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 10.18926/14158
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
JaLCDOI 10.18926/46955
FullText URL mfe_38_1-2_091_096.pdf
Author Kanayama, Naoki| Yamakoshi, Kimi| Kiyomi, Masaaki| Magari, Masaki| Ohmori, Hitoshi|
Abstract Generally, IgM antibodies (Abs) produced in a primary immune response show lower affinity for an inducing antigen (Ag) compared with the corresponding IgG Abs that are major switched isotypes formed in the secondary response. An IgM molecule is a pentamer with 10 Ag-binding sites that will contribute to an increase of avidity for an Ag. To estimate the contribution of the pentameric structure to the avidity of an IgM Ab, we generated IgM and IgG1 monoclonal Abs (mAbs) with identical V regions that are specific for 4-hydroxy-3-nitrophenylacetyl (NP) by in vitro class switching of B cells followed by the cell fusion with a mouse myeloma cell line. Compared with an anti-NP IgG1 mAb, the corresponding IgM mAb showed much higher avidity for NP-conjugated bovine serum albumin, which was drastically reduced after being dissociated into monomers.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2004-03
Volume volume38
Issue issue1-2
Start Page 91
End Page 96
ISSN 0475-0071
language 英語
File Version publisher
NAID 80017001822
JaLCDOI 10.18926/47025
FullText URL mfe_36_2_051_060.pdf
Author Hikida, Masaki| Magari, Masaki| Nakayama, Yasunori| Kanayama, Naoki| Ohmori, Hitoshi|
Abstract A population of peripheral B cells have been shown to express recombination activating gene products, RAG-1 and RAG-2, which are considered to be involved in revising the B cell antigen receptor (BCR) in the periphery. BCR engagement has been reported to turn off RAG expression in peripheral B cells, whereas the same treatment has an opposite effect in immature B cells in the bone marrow. In contrast to receptor editing that is involved in the removal of autoreactivity in immature B cells, it has been shown that secondary V(D)J rearrangement in peripheral B cells, termed receptor revision, contributes to affinity maturation of antibodies. Here, we show that RAG-2 expression in murine splenic B cells was abrogated by the coligation of BCR with complement receptors (CD21/CD35) much more efficiently than by the engagement of BCR alone. On the other hand, the same coligation augmented proliferation of anti-CD40-stimulated B cells. Consistent with these observations, RAG-2 expression was lower in the draining lymph nodes of the quasi-monoclonal mice when they were immunized with a high-affinity antigen than with a low-affinity one. These findings suggest a crucial role for CD21/CD35 in directing the conservation or the revision of BCRs in peripheral B cells.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2002-03
Volume volume36
Issue issue2
Start Page 51
End Page 60
ISSN 0475-0071
language 英語
File Version publisher
NAID 80015582223
JaLCDOI 10.18926/19962
FullText URL Mem_Fac_Eng_OU_44_73.pdf
Author Imanaka, Hiroyuki| Tanaka, Soukichi| Feng, Bin| Imamura, Koreyoshi| Nakanishi, Kazuhiro|
Abstract We used modified Czapek-Dox (mCD) or dextrin-peptone-yeast extract (DPY) media to cultivate a filamentous fungus, Aspergillus oryzae IAM 2706 by three different cultivation methods, i.e., shaking-flask culture (SFC), agar-plate culture (APC), and membrane-surface liquid culture (MSLC), to identify the differences in cultivation behaviors and gene transcriptional profiles. The fungi cultivated by APC or MSLC secreted a greater number of different proteins/enzymes in larger quantities compared with fungi cultivated by SFC, particularly when DPY medium was used. In particular, the amounts of protease secreted by fungi cultivated via MSLC or APC were much greater compared with SFC. When mCD medium was used, α-amylase activity was barely detectable in all cultures while the activity was detected in MSLC and APC in a quantity that was several times higher than that in SFC using DPY medium. SDS-PAGE analysis and N-terminal amino acid sequences confirmed 6 proteins in the culture supernatants when DPY medium was used. Among these proteins oryzin (an alkaline protease) and α-amylase were detected at much higher levels in APC and MSLC compared with SFC, which was consistent with the measured activity of the secreted enzymes. However, when mCD medium was used, only oryzin was detected in significant amounts in MSLC and APC. Microarray analyses of the fungi cultivated by SFC, APC or MSLC using either mCD or DPY media indicated that the gene transcriptional profile of the MSLC sample was similar to that of the APC sample but different from that of the SFC sample. When mCD medium was used, most of the genes that were up-regulated 10-folds or greater in the MSLC sample relative to the SFC sample were unknown or predicted proteins. Transcription of the oryzin gene was only slightly up-regulated in the MSLC sample while transcription of the α-amylase gene was slightly down-regulated. On the other hand, when DPY medium was used, many known genes including the oryzin gene were up-regulated in the MSLC sample versus the SFC sample.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 73
End Page 83
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309053
JaLCDOI 10.18926/19957
FullText URL Mem_Fac_Eng_OU_44_32.pdf
Author Kanatani, Kenichi| Niitsuma Hirotaka| Sugaya Yasuyuki|
Abstract We present an alternative approach to what we call the “standard optimization”, which minimizes a cost function by searching a parameter space. Instead, the input is “orthogonally projected” in the joint input space onto the manifold defined by the “consistency constraint”, which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss optimality of our approach.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 32
End Page 41
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002309124
JaLCDOI 10.18926/19959
FullText URL Mem_Fac_Eng_OU_44_50.pdf
Author Kanatani, Kenichi| Niitsuma Hirotaka| Rangrajan Prasanna|
Abstract We present highly accurate least-squares (LS) alternatives to the theoretically optimal maximum likelihood (ML) estimator for homographies between two images. Unlike ML, our estimators are non-iterative and yield solutions even in the presence of large noise. By rigorous error analysis, we derive a “hyperaccurate” estimator which is unbiased up to second order noise terms. Then, we introduce a computational simplification, which we call “Taubin approximation”, without incurring a loss in accuracy. We experimentally demonstrate that our estimators have accuracy surpassing the traditional LS estimator and comparable to the ML estimator.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2010-01
Volume volume44
Start Page 50
End Page 59
ISSN 1349-6115
language 英語
File Version publisher
NAID 120002308986
JaLCDOI 10.18926/44496
FullText URL mfe_045_015_026.pdf
Author Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka|
Abstract We present a new least squares (LS) estimator, called “HyperLS”, specifically designed for parameter estimation in computer vision applications. It minimizes the algebraic distance under a special scale normalization, which is derived by rigorous error analysis in such a way that statistical bias is removed up to second order noise terms. Numerical experiments suggest that our HyperLS is far superior to the standard LS and comparable in accuracy to maximum likelihood (ML), which is known to produce highly accurate results in image applications but may fail to converge if poorly initialized. Our HyperLS is a perfect candidate for ML initialization. In addition, we discuss how image-based inference problems have different characteristics form conventional statistical applications, with a view to serving as a bridge between mathematicians and computer engineers.
Publication Title Memoirs of the Faculty of Engineering, Okayama University
Published Date 2011-01
Volume volume45
Start Page 15
End Page 26
ISSN 1349-6115
language 英語
Copyright Holders Copyright © by the authors
File Version publisher
NAID 120002905952