| 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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| 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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