JaLCDOI 10.18926/44500
フルテキストURL mfe_045_054_059.pdf
著者 Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki| Morikawa, Yoshitaka|
抄録 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.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 54
終了ページ 59
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80021759252
JaLCDOI 10.18926/44499
フルテキストURL mfe_045_046_053.pdf
著者 Nogami, Yasuyuki| Yanagi, Erika| Izuta, Tetsuya| Morikawa, Yoshitaka|
抄録 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.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 46
終了ページ 53
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120002905955
JaLCDOI 10.18926/44498
フルテキストURL mfe_045_036_045.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 We present a new method for optimally computing the 3-D rotation from two sets of 3-D data. Unlike 2-D data, the noise in 3-D data is inherently inhomogeneous and anisotropic, reflecting the characteristics of the 3-D sensing used. To cope with this, Ohta and Kanatani introduced a technique called “renormalization”. Following them, we represent a 3-D rotation in terms of a quaternion and compute an exact maximum likelihood solution using the FNS of Chojnacki et al. As an example, we consider 3-D data obtained by stereo vision and optimally compute the 3-D rotation by analyzing the noise characteristics of stereo reconstruction. We show that the widely used method is not suitable for 3-D data. We confirm that the renormalization of Ohta and Kanatani indeed computes almost an optimal solution and that, although the difference is small, the proposed method can compute an even better solution.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 36
終了ページ 45
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80021759250
JaLCDOI 10.18926/44496
フルテキストURL mfe_045_015_026.pdf
著者 Kanatani, Kenichi| Rangrajan, Prasanna| Sugaya, Yasuyuki| Niitsuma, Hirotaka|
抄録 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.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2011-01
45巻
開始ページ 15
終了ページ 26
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120002905952
JaLCDOI 10.18926/48126
フルテキストURL mfe_046_010_020.pdf
著者 Kanatani, Kenichi|
抄録 We present a new technique for calibrating ultra-wide fisheye lens cameras by imposing the constraint that collinear points be rectified to be collinear, parallel lines to be parallel, and orthogonal lines to be orthogonal. Exploiting the fact that line fitting reduces to an eigenvalue problem, we do a rigorous perturbation analysis to obtain a Levenberg-Marquardt procedure for the optimization. Doing experiments, we point out that spurious solutions exist if collinearity and parallelism alone are imposed. Our technique has many desirable properties. For example, no metric information is required about the reference pattern or the camera position, and separate stripe patterns can be displayed on a video screen to generate a virtual grid, eliminating the grid point extraction processing.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2012-01
46巻
開始ページ 10
終了ページ 20
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80022451621
JaLCDOI 10.18926/48127
フルテキストURL mfe_046_021_033.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first point out that the Gauss-Newton and the Gauss-Helmert methods, regarded as different techniques, have similar structures. We then combine them to define what we call the modified Gauss-Helmert method and do stereo vision simulation to show that it is superior to either of the two in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient and that GPS geodetic data are prone to numerical problems.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2012-01
46巻
開始ページ 21
終了ページ 33
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80022451622
著者 Faculty of Engineering, Okayama University|
発行日 2012-01
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
46巻
資料タイプ その他
JaLCDOI 10.18926/48125
フルテキストURL mfe_046_001_009.pdf
著者 Kanatani, Kenichi| Niitsuma, Hirotaka|
抄録 We optimally estimate the similarity (rotation, translation, and scale change) between two sets of 3-D data in the presence of inhomogeneous and anisotropic noise. Adopting the Lie algebra representation of the 3-D rotational change, we derive the Levenberg-Marquardt procedure for simultaneously optimizing the rotation, the translation, and the scale change. We test the performance of our method using simulated stereo data and real GPS geodetic sensing data. We conclude that the conventional method assuming homogeneous and isotropic noise is insufficient and that our simultaneous optimization scheme can produce an accurate solution.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2012-01
46巻
開始ページ 1
終了ページ 9
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 80022451620
JaLCDOI 10.18926/49322
フルテキストURL mfe_047_025_032.pdf
著者 Nekado, Kenta| Takai, Yusuke| Nogami, Yasuyuki|
抄録 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.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2013-01
47巻
開始ページ 25
終了ページ 32
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120005232374
JaLCDOI 10.18926/49320
フルテキストURL mfe_047_001_018.pdf
著者 Kanatani, Kenichi|
抄録 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.
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2013-01
47巻
開始ページ 1
終了ページ 18
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120005232372
著者 Faculty of Engineering, Okayama University|
発行日 2013-01
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
47巻
資料タイプ その他
JaLCDOI 10.18926/49321
フルテキストURL mfe_047_019_024.pdf
著者 Nogami, Yasuyuki| Sumo, Taichi|
抄録 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.
キーワード pairing–friendly curve torsion point group structure rank
出版物タイトル Memoirs of the Faculty of Engineering, Okayama University
発行日 2013-01
47巻
開始ページ 19
終了ページ 24
ISSN 1349-6115
言語 English
著作権者 Copyright © by the authors
論文のバージョン publisher
NAID 120005232373