Efficient methods for Groebner basis computation, verification and thier applications
| Project/Area Number |
15K05008
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Rikkyo University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
横山 和弘 立教大学, 理学部, 教授 (30333454)
篠原 直行 国立研究開発法人情報通信研究機構, サイバーセキュリティ研究所セキュリティ基盤研究室, 主任研究員 (70565986)
|
|---|
| Research Collaborator |
AOYAMA Toru 神戸大学, 理学研究科
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 応用数学 / 計算代数 / グレブナー基底 / モジュラー計算 / Ｆ５アルゴリズム / 楕円曲線 / ホロノミック勾配法 / 行列変数1F1 / 有限体 / 暗号 / Wishart分布 / signature / F5 / 同種写像 |
|---|
| Outline of Final Research Achievements |
We published a paper describing various modular methods for efficient Groebner basis computation. We published two papers concerned with the signature based
algorithm (SBA). In these papers we proposed several variants of SBA and showed their correctness and termination. F4 and SBA are main methods for attacking elliptic curve cryptography and post-quantum cryptography. We analyzed the complexity when we applied these methods to cryptanalysis. We studied the system of partial differential equations (PDE) satisfied by the cumulative distribution function (CDF) of Wishart matrices and proposed an efficient method for deriving a system of PDE satisfied by the restriction of the CDF on diagonal regions. This is an application of Groebner basis theory to statistics that is a very active research area.
|
Report
(4 results)
Research Products
(21 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Stability of Parametric Decomposition2015
Author(s)
Kazuhiro Yokoyama
Organizer
Dagstuhl Seminar 15471 Symbolic Computation and Satisfiability
Place of Presentation
Schloss Dagstuhl, Wadern(Germany)
Year and Date
2015-11-15
Related Report
Int'l Joint Research / Invited
-
[Presentation] グレブナー基底計算の効率化2015
Author(s)
横山和弘
Organizer
RIMS研究集会「数式処理研究の新たな発展」
Place of Presentation
京都大学数理解析研究所(京都府・京都市)
Year and Date
2015-08-19
Related Report
Invited
-
