• ETRI Journal
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• v.32 no.3
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• pp.362-369
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• 2010

While the elliptic curve cryptosystem (ECC) is getting more popular in securing numerous systems, implementations without consideration for side-channel attacks are susceptible to critical information leakage. This paper proposes new power attack countermeasures for ECC over Koblitz curves. Based on some special properties of Koblitz curves, the proposed methods randomize the involved elliptic curve points in a highly regular manner so the resulting scalar multiplication algorithms can defeat the simple power analysis attack and the differential power analysis attack simultaneously. Compared with the previous countermeasures, the new methods are also noticeable in terms of computational cost.

• Journal of Korea Multimedia Society
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• v.20 no.2
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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.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.3
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• pp.389-395
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• 2011

Since Elliptic Curve Cryptosystems(ECCs) support the same security as RSA cryptosystem and ElGamal cryptosystem with 1/6 size key, ECCs are the most efficient to smart cards, cellular phone and small-size computers restricted by high memory capacity and power of process. In this paper, we explicitly explain methods for finite fields operations used in ECC, and then construct some composite fields over finite fields which are secure under Weil's decent attack and maximize the speed of operations. Lastly, we propose a fast multiplier over our composite fields.

• 한국IT서비스학회:학술대회논문집
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• 2009.05a
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• pp.205-208
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• 2009

이 논문에서는 RFID(Radio Frequency IDentification)에 대한 여러 가지 보안위협에 대하여 간단히 알아보고 그에 대응하는 안전한 암호학적 도구(Primitive)에 대하여 알아보겠다. 공개키 암호시스템(PKC, Public Key Cryptosystem)에 사용되는 타원곡선(EC, Elliptic Curve) 암호, NTRU(N-th degree TRUncated polynomial ring) 암호, Rabin 암호 등은 초경량 하드웨어 구현에 적합한 차세대 암호시스템으로서 안전한 RFID 인증서비스 제공과 프라이버시보호를 가능케 한다. 특히, 본고에서는 초경량 키의 길이, 저전력 소모성, 고속구현 속도를 갖는 타원곡선암호의 안전성에 대한 가이드라인을 제공하겠다.

• Proceedings of the IEEK Conference
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• 2004.06b
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• pp.529-532
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• 2004

The ECC(Elliptic Curve Cryptogrphics), one of the representative Public Key encryption algorithms, is used in Digital Signature, Encryption, Decryption and Key exchange etc. The key operation of an Elliptic curve cryptosystem is a scalar multiplication, hence the design of a scalar multiplier is the core of this paper. Although an Integer operation is computed in infinite field, the scalar multiplication is computed in finite field through adding points on Elliptic curve. In this paper, we implemented scalar multiplier in Elliptic curve based on the finite field GF($2^{163}$). And we verified it on the Embedded digital system using Xilinx FPGA connected to an EISC MCU. If my design is made as a chip, the performance of scalar multiplier applied to Samsung $0.35 {\mu}m$ Phantom Cell Library is expected to process at the rate of 8kbps and satisfy to make up an encryption processor for the Embedded digital doorphone.

• Proceedings of the Korea Information Processing Society Conference
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• 2005.05a
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• pp.1071-1074
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• 2005

The ECC(Elliptic Curve Cryptogrphics), one of the representative Public Key encryption algorithms, is used in Digital Signature, Encryption, Decryption and Key exchange etc. The key operation of an Elliptic curve cryptosystem is a scalar multiplication, hence the design of a scalar multiplier is the core of this paper. Although an Integer operation is computed in infinite field, the scalar multiplication is computed in finite field through adding points on Elliptic curve. In this paper, we implemented scalar multiplier in Elliptic curve based on the finite field $GF(2^{163})$. And we verified it on the Embedded digital system using Xilinx FPGA connected to an EISC MCU(Agent 2000). If my design is made as a chip, the performance of scalar multiplier applied to Samsung $0.35\;{\mu}m$ Phantom Cell Library is expected to process at the rate of 8kbps and satisfy to make up an encryption processor for the Embedded digital information home system.

• Journal of Information Processing Systems
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• v.13 no.4
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• pp.970-986
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• 2017

Certificateless public key cryptography (CL-PKC) is a new benchmark in modern cryptography. It not only simplifies the certificate management problem of PKC, but also avoids the key escrow problem of the identity based cryptosystem (ID-PKC). In this article, we propose a certificateless blind signature protocol which is based on elliptic curve cryptography (CLB-ECC). The scheme is suitable for the wireless communication environment because of smaller parameter size. The proposed scheme is proven to be secure against attacks by two different kinds of adversaries. CLB-ECC is efficient in terms of computation compared to the other existing conventional schemes. CLB-ECC can withstand forgery attack, key only attack, and known message attack. An e-cash framework, which is based on CLB-ECC, has also been proposed. As a result, the proposed CLB-ECC scheme seems to be more effective for applying to real life applications like e-shopping, e-voting, etc., in handheld devices.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.3
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• pp.511-514
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• 2019

Elliptic Curves Cryptosystem(ECC) provides the same level of security with relatively small key sizes, as compared to the traditional cryptosystems. The performance of ECC over GF(2m) and GF(p) depends on the efficiency of finite field arithmetic, especially the modular multiplication which is based on the reduction algorithm. In this paper, we propose a new modular reduction algorithm which provides high-speed ECC over NIST prime P-256. Detailed experimental results show that the proposed algorithm is about 25% faster than the previous methods.

• 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 Communications and Networks
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• v.12 no.1
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• pp.1-4
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• 2010

As a countermeasure to simple power attack, the unified point addition codes for the elliptic curve cryptosystem were introduced. However, some authors proposed a different kind of power attacks to the codes. This power attack uses the observation that some internal operations in the codes behave differently for addition and doubling. In this paper, we propose a new countermeasure against such an attack. The basic idea of the new countermeasure is that, if one of the input points of the codes is transformed to an equivalent point over the underlying finite field, then the code will behave in the same manner for addition and doubling. The new countermeasure is highly efficient in that it only requires 27(n-1)/3 extra ordinary integer subtractions (in average) for the whole n-bit scalar multiplication. The timing analysis of the proposed countermeasure is also presented to confirm its SPA resistance.