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JaLCDOI 10.18926/15380 Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. finite field minimal polynomial irreducible polynomial higher degree trace trace cryptography Memoirs of the Faculty of Engineering, Okayama University 2001-03-27 volume35 issue1-2 197 205 0475-0071 英語 publisher
JaLCDOI 10.18926/17849 Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2009-01 volume43 99 107 1349-6115 英語 publisher
JaLCDOI 10.18926/17851 Nekado, Kenta| Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2009-01 volume43 108 112 1349-6115 英語 publisher
JaLCDOI 10.18926/17853 Sakemi, Yumi| Kato, hidehiro| Nogami, Yasuyuki| Morikawa, Yoshikawa| 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. Memoirs of the Faculty of Engineering, Okayama University 2009-01 volume43 113 116 1349-6115 英語 publisher
JaLCDOI 10.18926/19960 Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2010-01 volume44 60 68 1349-6115 英語 publisher
JaLCDOI 10.18926/19961 Nekado, Kenta| Kato, Hidehiro| Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2010-01 volume44 69 72 1349-6115 英語 publisher
JaLCDOI 10.18926/44499 Nogami, Yasuyuki| Yanagi, Erika| Izuta, Tetsuya| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2011-01 volume45 46 53 1349-6115 英語 Copyright © by the authors publisher
JaLCDOI 10.18926/44500 Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2011-01 volume45 54 59 1349-6115 英語 Copyright © by the authors publisher
JaLCDOI 10.18926/46982 Nogami, Yasuyuki| Morikawa, Yoshitaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2003-03 volume37 issue2 73 87 0475-0071 英語 publisher
JaLCDOI 10.18926/49321 Nogami, Yasuyuki| Sumo, Taichi| 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. pairing–friendly curve torsion point group structure rank Memoirs of the Faculty of Engineering, Okayama University 2013-01 volume47 19 24 1349-6115 英語 Copyright © by the authors publisher
JaLCDOI 10.18926/49322 Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| 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. Memoirs of the Faculty of Engineering, Okayama University 2013-01 volume47 25 32 1349-6115 英語 Copyright © by the authors publisher
JaLCDOI 10.18926/14158 Iokibe, Kengo| Toyota, Yoshitaka| Wada, Osami| Koga, Ryuji| 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. Memoirs of the Faculty of Engineering, Okayama University 2005-01 volume39 issue1 93 101 0475-0071 英語 publisher
JaLCDOI 10.18926/15360 Wei, He| Koga, Ryuji| Iokibe, Kengo| Wada, Osami| Toyota, Yoshitaka| 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. Mie lidar Asian dust (KOSA) depolarization ratio backscattering ratio range normalized Memoirs of the Faculty of Engineering, Okayama University 2000-03-27 volume34 issue1-2 27 37 0475-0071 英語 publisher
JaLCDOI 10.18926/46983 Iokibe, Kengo| Toyota, Yoshitaka| Wada, Osami| Koga, Ryuji| 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. Memoirs of the Faculty of Engineering, Okayama University 2003-03 volume37 issue2 89 97 0475-0071 英語 publisher
JaLCDOI 10.18926/46955 Kanayama, Naoki| Yamakoshi, Kimi| Kiyomi, Masaaki| Magari, Masaki| Ohmori, Hitoshi| 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. Memoirs of the Faculty of Engineering, Okayama University 2004-03 volume38 issue1-2 91 96 0475-0071 英語 publisher
JaLCDOI 10.18926/47025 Hikida, Masaki| Magari, Masaki| Nakayama, Yasunori| Kanayama, Naoki| Ohmori, Hitoshi| 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. Memoirs of the Faculty of Engineering, Okayama University 2002-03 volume36 issue2 51 60 0475-0071 英語 publisher
JaLCDOI 10.18926/19962 Imanaka, Hiroyuki| Tanaka, Soukichi| Feng, Bin| Imamura, Koreyoshi| Nakanishi, Kazuhiro| 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. Memoirs of the Faculty of Engineering, Okayama University 2010-01 volume44 73 83 1349-6115 英語 publisher
JaLCDOI 10.18926/19957 Kanatani, Kenichi| Niitsuma Hirotaka| Sugaya Yasuyuki| 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. Memoirs of the Faculty of Engineering, Okayama University 2010-01 volume44 32 41 1349-6115 英語 publisher
JaLCDOI 10.18926/19959 Kanatani, Kenichi| Niitsuma Hirotaka| Rangrajan Prasanna| 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. Memoirs of the Faculty of Engineering, Okayama University 2010-01 volume44 50 59 1349-6115 英語 publisher
JaLCDOI 10.18926/44496 Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka| 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. Memoirs of the Faculty of Engineering, Okayama University 2011-01 volume45 15 26 1349-6115 英語 Copyright © by the authors publisher