• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2003.07a
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• pp.83-88
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• 2003

부채널 공격(side channel attack)을 막는 새로운 접근방법으로 생각되는 랜덤 부호화 스칼라 곱 알고리즘은 Ha와 Moon에 의해서 제안되었다. 그러나 이 방법은 여전히 논쟁의 여지가 있다. 본 논문에서는 Ha-Moon 알고리즘이 기존의 세 가지 단순 전력 소모량 분석(simple power analysis, SPA)에 안전함을 보인다. 그리고 정수론의 성질을 이용하여 두 가지 중요한 정리를 제시하고 이 정리들을 이용하여 Ha-Moon 알고리즘에 적용할 수 있는 공격 알고리즘을 개발한다. 예를 들면, 163-비트 키들에 대하여 제안 알고리즘은 20개의 전력 소모량을 이용하여 키 복잡도 Ο(2$^{8}$ )를 가지고 공격할 수 있다.

• Proceedings of the Korean Information Science Society Conference
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• 2000.10a
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• pp.593-595
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• 2000

본 논문에서는 최적확장체(Optimal Extension Field; OEF)에서 정의되는 타원곡선 상에서 효율적인 스칼라 곱셈 알고리즘을 제안한다. 이 스칼라 곱셈 알고리즘은 프로비니어스 사상(Frobenius map)을 이용하여 스칼라 값을 Horner의 방법으로 Base-Ф 전개하고, 이 전개된 수식을 일괄처리 기법(batch-processing technique)을 사용하여 연산한다. 이 알고리즘을 적용할 경우, Kobayashi 등이 제안한 스칼라 곱셈 알고리즘보다 40% 정도의 성능향상을 보인다.

• 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.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2003.12a
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• pp.185-189
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• 2003

최근 스마트카드에 대한 수요가 증가함에 따라 스마트카드에 대한 보안상의 문제가 대두되고 있다. 스마트카드의 안전성을 위협하는 공격 방법 중 전력공격은 가장 강력한 공격으로 많은 연구가 되고 있다. 본 논문에서는 전력분석 공격의 한 방법인 MESD 공격에 대해 알아보고 이에 대한 대응 방법으로 제안된 RSM 알고리듬에 대해 알아본다. 또한 이 알고리듬의 연산 속도 향상을 위해 folding 기법을 사용한 알고리듬에 대해서도 알아보고 MESD 공격에 안전한지를 실험을 통해 검증한다.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.497-504
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• 2020

A weight ω on the positive half real line [0, ∞) is a positive continuous function such that ω(s + t) ≤ ω(s)ω(t), for all s, t ∈ [0, ∞), and ω(0) = 1. The weighted convolution Banach algebra L1(ω) is the algebra of all equivalence classes of Lebesgue measurable functions f such that ‖f‖ = ∫0∞|f(t)|ω(t)dt < ∞, under pointwise addition, scalar multiplication of functions, and the convolution product (f ⁎ g)(t) = ∫0t f(t - s)g(s)ds. We give a sufficient condition on a weight function ω(t) in order that L1(ω) has a bounded approximate identity.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.47 no.1
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• pp.139-149
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• 2010

Random scalar countermeasures, which carry out the scalar multiplication by the ephemeral secret key, against the differential power analysis of ECIES and ECDH have been known to be secure against various power analyses. However, if an attacker can find this ephemeral key from the one power signal, these countermeasures can be analyzed. In this paper, we propose a new power attack method which can do this analysis. Proposed attack method can be accomplished while an attacker compares the elliptic curve doubling operations and we use the principle component analysis in order to ease this comparison. When we have actually carried out the proposed power analysis, we can perfectly eliminate the error of existing function for the comparison and find a private key from this elimination of the error.

• Journal of IKEEE
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• v.22 no.3
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• pp.522-531
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• 2018

A public-key cryptography processor EC-RSA was designed, which integrates a 224-bit prime field elliptic curve cryptography (ECC) defined in the FIPS 186-2 as well as RSA with 2048-bit key length into a single hardware structure. A finite field arithmetic core used in both scalar multiplication for ECC and exponentiation for RSA was designed with 32-bit data-path. A lightweight implementation was achieved by an efficient hardware sharing of the finite field arithmetic core and internal memory for ECC and RSA operations. The EC-RSA processor was verified by FPGA implementation. It occupied 11,779 gate equivalents (GEs) and 14 kbit RAM synthesized with a 180-nm CMOS cell library and the estimated maximum clock frequency was 133 MHz. It takes 867,746 clock cycles for ECC scalar multiplication resulting in the estimated throughput of 34.3 kbps, and takes 26,149,013 clock cycles for RSA decryption resulting in the estimated throughput of 10.4 kbps.

• Convergence Security Journal
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• v.23 no.1
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• pp.45-54
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• 2023

Recently, with the development of the Internet of Things, research on protocols that can easily connect devices without a UI to the network has been steadily conducted. To this end, the Wi-Fi Alliance announced Wi-Fi Easy Connect, which can connect to a network using a QR code. However, since Wi-Fi Easy Connect requires a large amount of computation for safety, it is difficult to apply to low-power and miniaturized IoT devices. In addition, Wi-Fi Easy Connect considering scalability is designed to operate in a wired environment, but problems such as duplicate encryption occur because it does not consider a security environment like TLS. Therefore, in this paper, we analyze the Wi-Fi Easy Connect protocol and propose a protocol that can operate efficiently in the TLS environment. It was confirmed that the proposed protocol satisfies the existing security requirements and at the same time reduces about 67% of ECC scalar multiplication operations with a large amount of computation.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.425-441
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• 2013

In literature, several strong designated verifier signature (SDVS) schemes have been devised using elliptic curve bilinear pairing and map-topoint (MTP) hash function. The bilinear pairing requires a super-singular elliptic curve group having large number of elements and the relative computation cost of it is approximately two to three times higher than that of elliptic curve point multiplication, which indicates that bilinear pairing is an expensive operation. Moreover, the MTP function, which maps a user identity into an elliptic curve point, is more expensive than an elliptic curve scalar point multiplication. Hence, the SDVS schemes from bilinear pairing and MTP hash function are not efficient in real environments. Thus, a cost-efficient SDVS scheme using elliptic curve cryptography with pairingfree operation is proposed in this paper that instead of MTP hash function uses a general cryptographic hash function. The security analysis shows that our scheme is secure in the random oracle model with the hardness assumption of CDH problem. In addition, the formal security validation of the proposed scheme is done using AVISPA tool (Automated Validation of Internet Security Protocols and Applications) that demonstrated that our scheme is unforgeable against passive and active attacks. Our scheme also satisfies the different properties of an SDVS scheme including strongness, source hiding, non-transferability and unforgeability. The comparison of our scheme with others are given, which shows that it outperforms in terms of security, computation cost and bandwidth requirement.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.5
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• pp.17-30
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• 2001

In this paper, we implemented a scalar multiplier needed at an elliptic curve cryptosystem over standard basis in $GF(2^{163})$. The scalar multiplier consists of a radix-16 finite field serial multiplier and a finite field inverter with some control logics. The main contribution is to develop a new fast finite field inverter, which made it possible to avoid time consuming iterations of finite field multiplication. We used an algorithmic transformation technique to obtain a data-independent computational structure of the Extended Euclid GCD algorithm. The finite field multiplier and inverter shown in this paper have regular structure so that they can be easily extended to larger word size. Moreover they can achieve 100% throughput using the pipelining. Our new scalar multiplier is synthesized using Hyundai Electronics 0.6$\mu\textrm{m}$ CMOS library, and maximum operating frequency is estimated about 140MHz. The resulting data processing performance is 64Kbps, that is it takes 2.53ms to process a 163-bit data frame. We assure that this performance is enough to be used for digital signature, encryption & decryption and key exchange in real time embedded-processor environments.