A study of algorithms on the arithmetic of algebraic curves and Abelian varieties
| Project/Area Number |
25800023
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
UCHIDA Yukihiro 首都大学東京, 理工学研究科, 准教授 (90533258)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | アーベル多様体 / ヤコビ多様体 / 高さ関数 / 楕円曲線 / 超楕円曲線 / 暗号 / 位数計算 / 等分多項式 / 秘密分散 / 不定方程式 / ディクソン多項式 / 楕円曲線暗号 |
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| Outline of Final Research Achievements |
The arithmetic of algebraic curves and Abelian varieties is a very important subject in both theory and applications. We studied algorithms and their applications on the arithmetic of algebraic curves and Abelian varieties defined over a number field or a finite field. We obtained results on computationally hard problems for cryptography, attacks against a certain cryptosystem, computation of heights on Jacobian varieties, secret sharing using elliptic curves, Diophantine equations related to Waring’s problem, and counting points on curves of genus 2.
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Report
(5 results)
Research Products
(12 results)
