| Project/Area Number |
16340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
NAKAMURA Ken Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Professor (80110849)
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| Co-Investigator(Kenkyū-buntansha) |
UCHIYAMA Shigenori Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Associate professor (40433172)
SUZUKI Toshio Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Associate professor (30235973)
TSUMURA Hirofumi Tokyo Metropolitan University, Department of Mathematics and Information Sciences, Professor (20310419)
KIDA Masanari The Univ. of Electro-Communications, 大学院・理工学研究, Associate professor (20272057)
NAGAO Ko-ichi Kanto Gakuin University, 工学部, Professor (00308321)
福永 力 首都大学東京, 大学院・理工学研究科, 教授 (00189961)
松野 一夫 津田塾大学, 学芸学部・数学科, 准教授 (40332936)
栗原 将人 東京都立大学, 理学研究科, 助教授 (40211221)
徳永 浩雄 東京都立大学, 理学研究科, 助教授 (30211395)
福田 隆 日本大学, 生産工学部, 助教授 (00181272)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥11,710,000 (Direct Cost: ¥10,900,000、Indirect Cost: ¥810,000)
Fiscal Year 2007: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2006: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2005: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2004: ¥2,700,000 (Direct Cost: ¥2,700,000)
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| Keywords | algorithmic number theory / cryptologic research / system for number theory / Python / NZMATH / 量子公開鍵暗号 / 楕円曲線 |
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| Research Abstract |
We started the development of a system for number theory by Python language and named it as NZMATH. Implemented packages are as follows : number theory, finite fields, combinatrics, several integer facorization algorithms, elliptic curves, structure computation of several finite commutative groups, quantum public key cryptosystem on imaginary quadratic fields, pairing on elliptic curves, structure of ring class groups of imaginary quadratic fields, successive division on some imaginary quadratic fields, cubic residues and related cubic roots in some imaginary quadratic fields, elliptic curve method for integer facorization. Number fields are going to be released soon in this April. Main web page is
http://tnt.math.metro-u.ac.jp/nzmath/
We also studied on algorithmic number theory and its application as in published papers and talks. In order to communicate the results, we mainly worked in the research group JANT in JSIAM. We organized 4 research meetings every year with about 50 participants. We published a special volume of JJAIM, an official journal of JSIAM, on algorithmic number theory. Main web page is
http://ntw.e-one.uec.ac.jp/jant/
For active interrelationship between algorithmic number theory and other areas on computer algebra, we organized the 6th and the 7th international Symposium on Algebra and Computation, AC2005 and AC2007, with more than 100 participants. Main web page is
http://tnt.math.metro-u.ac.jp/ac/
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