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Computer intensive method for extended Euclidean algorithm (확장 유클리드 알고리즘에 대한 컴퓨터 집약적 방법에 대한 연구)

Kim, Daehak;Oh, Kwang Sik
- Journal of the Korean Data and Information Science Society
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- v.25 no.6
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- pp.1467-1474
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- 2014
In this paper, we consider the two computer intensive methods for extended Euclidean algdrithm. Two methods we propose are C-programming based approach and Microsoft excel based method, respectively. Thses methods are applied to the derivation of greatest commnon devisor, multiplicative inverse for modular operation and the solution of diophantine equation. Concrete investigation for extended Euclidean algorithm with the computer intensive process is given. For the application of extended Euclidean algorithm, we consider the RSA encrytion method which is still popular recently.
https://doi.org/10.7465/jkdi.2014.25.6.1467 인용 PDF KSCI

Secure Scalar Multiplication with Simultaneous Inversion Algorithm in Hyperelliptic Curve Cryptosystem (초 타원 곡선 암호시스템에서 동시 역원 알고리즘을 가진 안전한 스칼라 곱셈)

Park, Taek-Jin
- The Journal of Korea Institute of Information, Electronics, and Communication Technology
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- v.4 no.4
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- pp.318-326
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- 2011
Public key cryptosystem applications are very difficult in Ubiquitos environments due to computational complexity, memory and power constrains. HECC offers the same of levels of security with much shorter bit-lengths than RSA or ECC. Scalar multiplication is the core operation in HECC. T.Lange proposed inverse free scalar multiplication on genus 2 HECC. However, further coordinate must be access to SCA and need more storage space. This paper developed secure scalar multiplication algorithm with simultaneous inversion algorithm in HECC. To improve the over all performance and security, the proposed algorithm adopt the comparable technique of the simultaneous inversion algorithm. The proposed algorithm is resistant to DPA and SPA.
https://doi.org/10.17661/jkiiect.2011.4.4.318 인용 PDF

A Fast Algorithm for Computing Multiplicative Inverses in GF(2$^{m}$) using Factorization Formula and Normal Basis (인수분해 공식과 정규기저를 이용한 GF(2$^{m}$ ) 상의 고속 곱셈 역원 연산 알고리즘)

장용희;권용진
- Journal of KIISE:Computer Systems and Theory
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- v.30 no.5_6
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- pp.324-329
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- 2003
The public-key cryptosystems such as Diffie-Hellman Key Distribution and Elliptical Curve Cryptosystems are built on the basis of the operations defined in GF(2$^{m}$ ):addition, subtraction, multiplication and multiplicative inversion. It is important that these operations should be computed at high speed in order to implement these cryptosystems efficiently. Among those operations, as being the most time-consuming, multiplicative inversion has become the object of lots of investigation Formant's theorem says $\beta$$^{-1}$ =$\beta$$^{2}$sup m/-2/, where $\beta$$^{-1}$ is the multiplicative inverse of $\beta$$\in$GF(2$^{m}$ ). Therefore, to compute the multiplicative inverse of arbitrary elements of GF(2$^{m}$ ), it is most important to reduce the number of times of multiplication by decomposing 2$^{m}$ -2 efficiently. Among many algorithms relevant to the subject, the algorithm proposed by Itoh and Tsujii[2] has reduced the required number of times of multiplication to O(log m) by using normal basis. Furthermore, a few papers have presented algorithms improving the Itoh and Tsujii's. However they have some demerits such as complicated decomposition processes[3,5]. In this paper, in the case of 2$^{m}$ -2, which is mainly used in practical applications, an efficient algorithm is proposed for computing the multiplicative inverse at high speed by using both the factorization formula x$^3$-y$^3$=(x-y)(x$^2$＋xy＋y$^2$) and normal basis. The number of times of multiplication of the algorithm is smaller than that of the algorithm proposed by Itoh and Tsujii. Also the algorithm decomposes 2$^{m}$ -2 more simply than other proposed algorithms.
PDF KSCI