• Journal of KIISE:Computer Systems and Theory
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• v.26 no.7
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• pp.743-751
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• 1999

공개키 암호 시스템에서 모듈러 지수 연산은 주된 연산으로, 이 연산은 내부적으로 모듈러 곱셈을 반복적으로 수행함으로써 계산된다. 본 논문에서는 GF(2m)상에서 수행할 수 있는 Montgomery 알고리즘을 분석하여 right-to-left 방식의 모듈러 지수 연산에서 공통으로 계산 가능한 부분을 이용하여 모듈러 제곱과 모듈러 곱셈을 동시에 수행하는 선형 시스톨릭 어레이를 설계한다. 본 논문에서 설계한 시스톨릭 어레이는 기존의 곱셈기보다 모듈러 지수 연산시 약 0.67배 처리속도 향상을 가진다. 그리고, VLSI 칩과 같은 하드웨어로 구현함으로써 IC 카드에 이용될 수 있다.Abstract One of the main operations for the public key cryptographic system is the modular exponentiation, it is computed by performing the repetitive modular multiplications. In this paper, we analyze Montgomery's algorithm and design a linear systolic array to perform modular multiplication and modular squaring simultaneously. It is done by using common-multiplicand modular multiplication in the right-to-left modular exponentiation over GF(2m). The systolic array presented in this paper improves about 0.67 times than existing multipliers for performing the modular exponentiation. It could be designed on VLSI hardware and used in IC cards.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.1
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• pp.1-9
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• 2021

This paper proposes to automate the process of predicting crypto-operations from the power signal generated in RSA decoding process by frequency analysis and K-means algorithm. RSA decoding process is divided into square and multiply operation, and if we can predict the type of operations over time, we will know the RSA key value. After converting the power signal generated in the process of decoding into two-dimensional frequency signal, this paper used K-means algorithm to classify the frequency vector according to the type of operation. these classified frequency vector were used to predict the types of operations.

• Journal of KIISE:Computer Systems and Theory
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• v.26 no.9
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• pp.1055-1063
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• 1999

공개키 암호화 시스템에서 주된 연산은 512비트 이상의 큰 수에 의한 모듈러 지수 연산으로 표현되며, 이 연산은 내부적으로 모듈러 곱셈을 반복적으로 수행함으로써 계산된다. 본 논문에서는 Montgomery 알고리즘을 분석하여 right-to-left 방식의 모듈러 지수 연산에서 공통으로 계산 가능한 부분을 이용하여 모듈러 제곱과 모듈러 곱셈을 동시에 수행하는 선형 시스톨릭 어레이를 설계한다. 설계된 시스톨릭 어레이는 VLSI 칩과 같은 하드웨어로 구현함으로써 IC 카드나 smart 카드에 이용될 수 있다.Abstract The main operation of the public-key cryptographic system is represented the modular exponentiation containing 512 or more bits and computed by performing the repetitive modular multiplications. In this paper, we analyze Montgomery algorithm and design the linear systolic array for performing modular multiplication and modular squaring simultaneously using the computable part in common in right-to-left modular exponentiation. The systolic array presented in this paper could be designed on VLSI hardware and used in IC and smart card.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.18 no.4
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• pp.17-25
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• 2008

Because Chinese Remainder Theorem based RSA (RSA CRT) offers a faster version of modular exponentiation than ordinary repeated squaring, it is promoting with standard. Unfortunately there are major security issues associated with RSA CRT, since Bellcore announced a fault-based cryptanalysis against RSA CRT in 1996. In 1997, Shamir developed a countermeasure using error free immune checking procedure. And soon it became known that the this checking procedure can not effect as the countermeasures. Recently Yen proposed two hardware fault immune protocols for RSA CRT, and this two protocols do not assume the existence of checking procedure. However, in FDTC 2006, the method of attack against the Yen's two protocols was introduced. In this paper, the main purpose is to present a countermeasure against the method of attack from FDTC 2006 for CRT-RSA. The proposed countermeasure use a characteristic bit operation and dose not consider an additional operation.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.11
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• pp.32-39
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• 2009

In this thesis, design effective elimination interference algorithm of ICS repeat system for repeater that improve frequency efficiency. Gennerally, LMS Algorithm apply to ICS repeat system. Error convergence speed and accuracy of LMS Algorithm are influenced by reference signal. For improve LMS Algorithm, suggest Adaptive searching channel estimate algorithm. For using channel characteristic, adaptive searching channel estimate algorithm make reference signal similar interference signal by convolution operation and complement LMS algorithm demerit. For make channel similar pratical channel, apply Jake's Rayleigh multi-path model. LMS algorithm and suggested adaptive searching channel estimate algorithm that have 16 taps apply to ICS repeat system under Rayleigh multi-path channel, so simulate with MATLAB. According to simulate, ICS repeat system with LMS algorithm show -40 dB mean square error convergent after 110 datas iteration and ICS repeat system with adaptive searching channel estimate algorithm show -80 dB mean square en-or convergent after 120 datas iteration. Analyze simulation result, suggested adaptive searching channel estimate algorithm show 40 dB accuracy than LMS algorithm.

• Journal of KIISE:Computing Practices and Letters
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• v.15 no.6
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• pp.425-429
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• 2009

Recently, Chen et al.'s proposed mutual authentication scheme based on the quadratic resiidue, finding the squaring root problem, for avoiding exhaustive search on the server. But, if a malicious reader sends same random value, the tag is traced by an adversary. Moreover, there is realization problem because of its limited ability to compute squaring and hash function. In this paper, we analyze Chen et al.'s scheme and its weakness. Furthermore we present an improved mutual authentication scheme based on the quadratic residue which solves the tracing problem by generating random value on the tag and uses only squaring. We also make the scheme satisfy to forward secrecy without updating and synchronizing and avoid exhaustive search.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.6
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• pp.502-510
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• 2009

Multiprecision squaring is one of the most significant algorithms in the core public key cryptography operation. The aim of this work is to present a new improved squaring algorithm compared with the MIRACL's multi precision squaring algorithm in which the previous work [1] on multiprecision multiplication is implemented. First, previous works on multiprecision multiplication and standard squaring are analyzed. Then, our new Lazy Doubling squaring algorithm is introduced. In MIRACLE library [3], Scott's Carry-Catcher Hybrid multiplication technique [1] is applied to implementation of multiprecision multiplication and squaring. Experimental results of the Carry-Catcher hybrid squaring algorithm and the proposed Lazy Doubling squaring algorithm both of which are tested on Atmega128 CPU show that proposed idea has achieved significant performance improvements. The proposed Lazy Doubling Squaring algorithm reduces addition instructions by the fact $a_0\;{\ast}\;2\;+\;a_1\;{\ast}\;2\;+\;...\;+\;a_{n-1}\;{\ast}\;2\;+\;a_n\;{\ast}\;2\;=\;(a_0\;+\;a_1\;+\;...\;+\;a_{n-1}\;+\;a_n)\;{\ast}\;2$ while the standard squaring algorithm reduces multiplication instructions by the fact $S_{ij}\;=\;x_i\;{\ast}\;x_j\;=\;S_{ij}$. Experimental results show that the proposed squaring method is 25% faster than that in MIRACL.

• The KIPS Transactions:PartC
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• v.18C no.1
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• pp.1-6
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• 2011

The performance and practicality of cryptosystem for encryption, decryption, and primality test is primarily determined by the implementation efficiency of the modular exponentiation of $a^b$(mod n). To compute $a^b$(mod n), the standard binary squaring still seems to be the best choice. But, the d-ary, (d=2,3,4,5,6) method is more efficient in large b bits. This paper suggests m-numeral system modular exponentiation. This method can be apply to$b{\equiv}0$(mod m), $2{\leq}m{\leq}16$. And, also suggests the another method that is exit the algorithm in the case of the result is 1 or a.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.3
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• pp.19-25
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• 2009

In this thesis, design effective elimination interference algorithm of ICS repeat system for repeater that improve frequency efficiency. Error convergence speed and accuracy of LMS Algorithm are influenced by reference signal. For improve LMS Algorithm, suggest Adaptive channel estimate algorithm. For using channel characteristic, adaptive channel estimate algorithm make reference signal similar interference signal by convolution operation and complement LMS algorithm demerit. For make channel similar piratical channel, apply Jake's Rayleigh multi-path model that random five path with 130Hz Doppler frequency. LMS algorithm and suggested adaptive channel estimate algorithm that have 16 taps apply to ICS repeat system under Rayleigh multi-path channel, so simulate with MATLAB. According to simulate, ICS repeat system with LMS algorithm show -40dB square error convergent after 150 datas iteration and ICS repeat system with adaptive channel estimate algorithm show -80dB square error convergent after 200 datas iteration. Analyze simulation result, suggested adaptive channel estimate algorithm show more three times iteration performance than LMS algorithm, and 40dB accuracy.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10b
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• pp.521-523
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• 1999

본 논문에서는 입력 영상 열에서 얼굴 영역을 추출하고, 영역 내 특징점들의 움직임 벡터를 원근 움직임 모델에 정합하여 얼굴 영역을 추적하는 새로운 방법을 제안한다. 제안된 방법은 계층적 형판정합을 이용하여 얼굴 영역을 추출하고, 해당 영역에서 DoG 반응의 국부최대치를 찾아 특징점을 구한다. 그리고 최소제곱추정기법을 이용하여 각 특징점에서 얻어진 움직임 벡터를 원근 모델에 정합한다. 제안된 방법은 선별된 특징점에서 움직임 벡터를 계산함으로써 연산량을 줄일 수 있었고, 원근 움직임 모델을 이용함으로써 잡영에 강한 특성을 보인다.