JaLCDOI 10.18926/14126
FullText URL Mem_Fac_Eng_OU_40_1_84.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract This paper particularly deals with elliptic curves in the form of E(x, y) = y(2) − x(3) −b = 0, b ∈ F(* q) , where 3 divides q−1. In this paper, we refer to the well-known twist technique as x-twist and propose y-twist. By combining x-twist and y-twist, we can consider six elliptic curves and this paper proposes a method to obtain the orders of these six curves by counting only one order among the six curves.
Keywords elliptic curve twist third power residue/non-residue
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2006-01
Volume volume40
Issue issue1
Start Page 83
End Page 94
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308548
JaLCDOI 10.18926/14156
FullText URL Mem_Fac_Eng_39_1_71.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract This paper proposes an algorithm for generating prime order elliptic curves over extension field whose extension degree is a power of 2. The proposed algorithm is based on the fact that the order of the twisted elliptic curve is able to be a prime number when the extension degree for the twist operation is a power of 2. When the definition field is F(2(40)−87)(4) , the proposed algorithm can generate a prime order elliptic curve within 5 seconds on PentiumIII (800MHz) with C language.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2005-01
Volume volume39
Issue issue1
Start Page 71
End Page 81
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308036
JaLCDOI 10.18926/14157
FullText URL Mem_Fac_Eng_39_1_82.pdf
Author Wang, Feng| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract In this paper, we focus on developing a high-speed square root (SQRT) algorithm required for an elliptic curve cryptosystem. Examining Smart algorithm, the previously well-known SQRT algorithm, we can see that there is a lot of computation overlap in Smart algorithm and the quadratic residue (QR) test, which must be implemented prior to a SQRT computation. It makes Smart algorithm inefficient. The essence of our proposition is thus to present a new QR test and an efficient SQRT algorithm to avoid all the overlapping computations. The authors devised a SQRT algorithm for which most of the data required have been computed in the proposed QR test. Not only there is no computation overlap in the proposed algorithm and the proposed QR test, but also in the proposed algorithm over GF(p(2)) (4 | p − 1) some computations can be executed in GF(p); whereas in Smart algorithm over GF(p(2)) all the computations must be executed in GF(p(2)). These yield many reductions in the computational time and complexity. We implemented the two QR tests and the two SQRT algorithms over GF(pm) (m=1, 2) in C++ language with NTL (Number Theory Library) on Pentium4 (2.6GHz), where the size of p is around 160 bits. The computer simulations showed that the proposed QR test and the proposed algorithm over GF(p(m)) were about 2 times faster than the conventional QR test and Smart algorithm over GF(p(m)).
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2005-01
Volume volume39
Issue issue1
Start Page 82
End Page 92
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308422
JaLCDOI 10.18926/15380
FullText URL Mem_Fac_Eng_OU_35_197.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Modern communication engineerings, such as elliptic curve cryptographies, often requires algebra on finite extension field defined by modulus arithmetic with an irreducible polynomial. This paper provides a new method to detemine the minimal (irreducible) polynomial of a given proper element in finite extension field. In the conventional determination method, as we have to solve the simultaneous equations, the computation is very involved. In this paper, the well known "trace" is extended to higher degree traces. Using the new traces, we yield the coefficient formula of the desired minimal polynomial. The new method becomes very simple without solving the simultaneous equations, and about twice faster than the conventional method in computation speed.
Keywords finite field minimal polynomial irreducible polynomial higher degree trace trace cryptography
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2001-03-27
Volume volume35
Issue issue1-2
Start Page 197
End Page 205
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002307992
JaLCDOI 10.18926/17849
FullText URL Mem_Fac_Eng_OU_43_99.pdf
Author Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract A square root (SQRT) algorithm in extension field F(p(m))(m = r(0)r(1)・・・r(n−1)・2(d), r(i) : odd prime, d : positive integer) is proposed in this paper. First, a conventional SQRT algorithm, the Tonelli-Shanks algorithm, is modified to compute the inverse SQRT in F(p(2d)), where most of the computations are performed in the corresponding subfields F(p(2i)) for 0 ≤ i ≤ d-1. Then the Frobenius mappings with addition chain are adopted for the proposed SQRT algorithm, in which a lot of computations in a given extension field F(p(m)) are also reduced to those in a proper subfield by the norm computations. Those reductions of the field degree increase efficiency in the SQRT implementation. The Tonelli-Shanks algorithm and the proposed algorithm in F(p(6)) and F(p(10)) were implemented on a Core2 (2.66 GHz) using the C++ programming language. The computer simulations showed that, on average, the proposed algorithm accelerated the SQRT computation by 6 times in F(p(6)), and by 10 times in F(p(10)), compared to the Tonelli-Shanks algorithm.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2009-01
Volume volume43
Start Page 99
End Page 107
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002308980
JaLCDOI 10.18926/17851
FullText URL Mem_Fac_Eng_OU_43_108.pdf
Author Nekado, Kenta| Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Recently, pairing-based cryptographies such as ID-based cryptography and group signature have been studied. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field must be efficiently carried out. The authors show efficient arithmetic operations of extension field for Xate pairing especially with Freeman curve.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2009-01
Volume volume43
Start Page 108
End Page 112
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002308904
JaLCDOI 10.18926/17853
FullText URL Mem_Fac_Eng_OU_43_113.pdf
Author Sakemi, Yumi| Kato, hidehiro| Nogami, Yasuyuki| Morikawa, Yoshikawa|
Abstract Barreto–Naehrig (BN) curve has been introduced as an efficient pairing-friendly elliptic curve over prime field F(p) whose embedding degree is 12. The characteristic and Frobenius trace are given as polynomials of integer variable X. The authors proposed an improvement of Miller's algorithm of twisted Ate pairing with BN curve by applying X of small hamming weight in ITC–CSCC2008; however, its cost evaluation has not been explicitly shown. This paper shows the detail of the cost evaluation.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2009-01
Volume volume43
Start Page 113
End Page 116
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002308945
JaLCDOI 10.18926/19960
FullText URL Mem_Fac_Eng_OU_44_60.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract This paper proposes a method for generating a certain composite order ordinary pairing–friendly elliptic curve of embedding degree 3. In detail, the order has two large prime factors such as the modulus of RSA cryptography. The method is based on the property that the order of the target pairing–friendly curve is given by a polynomial as r(X) of degree 2 with respect to the integer variable X. When the bit size of the prime factors is about 500 bits, the proposed method averagely takes about 15 minutes on Core 2 Quad (2.66Hz) for generating one.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 60
End Page 68
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309063
JaLCDOI 10.18926/19961
FullText URL Mem_Fac_Eng_OU_44_69.pdf
Author Nekado, Kenta| Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Recently, pairing–based cryptographies have attracted much attention. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field should be efficient. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper proposes an efficient squaring algorithm in extension field for Freeman curve.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 69
End Page 72
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309070
JaLCDOI 10.18926/44499
FullText URL mfe_045_046_053.pdf
Author Nogami, Yasuyuki| Yanagi, Erika| Izuta, Tetsuya| Morikawa, Yoshitaka|
Abstract Recently, composite order pairing–based cryptographies have received much attention. The composite order needs to be as large as the RSA modulus. Thus, they require a certain pairing–friendly elliptic curve that has such a large composite order. This paper proposes an efficient algorithm for generating an ordinary pairing–friendly elliptic curve of the embedding degree 1 whose order has two large prime factors as the RSA modulus. In addition, the generated pairing–friendly curve has an efficient structure for the Gallant–Lambert–Vanstone (GLV) method.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 46
End Page 53
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120002905955
JaLCDOI 10.18926/44500
FullText URL mfe_045_054_059.pdf
Author Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Recently, pairing–based cryptographies have attracted much attention. For fast pairing calculation, not only pairing algorithms but also arithmetic operations in extension field should be efficient. Especially for final exponentiation included in pairing calculation, squaring is more important than multiplication. This paper considers squaring algorithms efficient for cubic extension field which is often used for pairing implementaions.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 54
End Page 59
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 80021759252
JaLCDOI 10.18926/46982
FullText URL mfe_37_2_073_087.pdf
Author Nogami, Yasuyuki| Morikawa, Yoshitaka|
Abstract Public key cryptosystem has many uses, such as to sign digitally, to realize electronic commerce. Especially, RSA public key cryptosystem has been the most widely used, but its key for ensuring sufficient security reaches about 2000 bits long. On the other hand, elliptic curve cryptosystem(ECC) has the same security level with about 7-fold smaller length key. Accordingly, ECC has been received much attention and implemented on various processors even with scarce computation resources. In this paper, we deal with an elliptic curve which is defined over extension field F(p2c) and has a prime order, where p is the characteristic and c is a non negative integer. In order to realize a fast software implementation of ECC adopting such an elliptic curve, a fast implementation method of definition field F(p2c) especially F(p8) is proposed by using a technique called successive extension. First, five fast implementation methods of base field F(p2) are introduced. In each base field implementation, calculation costs of F(p2)-arithmetic operations are evaluated by counting the numbers of F(p)-arithmetic operations. Next, a successive extension method which adopts a polynomial basis and a binomial as the modular polynomial is proposed with comparing to a conventional method. Finally, we choose two prime numbers as the characteristic, and consider several implementations for definition field F(p8) by using five base fields and two successive extension methods. Then, one of these implementations is especially selected and implemented on Toshiba 32-bit micro controller TMP94C251(20MHz) by using C language. By evaluating calculation times with comparing to previous works, we conclude that proposed method can achieve a fast implementation of ECC with a prime order.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2003-03
Volume volume37
Issue issue2
Start Page 73
End Page 87
ISSN 0475-0071
language 英語
File Version publisher
NAID 80015999992
JaLCDOI 10.18926/49321
FullText URL mfe_047_019_024.pdf
Author Nogami, Yasuyuki| Sumo, Taichi|
Abstract Recent efficient pairings such as Ate pairing use two efficient rational point subgroups such that π(P) = P and π(Q) = [p]Q, where π, p, P, and Q are the Frobenius map for rational point, the characteristic of definition field, and torsion points for pairing, respectively. This relation accelerates not only pairing but also pairing–related operations such as scalar multiplications. It holds in the case that the embedding degree k divides r − 1, where r is the order of torsion rational points. Thus, such a case has been well studied. Alternatively, this paper focuses on the case that the degree divides r + 1 but does not divide r − 1. Then, this paper shows a multiplicative representation for r–torsion points based on the fact that the characteristic polynomial f(π) becomes irreducible over Fr for which π also plays a role of variable.
Keywords pairing–friendly curve torsion point group structure rank
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 19
End Page 24
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232373
JaLCDOI 10.18926/49322
FullText URL mfe_047_025_032.pdf
Author Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki|
Abstract Pairing–based cryptosystems are well implemented with Ate–type pairing over Barreto–Naehrig (BN) curve. Then, for instance, their securities depend on the difficulty of Discrete Logarithm Problem (DLP) on the so–denoted G3 over BN curve. This paper, in order to faster solve the DLP, first proposes to utilize Gauss period Normal Basis (GNB) for Pollard’s rho method, and then considers to accelerate the solving by an adoption of lazy random walk, namely tag tracing technique proposed by Cheon et al.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 25
End Page 32
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232374
JaLCDOI 10.18926/46947
FullText URL mfe_38_1-2_005_014.pdf
Author Ishimaru, Kazuhito| Konishi, Masami| Imai, Jun| Nishi, Tatsushi|
Abstract Temperature distribution in the reactor furnace is mainly operated by gas blowing from multiple tuyeres and material charge distribution. The objective of our research is obtain the optimal profile of gas flow to control temperature distribution in the reactor furnace in the shortest possible time. We formulated the optimization problem to reduce deviation of temperature distribution from its desired one in the reactor furnace. Based on the formulation, gas blow conditions are optimized by a sequential quadratic programming method to realize the desired temperature distribution. The validity of the method was checked through numerical experiments.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2004-03
Volume volume38
Issue issue1-2
Start Page 5
End Page 14
ISSN 0475-0071
language 英語
File Version publisher
NAID 80016785933
JaLCDOI 10.18926/46948
FullText URL mfe_38_1-2_015_027.pdf
Author Torigoe, Takashi| Konishi, Masami| Imai, Jun| Nishi, Tatsushi|
Abstract In these days, mechanical systems are becoming more complex and highly automated. So, there exist wide variety of demands for reliable diagnostic technology. A reliable data analysis and quantitative diagnosis method of mechanical system is necessary for the purpose. In this paper a quantitative diagnosis method for looper height control system has been developed based on neural network technologies. The wavelet transformation is used for pre-processing to analyze characteristics of looper height control system. And, self organizing map neural network is used for the purpose of classification based on the pre-processed data. After that, the classified results are used for quantitative diagnosis in hierarchical neural network.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2004-03
Volume volume38
Issue issue1-2
Start Page 15
End Page 27
ISSN 0475-0071
language 英語
File Version publisher
NAID 80016785934
JaLCDOI 10.18926/49320
FullText URL mfe_047_001_018.pdf
Author Kanatani, Kenichi|
Abstract We summarize techniques for optimal geometric estimation from noisy observations for computer vision applications. We first discuss the interpretation of optimality and point out that geometric estimation is different from the standard statistical estimation. We also describe our noise modeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimation techniques based on minimization of a given cost function: least squares (LS), maximum likelihood (ML), which includes reprojection error minimization as a special case, and Sampson error minimization. We describe bundle adjustment and the FNS scheme for numerically solving them and the hyperaccurate correction that improves the accuracy of ML. Next, we formulate estimation techniques not based on minimization of any cost function: iterative reweight, renormalization, and hyper-renormalization. Finally, we show numerical examples to demonstrate that hyper-renormalization has higher accuracy than ML, which has widely been regarded as the most accurate method of all. We conclude that hyper-renormalization is robust to noise and currently is the best method.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2013-01
Volume volume47
Start Page 1
End Page 18
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120005232372
JaLCDOI 10.18926/14158
FullText URL Mem_Fac_Eng_39_1_93.pdf
Author Iokibe, Kengo| Toyota, Yoshitaka| Wada, Osami| Koga, Ryuji|
Abstract The optical properties of clouds were measured with a polarization Mie lidar during April, 2004 and investigated to categorize the particles detected by the lidar. The cloud layers were categorized into five types according to the depolarization ratios, as follows: (I) constant and small (less than 5%); increasing with height (II) nearly from 0% and (III) from about 50%; (IV) large and varying with the backscattering coefficient; and (V) sharply decreasing. This categorization of clouds enabled us to separate aerosols from clouds in a lidar signal. Comparison of the backscattering coefficients between clouds of types (I) and (II) suggested that the depolarization ratio induced by multiple scattering in dense clouds does not depend on the particle density. Estimation of the particle phase for the five cloud categories was also examined.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2005-01
Volume volume39
Issue issue1
Start Page 93
End Page 101
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002308479
JaLCDOI 10.18926/15360
FullText URL Mem_Fac_Eng_OU_34_27.pdf
Author Wei, He| Koga, Ryuji| Iokibe, Kengo| Wada, Osami| Toyota, Yoshitaka|
Abstract In spring of 1998, Asian dust was observed with a Mie LIDAR in Okayama University, which can measure depolarization ratio. Three events of intense Asian dust were occurred in the period and medially detailed structure of atmosphere was found after examining records. Asian dust was distinguished from water droplets and the possibility to study three dimensional dynamic structure of atmosphere were demonstrated.
Keywords Mie lidar Asian dust (KOSA) depolarization ratio backscattering ratio range normalized
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2000-03-27
Volume volume34
Issue issue1-2
Start Page 27
End Page 37
ISSN 0475-0071
language 英語
File Version publisher
NAID 120002307539
JaLCDOI 10.18926/46983
FullText URL mfe_37_2_089_097.pdf
Author Iokibe, Kengo| Toyota, Yoshitaka| Wada, Osami| Koga, Ryuji|
Abstract Aerosol extinction coefficients of clouds and dust were continuously measured in the year of 2002 with a polarized Mie-scattering lidar controlled by an automatic and remotely operating system utilizing internet services. Measured cloud extinctions were greater than 1.0 km(-1) below the altitude 6 km, 0.17 - 1.0 km(-1) between 6 and 10 km, and 0.091 - 0.3 km(-1) beyond 10km. Extinction of dust were 0.10 and 0.20 km(-1) for Asian dust and 0.057 km(-1) for urban dust.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2003-03
Volume volume37
Issue issue2
Start Page 89
End Page 97
ISSN 0475-0071
language 英語
File Version publisher
NAID 120003457336