreducible trinomial equations. A digit-serial multiplier with a digit size of 32 is proposed, which has more advantages than the 193bit serial LFSR architecture. The proposed multiplier is verified with a VHDL description using an elliptic curve addition. The elliptic curve used in this implementation is defined by Weierstrass equations. The measured results show that the proposed multiplier it 0.3 times smaller than the bit-serial LFSR multiplier.lier.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2002.11a
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• pp.306-310
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• 2002

이동 통신의 급격한 발달로 다양한 부가가치서비스가 등장하고, 이러한 서비스를 좀더 편리하고 안전하게 사용하고 싶어하는 사용자와 부가가치서비스를 제공하는 VASP(Value -Added Service Provider) 사이의 보안이 필수적인 것이 되었다. 이를 위하여 이동 통신 환경의 한계인 제한된 자원과 제한된 계산력을 극복할 수 있도록 적은키 길이를 가지고 보다 안전한 서비스를 제공할 수 있는 타원곡선 암호시스템(ECC)를 기반으로 하여 부가가치서비스에 효율적인 인증 및 키 합의 프로토콜을 제안하고, 차세대 이동통신시스템에 적용해본다.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07a
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• pp.187-189
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• 2005

최적확장체(Optimal Extension Field:OEF)는 유한체의 일종으로서, 타원곡선 암호시스템의 소프트웨어 구현에 있어 매우 유용하다. Bailey및 Paar는 $p^i$거듭제곱 연산을 비롯하여 다수의 효율적인 OEF연산 알고리즘을 제안하였으며, 또한 암호 응용에 적합한 OEF를 생성하기 위한 효과적인 알고리즘을 제안하였다. 본 논문에서는 Bailey-Paar의 $p^i$거듭제곱 알고리즘이 적용되지 않는 반례를 제시하며, 또한 그들의 OEF생성 알고리즘은 실제로 OEF가 아닌 유한체를 OEF로 출력하는 오류가 있음을 보인다. 본 논문에서는 이러한 문제들을 해결한 개선된 알고리즘들을 제시하고, OEF의 개수에 관한 수정된 통계치를 제시한다.

• Review of KIISC
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• v.8 no.2
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• pp.37-48
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• 1998

수많은 암호시스템과 관련 프로토콜의 안전이 소인수분해 문제의 어려움에 기반하고 있다 본 논문에서는 암호해독과 설계에 영향을 줄 수 있는 소인수분해 알고리즘에 대하여 현재까지의 연구동향과 성과를 기술하였으며, 연분수를 이용한 인수분해 알고리즘(CFRACT), QS(Quadratic Sieve), NFS(Number Field Sieve),타원곡선 알고리즘 및 Pollard's p-1알고리즘 Pollard's rho알로리즘을 분석하였다.

• Journal of KIISE:Computing Practices and Letters
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• v.8 no.1
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• pp.88-95
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• 2002

In recent years, the security of hardware and software systems is one of the most essential factor of our safe network community. As elliptic Curve Cryptosystems proposed by N. Koblitz and V. Miller independently in 1985, require fewer bits for the same security as the existing cryptosystems, for example RSA, there is a net reduction in cost size, and time. In this thesis, we propose an efficient hardware architecture of underlying field arithmetic processor for Elliptic Curve Cryptosystems, and a very useful method for implementing the architecture, especially multiplicative inverse operator over GF$GF (2^m)$ onto FPGA and futhermore VLSI, where the method is based on optimized unit operation components. We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed We optimize the arithmetic processor for speed so that it has a resonable number of gates to implement. The proposed architecture could be applied to any finite field $F_{2m}$. According to the simulation result, though the number of gates are increased by a factor of 8.8, the multiplication speed and inversion speed has been improved 150 times, 480 times respectively compared with the thesis presented by Sarwono Sutikno et al. [7]. The designed underlying arithmetic processor can be also applied for implementing other crypto-processor and various finite field applications.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.05a
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• pp.656-658
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• 2013

Due to increasing demand of new technology, the complexity of hardware and software consisting embedded systems is rapidly growing. Consequently, it is getting hard to design complex devices only with traditional methodology. In this contribution, I introduce a new approach of designing complex hardware with SystemVerilog. I adopted the idea of object oriented implementation of the SystemVerilog to the design of an elliptic curve crypto-engine server farm. I successfully implemented the whole system including the test bench in one integrated environment, otherwise in the traditional way it would have cost Verilog simulation and C/SystemC verification which means much more time and effort.

• The KIPS Transactions:PartC
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• v.11C no.5
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• pp.569-576
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• 2004

Conventional researches of standard tool validating public key cryptographic algorithm have been studied for the internet environment, not for the mobile internet. It is important to develop the validation tool for establishment of interoperability and convenience of users in mobile internet. Therefore, this paper presents the validation tool of Elliptic Curie Cryptography algorithm that can test if following X9.62 technology standard specification. The validation tool can be applied all information securities using ECDSA, ECKCDSA, ECDH, etc. Moreover, we can en-hace the precision of validation through several experiments and perform the validation tool in the online environment.

• Journal of the Korea Society of Computer and Information
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• v.8 no.4
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• pp.104-110
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• 2003

In this paper, we proposed hybrid cryptosystem of Diffie-Hellman base in Elliptic Curve, and explained for specific protocol design. The proposed system is efficient hybrid cryptosystems system that offer implicit key authentication about sender and receiver unlike existing hybrid system. This system increased safety generating session key using pseudo-random number generator by cryptographic. Because the system is hybrid system, it is more efficient in calculation amount aspect supplementing merit and fault of public key system and secret key system. Also, the system can not get right plaintext except receiver even if sender's secret key is revealed and impersonation attack is impossible. And the system offers security on known keys without influencing in safety of other session's cryptogram even if session key is exposed. And the system is provided safety about mutual entity authentication and replay attack.