| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 120005232374 |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 120005232373 |
| 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 | English |
| Copyright Holders | Copyright © by the authors |
| File Version | publisher |
| NAID | 120005232372 |
| Author | Faculty of Engineering, Okayama University| |
|---|---|
| Published Date | 2013-01 |
| Publication Title | Memoirs of the Faculty of Engineering, Okayama University |
| Volume | volume47 |
| Content Type | Others |
